TSTP Solution File: ITP269^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP269^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 03:29:05 EDT 2023
% Result : Theorem 8.97s 9.20s
% Output : Proof 9.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.71/2.71 % Problem : ITP269^1 : TPTP v8.1.2. Released v8.1.0.
% 2.71/2.72 % Command : do_cvc5 %s %d
% 2.73/2.93 % Computer : n009.cluster.edu
% 2.73/2.93 % Model : x86_64 x86_64
% 2.73/2.93 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.73/2.93 % Memory : 8042.1875MB
% 2.73/2.93 % OS : Linux 3.10.0-693.el7.x86_64
% 2.73/2.93 % CPULimit : 300
% 2.73/2.93 % WCLimit : 300
% 2.73/2.93 % DateTime : Sun Aug 27 11:15:08 EDT 2023
% 2.73/2.94 % CPUTime :
% 5.35/5.60 %----Proving TH0
% 5.44/5.60 %------------------------------------------------------------------------------
% 5.44/5.60 % File : ITP269^1 : TPTP v8.1.2. Released v8.1.0.
% 5.44/5.60 % Domain : Interactive Theorem Proving
% 5.44/5.60 % Problem : Sledgehammer problem VEBT_DeleteCorrectness 02234_143294
% 5.44/5.60 % Version : [Des22] axioms.
% 5.44/5.60 % English :
% 5.44/5.60
% 5.44/5.60 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.44/5.60 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.44/5.60 % Source : [Des22]
% 5.44/5.60 % Names : 0073_VEBT_DeleteCorrectness_02234_143294 [Des22]
% 5.44/5.60
% 5.44/5.60 % Status : Theorem
% 5.44/5.60 % Rating : 0.38 v8.1.0
% 5.44/5.60 % Syntax : Number of formulae : 11234 (5640 unt; 978 typ; 0 def)
% 5.44/5.60 % Number of atoms : 28487 (12351 equ; 0 cnn)
% 5.44/5.60 % Maximal formula atoms : 71 ( 2 avg)
% 5.44/5.60 % Number of connectives : 124868 (2806 ~; 484 |;1728 &;108542 @)
% 5.44/5.60 % ( 0 <=>;11308 =>; 0 <=; 0 <~>)
% 5.44/5.60 % Maximal formula depth : 39 ( 6 avg)
% 5.44/5.60 % Number of types : 93 ( 92 usr)
% 5.44/5.60 % Number of type conns : 4418 (4418 >; 0 *; 0 +; 0 <<)
% 5.44/5.60 % Number of symbols : 889 ( 886 usr; 60 con; 0-8 aty)
% 5.44/5.60 % Number of variables : 26599 (2305 ^;23606 !; 688 ?;26599 :)
% 5.44/5.60 % SPC : TH0_THM_EQU_NAR
% 5.44/5.60
% 5.44/5.60 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.44/5.60 % from the van Emde Boas Trees session in the Archive of Formal
% 5.44/5.60 % proofs -
% 5.44/5.60 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.44/5.60 % 2022-02-18 11:45:35.260
% 5.44/5.60 %------------------------------------------------------------------------------
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% 5.44/5.60
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% 5.44/5.60
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% 5.44/5.60
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Code____Numeral__Ointeger,type,
% 5.44/5.60 if_Code_integer: $o > code_integer > code_integer > code_integer ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Complex__Ocomplex,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Extended____Nat__Oenat,type,
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% 5.44/5.60
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
% 5.44/5.60 if_list_int: $o > list_int > list_int > list_int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
% 5.44/5.60 if_list_nat: $o > list_nat > list_nat > list_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Num__Onum,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Option__Ooption_It__Nat__Onat_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.44/5.60 if_option_num: $o > option_num > option_num > option_num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
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% 5.44/5.60
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% 5.44/5.60 thf(sy_c_If_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 5.44/5.60 if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Int_OAbs__Integ,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Int_ORep__Integ,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Int_Onat,type,
% 5.44/5.60 nat2: int > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Int_Opower__int_001t__Real__Oreal,type,
% 5.44/5.60 power_int_real: real > int > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 5.44/5.60 ring_1_Ints_real: set_real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 5.44/5.60 ring_18347121197199848620nteger: int > code_integer ).
% 5.44/5.60
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% 5.44/5.60 ring_17405671764205052669omplex: int > complex ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.44/5.60 ring_1_of_int_int: int > int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.44/5.60 ring_1_of_int_real: int > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Extended____Nat__Oenat,type,
% 5.44/5.60 inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.44/5.60 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.44/5.60 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oappend_001t__Int__Oint,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Ocount__list_001t__Int__Oint,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Ocount__list_001t__Nat__Onat,type,
% 5.44/5.60 count_list_nat: list_nat > nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Ocount__list_001t__Real__Oreal,type,
% 5.44/5.60 count_list_real: list_real > real > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 5.44/5.60 drop_nat: nat > list_nat > list_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.44/5.60 cons_int: int > list_int > list_int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Oset_001_Eo,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.44/5.60 set_complex2: list_complex > set_complex ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.44/5.60 set_int2: list_int > set_int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.44/5.60 list_update_o: list_o > nat > $o > list_o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.44/5.60 list_update_int: list_int > nat > int > list_int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.44/5.60 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.44/5.60 list_update_real: list_real > nat > real > list_real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Onth_001_Eo,type,
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% 5.44/5.60
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Onth_001t__Int__Oint,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Onth_001t__Nat__Onat,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Onth_001t__Num__Onum,type,
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% 5.44/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
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% 5.44/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
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% 5.44/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Onth_001t__Real__Oreal,type,
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% 5.44/5.60 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
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% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
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% 5.44/5.60 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
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% 5.44/5.60 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.44/5.60 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.44/5.60 produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.44/5.60 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.44/5.60 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.44/5.60 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.44/5.60 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.44/5.60 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.44/5.60 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.44/5.60 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 5.44/5.60 remdups_nat: list_nat > list_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.44/5.60 replicate_o: nat > $o > list_o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.44/5.60 replicate_complex: nat > complex > list_complex ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.44/5.60 replicate_int: nat > int > list_int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.44/5.60 replicate_nat: nat > nat > list_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.44/5.60 replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.44/5.60 replicate_real: nat > real > list_real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.44/5.60 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.44/5.60 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.44/5.60 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.44/5.60 take_nat: nat > list_nat > list_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oupt,type,
% 5.44/5.60 upt: nat > nat > list_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oupto,type,
% 5.44/5.60 upto: int > int > list_int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oupto__aux,type,
% 5.44/5.60 upto_aux: int > int > list_int > list_int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_List_Oupto__rel,type,
% 5.44/5.60 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_OSuc,type,
% 5.44/5.60 suc: nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.44/5.60 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.44/5.60 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.44/5.60 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.44/5.60 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Onat_Opred,type,
% 5.44/5.60 pred: nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.44/5.60 semiri4939895301339042750nteger: nat > code_integer ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.44/5.60 semiri8010041392384452111omplex: nat > complex ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.44/5.60 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.44/5.60 semiri1314217659103216013at_int: nat > int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.44/5.60 semiri1316708129612266289at_nat: nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.44/5.60 semiri5074537144036343181t_real: nat > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Ointeger,type,
% 5.44/5.60 semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.44/5.60 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Extended____Nat__Oenat,type,
% 5.44/5.60 semiri8563196900006977889d_enat: ( extended_enat > extended_enat ) > nat > extended_enat > extended_enat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.44/5.60 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.44/5.60 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.44/5.60 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.44/5.60 size_size_list_o: list_o > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.44/5.60 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.44/5.60 size_s3451745648224563538omplex: list_complex > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.44/5.60 size_size_list_int: list_int > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.44/5.60 size_size_list_nat: list_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.44/5.60 size_size_list_num: list_num > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.44/5.60 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.44/5.60 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 5.44/5.60 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.44/5.60 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 5.44/5.60 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.44/5.60 size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.44/5.60 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.44/5.60 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.44/5.60 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.44/5.60 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.44/5.60 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.44/5.60 size_size_list_real: list_real > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.44/5.60 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.44/5.60 size_size_num: num > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.44/5.60 size_size_option_nat: option_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.44/5.60 size_size_option_num: option_num > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.44/5.60 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 5.44/5.60 size_size_char: char > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.44/5.60 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.44/5.60 nat_list_encode: list_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.44/5.60 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.44/5.60 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.44/5.60 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.44/5.60 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.44/5.60 nat_set_decode: nat > set_nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.44/5.60 nat_set_encode: set_nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.44/5.60 nat_triangle: nat > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_NthRoot_Oroot,type,
% 5.44/5.60 root: nat > real > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_NthRoot_Osqrt,type,
% 5.44/5.60 sqrt: real > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_OBitM,type,
% 5.44/5.60 bitM: num > num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oinc,type,
% 5.44/5.60 inc: num > num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.44/5.60 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.44/5.60 neg_nu7009210354673126013omplex: complex > complex ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.44/5.60 neg_numeral_dbl_int: int > int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.44/5.60 neg_numeral_dbl_real: real > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.44/5.60 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.44/5.60 neg_nu6511756317524482435omplex: complex > complex ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.44/5.60 neg_nu3811975205180677377ec_int: int > int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.44/5.60 neg_nu6075765906172075777c_real: real > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.44/5.60 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.44/5.60 neg_nu8557863876264182079omplex: complex > complex ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.44/5.60 neg_nu5851722552734809277nc_int: int > int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.44/5.60 neg_nu8295874005876285629c_real: real > real ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.44/5.60 neg_numeral_sub_int: num > num > int ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Onum_OBit0,type,
% 5.44/5.60 bit0: num > num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Onum_OBit1,type,
% 5.44/5.60 bit1: num > num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Onum_OOne,type,
% 5.44/5.60 one: num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.44/5.60 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Onum_Osize__num,type,
% 5.44/5.60 size_num: num > nat ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Onum__of__nat,type,
% 5.44/5.60 num_of_nat: nat > num ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.44/5.60 numera6620942414471956472nteger: num > code_integer ).
% 5.44/5.60
% 5.44/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
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% 5.44/5.60 thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
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% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 5.44/5.61 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 5.44/5.61 set_or7049704709247886629st_num: num > num > set_num ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.44/5.61 set_or1222579329274155063t_real: real > real > set_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.44/5.61 set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.44/5.61 set_or7743017856606604397t_real: set_real > set_real > set_set_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 5.44/5.61 set_or4662586982721622107an_int: int > int > set_int ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 5.44/5.61 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 5.44/5.61 set_ord_atLeast_nat: nat > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 5.44/5.61 set_ord_atLeast_real: real > set_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Extended____Nat__Oenat,type,
% 5.44/5.61 set_or8332593352340944941d_enat: extended_enat > set_Extended_enat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 5.44/5.61 set_ord_atMost_int: int > set_int ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 5.44/5.61 set_ord_atMost_nat: nat > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 5.44/5.61 set_ord_atMost_num: num > set_num ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 5.44/5.61 set_ord_atMost_real: real > set_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.44/5.61 set_or4236626031148496127et_nat: set_nat > set_set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.44/5.61 set_or5092868708245317595t_real: set_real > set_set_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 5.44/5.61 set_or6656581121297822940st_int: int > int > set_int ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 5.44/5.61 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 5.44/5.61 set_or5832277885323065728an_int: int > int > set_int ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.44/5.61 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 5.44/5.61 set_or1633881224788618240n_real: real > real > set_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.44/5.61 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.44/5.61 set_or5849166863359141190n_real: real > set_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Extended____Nat__Oenat,type,
% 5.44/5.61 set_or8419480210114673929d_enat: extended_enat > set_Extended_enat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 5.44/5.61 set_ord_lessThan_int: int > set_int ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.44/5.61 set_ord_lessThan_nat: nat > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 5.44/5.61 set_ord_lessThan_num: num > set_num ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.44/5.61 set_or5984915006950818249n_real: real > set_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_String_Oascii__of,type,
% 5.44/5.61 ascii_of: char > char ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_String_Ochar_OChar,type,
% 5.44/5.61 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.44/5.61 comm_s629917340098488124ar_nat: char > nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_String_Ointeger__of__char,type,
% 5.44/5.61 integer_of_char: char > code_integer ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.44/5.61 unique3096191561947761185of_nat: nat > char ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.44/5.61 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.44/5.61 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.44/5.61 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.44/5.61 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.44/5.61 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.44/5.61 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.44/5.61 topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.44/5.61 topolo2489691266198938127t_real: ( nat > set_real ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.44/5.61 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.44/5.61 topolo2815343760600316023s_real: real > filter_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.44/5.61 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 5.44/5.61 topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 5.44/5.61 topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oarccos,type,
% 5.44/5.61 arccos: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.44/5.61 arcosh_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oarcsin,type,
% 5.44/5.61 arcsin: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oarctan,type,
% 5.44/5.61 arctan: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.44/5.61 arsinh_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.44/5.61 artanh_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.44/5.61 cos_complex: complex > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.44/5.61 cos_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.44/5.61 cos_coeff: nat > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Ocosh_001t__Complex__Ocomplex,type,
% 5.44/5.61 cosh_complex: complex > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.44/5.61 cosh_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
% 5.44/5.61 cot_complex: complex > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.44/5.61 cot_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Odiffs_001t__Code____Numeral__Ointeger,type,
% 5.44/5.61 diffs_Code_integer: ( nat > code_integer ) > nat > code_integer ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.44/5.61 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.44/5.61 diffs_int: ( nat > int ) > nat > int ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.44/5.61 diffs_real: ( nat > real ) > nat > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.44/5.61 exp_complex: complex > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.44/5.61 exp_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.44/5.61 ln_ln_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Olog,type,
% 5.44/5.61 log: real > real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Opi,type,
% 5.44/5.61 pi: real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.44/5.61 powr_real: real > real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.44/5.61 sin_complex: complex > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.44/5.61 sin_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.44/5.61 sin_coeff: nat > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
% 5.44/5.61 sinh_complex: complex > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.44/5.61 sinh_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.44/5.61 tan_complex: complex > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.44/5.61 tan_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.44/5.61 tanh_complex: complex > complex ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.44/5.61 tanh_real: real > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.44/5.61 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.44/5.61 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.44/5.61 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.44/5.61 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.44/5.61 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.44/5.61 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.44/5.61 vEBT_VEBT_high: nat > nat > nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.44/5.61 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.44/5.61 vEBT_VEBT_low: nat > nat > nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.44/5.61 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.44/5.61 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.44/5.61 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.44/5.61 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.44/5.61 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.44/5.61 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.44/5.61 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.44/5.61 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.44/5.61 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.44/5.61 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 5.44/5.61 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 5.44/5.61 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.44/5.61 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.44/5.61 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.44/5.61 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.44/5.61 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.44/5.61 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.44/5.61 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.44/5.61 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.44/5.61 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.44/5.61 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.44/5.61 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.44/5.61 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.44/5.61 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.44/5.61 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.44/5.61 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.44/5.61 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.44/5.61 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.44/5.61 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.44/5.61 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.44/5.61 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.44/5.61 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.44/5.61 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.44/5.61 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.44/5.61 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.44/5.61 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.44/5.61 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.44/5.61 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.44/5.61 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.44/5.61 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.44/5.61 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.44/5.61 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.44/5.61 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.44/5.61 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.44/5.61 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.44/5.61 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.44/5.61 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.44/5.61 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 5.44/5.61 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.44/5.61 fChoice_real: ( real > $o ) > real ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001_Eo,type,
% 5.44/5.61 member_o: $o > set_o > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.44/5.61 member_complex: complex > set_complex > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Extended____Nat__Oenat,type,
% 5.44/5.61 member_Extended_enat: extended_enat > set_Extended_enat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Int__Oint,type,
% 5.44/5.61 member_int: int > set_int > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.44/5.61 member_list_o: list_o > set_list_o > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.44/5.61 member_list_int: list_int > set_list_int > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.44/5.61 member_list_nat: list_nat > set_list_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.44/5.61 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Nat__Onat,type,
% 5.44/5.61 member_nat: nat > set_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Num__Onum,type,
% 5.44/5.61 member_num: num > set_num > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.44/5.61 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Real__Oreal,type,
% 5.44/5.61 member_real: real > set_real > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.44/5.61 member_set_nat: set_nat > set_set_nat > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.44/5.61 member_set_real: set_real > set_set_real > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.44/5.61 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_deg____,type,
% 5.44/5.61 deg: nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_lx____,type,
% 5.44/5.61 lx: nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_m____,type,
% 5.44/5.61 m: nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_ma____,type,
% 5.44/5.61 ma: nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_mi____,type,
% 5.44/5.61 mi: nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_na____,type,
% 5.44/5.61 na: nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_summary____,type,
% 5.44/5.61 summary: vEBT_VEBT ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_summin____,type,
% 5.44/5.61 summin: nat ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_treeList____,type,
% 5.44/5.61 treeList: list_VEBT_VEBT ).
% 5.44/5.61
% 5.44/5.61 thf(sy_v_xa____,type,
% 5.44/5.61 xa: nat ).
% 5.44/5.61
% 5.44/5.61 % Relevant facts (10211)
% 5.44/5.61 thf(fact_0__C3_C,axiom,
% 5.44/5.61 ( deg
% 5.44/5.61 = ( plus_plus_nat @ na @ m ) ) ).
% 5.44/5.61
% 5.44/5.61 % "3"
% 5.44/5.61 thf(fact_1_bit__split__inv,axiom,
% 5.44/5.61 ! [X: nat,D: nat] :
% 5.44/5.61 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 5.44/5.61 = X ) ).
% 5.44/5.61
% 5.44/5.61 % bit_split_inv
% 5.44/5.61 thf(fact_2__C5_Ohyps_C_I8_J,axiom,
% 5.44/5.61 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.44/5.61
% 5.44/5.61 % "5.hyps"(8)
% 5.44/5.61 thf(fact_3_pow__sum,axiom,
% 5.44/5.61 ! [A: nat,B: nat] :
% 5.44/5.61 ( ( 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 ) )
% 5.44/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % pow_sum
% 5.44/5.61 thf(fact_4_high__def,axiom,
% 5.44/5.61 ( vEBT_VEBT_high
% 5.44/5.61 = ( ^ [X2: nat,N: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % high_def
% 5.44/5.61 thf(fact_5_high__bound__aux,axiom,
% 5.44/5.61 ! [Ma: nat,N2: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.44/5.61 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % high_bound_aux
% 5.44/5.61 thf(fact_6__C9_C,axiom,
% 5.44/5.61 ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = na ) ).
% 5.44/5.61
% 5.44/5.61 % "9"
% 5.44/5.61 thf(fact_7_high__inv,axiom,
% 5.44/5.61 ! [X: nat,N2: nat,Y: nat] :
% 5.44/5.61 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
% 5.44/5.61 = Y ) ) ).
% 5.44/5.61
% 5.44/5.61 % high_inv
% 5.44/5.61 thf(fact_8_low__inv,axiom,
% 5.44/5.61 ! [X: nat,N2: nat,Y: nat] :
% 5.44/5.61 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
% 5.44/5.61 = X ) ) ).
% 5.44/5.61
% 5.44/5.61 % low_inv
% 5.44/5.61 thf(fact_9__C12_C,axiom,
% 5.44/5.61 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.44/5.61
% 5.44/5.61 % "12"
% 5.44/5.61 thf(fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,axiom,
% 5.44/5.61 ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ X_1 ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>\<exists>z. both_member_options (treeList ! summin) z\<close>
% 5.44/5.61 thf(fact_11_bit__concat__def,axiom,
% 5.44/5.61 ( vEBT_VEBT_bit_concat
% 5.44/5.61 = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % bit_concat_def
% 5.44/5.61 thf(fact_12__092_060open_062summin_A_060_A2_A_094_Am_092_060close_062,axiom,
% 5.44/5.61 ord_less_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>summin < 2 ^ m\<close>
% 5.44/5.61 thf(fact_13__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 5.44/5.61 ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>summin * 2 ^ n + lx < 2 ^ deg\<close>
% 5.44/5.61 thf(fact_14__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ama_An_J_A_Ilow_Ama_An_J_092_060close_062,axiom,
% 5.44/5.61 vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ na ) ) @ ( vEBT_VEBT_low @ ma @ na ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>both_member_options (treeList ! high ma n) (low ma n)\<close>
% 5.44/5.61 thf(fact_15__C115_C,axiom,
% 5.44/5.61 ( ~ ( ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma )
% 5.44/5.61 => ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) )
% 5.44/5.61 & ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 != ma )
% 5.44/5.61 => ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma ) ) )
% 5.44/5.61 => ! [I: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.44/5.61 => ( ( ( ( vEBT_VEBT_high
% 5.44/5.61 @ ( if_nat
% 5.44/5.61 @ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma )
% 5.44/5.61 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.44/5.61 @ ma )
% 5.44/5.61 @ na )
% 5.44/5.61 = I )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ I )
% 5.44/5.61 @ ( vEBT_VEBT_low
% 5.44/5.61 @ ( if_nat
% 5.44/5.61 @ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma )
% 5.44/5.61 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.44/5.61 @ ma )
% 5.44/5.61 @ na ) ) )
% 5.44/5.61 & ! [Y2: nat] :
% 5.44/5.61 ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 5.44/5.61 = I )
% 5.44/5.61 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ I ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ Y2 )
% 5.44/5.61 & ( ord_less_eq_nat @ Y2
% 5.44/5.61 @ ( if_nat
% 5.44/5.61 @ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma )
% 5.44/5.61 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.44/5.61 @ ma ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "115"
% 5.44/5.61 thf(fact_16_hprolist,axiom,
% 5.44/5.61 ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
% 5.44/5.61 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % hprolist
% 5.44/5.61 thf(fact_17_hlbound,axiom,
% 5.44/5.61 ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.44/5.61 & ( ord_less_nat @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % hlbound
% 5.44/5.61 thf(fact_18_notemp,axiom,
% 5.44/5.61 ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ X_1 ) ).
% 5.44/5.61
% 5.44/5.61 % notemp
% 5.44/5.61 thf(fact_19_nothprolist,axiom,
% 5.44/5.61 ! [I2: nat] :
% 5.44/5.61 ( ( ( I2
% 5.44/5.61 != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
% 5.44/5.61 & ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
% 5.44/5.61 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ I2 )
% 5.44/5.61 = ( nth_VEBT_VEBT @ treeList @ I2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nothprolist
% 5.44/5.61 thf(fact_20_False,axiom,
% 5.44/5.61 ~ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % False
% 5.44/5.61 thf(fact_21__C114_C,axiom,
% 5.44/5.61 ( ( ord_less_nat
% 5.44/5.61 @ ( if_nat
% 5.44/5.61 @ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma )
% 5.44/5.61 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.44/5.61 @ ma )
% 5.44/5.61 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
% 5.44/5.61 & ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 @ ( if_nat
% 5.44/5.61 @ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma )
% 5.44/5.61 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.44/5.61 @ ma ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "114"
% 5.44/5.61 thf(fact_22__C5_Ohyps_C_I7_J,axiom,
% 5.44/5.61 ord_less_eq_nat @ mi @ ma ).
% 5.44/5.61
% 5.44/5.61 % "5.hyps"(7)
% 5.44/5.61 thf(fact_23__C2_C,axiom,
% 5.44/5.61 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.44/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.44/5.61
% 5.44/5.61 % "2"
% 5.44/5.61 thf(fact_24__092_060open_062length_AtreeList_A_061_Alength_A_ItreeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_J_092_060close_062,axiom,
% 5.44/5.61 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.44/5.61 = ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>length treeList = length (treeList [high (summin * 2 ^ n + lx) n := vebt_delete (treeList ! high (summin * 2 ^ n + lx) n) (low (summin * 2 ^ n + lx) n)])\<close>
% 5.44/5.61 thf(fact_25_add__self__div__2,axiom,
% 5.44/5.61 ! [M: nat] :
% 5.44/5.61 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = M ) ).
% 5.44/5.61
% 5.44/5.61 % add_self_div_2
% 5.44/5.61 thf(fact_26__C112_C,axiom,
% 5.44/5.61 ( ( ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma )
% 5.44/5.61 => ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) )
% 5.44/5.61 & ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 != ma )
% 5.44/5.61 => ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma ) ) )
% 5.44/5.61 => ! [X3: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.44/5.61 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "112"
% 5.44/5.61 thf(fact_27__092_060open_062high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_060_Alength_AtreeList_092_060close_062,axiom,
% 5.44/5.61 ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>high (summin * 2 ^ n + lx) n < length treeList\<close>
% 5.44/5.61 thf(fact_28_nnvalid,axiom,
% 5.44/5.61 vEBT_invar_vebt @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ na ).
% 5.44/5.61
% 5.44/5.61 % nnvalid
% 5.44/5.61 thf(fact_29_divide__less__eq__numeral1_I1_J,axiom,
% 5.44/5.61 ! [B: real,W: num,A: real] :
% 5.44/5.61 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.44/5.61 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % divide_less_eq_numeral1(1)
% 5.44/5.61 thf(fact_30_less__divide__eq__numeral1_I1_J,axiom,
% 5.44/5.61 ! [A: real,B: real,W: num] :
% 5.44/5.61 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.61 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_divide_eq_numeral1(1)
% 5.44/5.61 thf(fact_31__C4_C,axiom,
% 5.44/5.61 ! [I: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.44/5.61 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X4 ) )
% 5.44/5.61 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "4"
% 5.44/5.61 thf(fact_32_newlistlength,axiom,
% 5.44/5.61 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) )
% 5.44/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.44/5.61
% 5.44/5.61 % newlistlength
% 5.44/5.61 thf(fact_33__C7_C,axiom,
% 5.44/5.61 ( ( mi != ma )
% 5.44/5.61 => ! [I: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.44/5.61 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.44/5.61 = I )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.44/5.61 & ! [Y2: nat] :
% 5.44/5.61 ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 5.44/5.61 = I )
% 5.44/5.61 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ mi @ Y2 )
% 5.44/5.61 & ( ord_less_eq_nat @ Y2 @ ma ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "7"
% 5.44/5.61 thf(fact_34_not__min__Null__member,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT] :
% 5.44/5.61 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.44/5.61 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_min_Null_member
% 5.44/5.61 thf(fact_35__C1_C,axiom,
% 5.44/5.61 vEBT_invar_vebt @ summary @ m ).
% 5.44/5.61
% 5.44/5.61 % "1"
% 5.44/5.61 thf(fact_36__C5_OIH_C_I1_J,axiom,
% 5.44/5.61 ! [X3: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.44/5.61 => ( ( vEBT_invar_vebt @ X3 @ na )
% 5.44/5.61 & ! [Xa: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ X3 @ Xa ) @ na ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "5.IH"(1)
% 5.44/5.61 thf(fact_37_dele__bmo__cont__corr,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 5.44/5.61 = ( ( X != Y )
% 5.44/5.61 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % dele_bmo_cont_corr
% 5.44/5.61 thf(fact_38_min__in__set__def,axiom,
% 5.44/5.61 ( vEBT_VEBT_min_in_set
% 5.44/5.61 = ( ^ [Xs: set_nat,X2: nat] :
% 5.44/5.61 ( ( member_nat @ X2 @ Xs )
% 5.44/5.61 & ! [Y3: nat] :
% 5.44/5.61 ( ( member_nat @ Y3 @ Xs )
% 5.44/5.61 => ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % min_in_set_def
% 5.44/5.61 thf(fact_39_max__in__set__def,axiom,
% 5.44/5.61 ( vEBT_VEBT_max_in_set
% 5.44/5.61 = ( ^ [Xs: set_nat,X2: nat] :
% 5.44/5.61 ( ( member_nat @ X2 @ Xs )
% 5.44/5.61 & ! [Y3: nat] :
% 5.44/5.61 ( ( member_nat @ Y3 @ Xs )
% 5.44/5.61 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_in_set_def
% 5.44/5.61 thf(fact_40__C5_C,axiom,
% 5.44/5.61 ( ( mi = ma )
% 5.44/5.61 => ! [X3: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.44/5.61 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "5"
% 5.44/5.61 thf(fact_41_inthall,axiom,
% 5.44/5.61 ! [Xs2: list_real,P: real > $o,N2: nat] :
% 5.44/5.61 ( ! [X5: real] :
% 5.44/5.61 ( ( member_real @ X5 @ ( set_real2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_real @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % inthall
% 5.44/5.61 thf(fact_42_inthall,axiom,
% 5.44/5.61 ! [Xs2: list_complex,P: complex > $o,N2: nat] :
% 5.44/5.61 ( ! [X5: complex] :
% 5.44/5.61 ( ( member_complex @ X5 @ ( set_complex2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_complex @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % inthall
% 5.44/5.61 thf(fact_43_inthall,axiom,
% 5.44/5.61 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N2: nat] :
% 5.44/5.61 ( ! [X5: product_prod_nat_nat] :
% 5.44/5.61 ( ( member8440522571783428010at_nat @ X5 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % inthall
% 5.44/5.61 thf(fact_44_inthall,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 5.44/5.61 ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % inthall
% 5.44/5.61 thf(fact_45_inthall,axiom,
% 5.44/5.61 ! [Xs2: list_o,P: $o > $o,N2: nat] :
% 5.44/5.61 ( ! [X5: $o] :
% 5.44/5.61 ( ( member_o @ X5 @ ( set_o2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_o @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % inthall
% 5.44/5.61 thf(fact_46_inthall,axiom,
% 5.44/5.61 ! [Xs2: list_nat,P: nat > $o,N2: nat] :
% 5.44/5.61 ( ! [X5: nat] :
% 5.44/5.61 ( ( member_nat @ X5 @ ( set_nat2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % inthall
% 5.44/5.61 thf(fact_47_inthall,axiom,
% 5.44/5.61 ! [Xs2: list_int,P: int > $o,N2: nat] :
% 5.44/5.61 ( ! [X5: int] :
% 5.44/5.61 ( ( member_int @ X5 @ ( set_int2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_int @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % inthall
% 5.44/5.61 thf(fact_48_numeral__eq__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ( numera1916890842035813515d_enat @ M )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_iff
% 5.44/5.61 thf(fact_49_numeral__eq__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ( numera6690914467698888265omplex @ M )
% 5.44/5.61 = ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_iff
% 5.44/5.61 thf(fact_50_numeral__eq__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ( numeral_numeral_real @ M )
% 5.44/5.61 = ( numeral_numeral_real @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_iff
% 5.44/5.61 thf(fact_51_numeral__eq__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ( numeral_numeral_nat @ M )
% 5.44/5.61 = ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_iff
% 5.44/5.61 thf(fact_52_numeral__eq__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ( numeral_numeral_int @ M )
% 5.44/5.61 = ( numeral_numeral_int @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_iff
% 5.44/5.61 thf(fact_53__C0_C,axiom,
% 5.44/5.61 ! [X3: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ X3 @ na ) ) ).
% 5.44/5.61
% 5.44/5.61 % "0"
% 5.44/5.61 thf(fact_54_mem__Collect__eq,axiom,
% 5.44/5.61 ! [A: int,P: int > $o] :
% 5.44/5.61 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.44/5.61 = ( P @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % mem_Collect_eq
% 5.44/5.61 thf(fact_55_mem__Collect__eq,axiom,
% 5.44/5.61 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.44/5.61 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 5.44/5.61 = ( P @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % mem_Collect_eq
% 5.44/5.61 thf(fact_56_mem__Collect__eq,axiom,
% 5.44/5.61 ! [A: complex,P: complex > $o] :
% 5.44/5.61 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.44/5.61 = ( P @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % mem_Collect_eq
% 5.44/5.61 thf(fact_57_mem__Collect__eq,axiom,
% 5.44/5.61 ! [A: real,P: real > $o] :
% 5.44/5.61 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.44/5.61 = ( P @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % mem_Collect_eq
% 5.44/5.61 thf(fact_58_mem__Collect__eq,axiom,
% 5.44/5.61 ! [A: list_nat,P: list_nat > $o] :
% 5.44/5.61 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.44/5.61 = ( P @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % mem_Collect_eq
% 5.44/5.61 thf(fact_59_mem__Collect__eq,axiom,
% 5.44/5.61 ! [A: nat,P: nat > $o] :
% 5.44/5.61 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.44/5.61 = ( P @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % mem_Collect_eq
% 5.44/5.61 thf(fact_60_Collect__mem__eq,axiom,
% 5.44/5.61 ! [A2: set_int] :
% 5.44/5.61 ( ( collect_int
% 5.44/5.61 @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 5.44/5.61 = A2 ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_mem_eq
% 5.44/5.61 thf(fact_61_Collect__mem__eq,axiom,
% 5.44/5.61 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.44/5.61 ( ( collec3392354462482085612at_nat
% 5.44/5.61 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A2 ) )
% 5.44/5.61 = A2 ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_mem_eq
% 5.44/5.61 thf(fact_62_Collect__mem__eq,axiom,
% 5.44/5.61 ! [A2: set_complex] :
% 5.44/5.61 ( ( collect_complex
% 5.44/5.61 @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 5.44/5.61 = A2 ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_mem_eq
% 5.44/5.61 thf(fact_63_Collect__mem__eq,axiom,
% 5.44/5.61 ! [A2: set_real] :
% 5.44/5.61 ( ( collect_real
% 5.44/5.61 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 5.44/5.61 = A2 ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_mem_eq
% 5.44/5.61 thf(fact_64_Collect__mem__eq,axiom,
% 5.44/5.61 ! [A2: set_list_nat] :
% 5.44/5.61 ( ( collect_list_nat
% 5.44/5.61 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 5.44/5.61 = A2 ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_mem_eq
% 5.44/5.61 thf(fact_65_Collect__mem__eq,axiom,
% 5.44/5.61 ! [A2: set_nat] :
% 5.44/5.61 ( ( collect_nat
% 5.44/5.61 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 5.44/5.61 = A2 ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_mem_eq
% 5.44/5.61 thf(fact_66_Collect__cong,axiom,
% 5.44/5.61 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.44/5.61 ( ! [X5: product_prod_nat_nat] :
% 5.44/5.61 ( ( P @ X5 )
% 5.44/5.61 = ( Q @ X5 ) )
% 5.44/5.61 => ( ( collec3392354462482085612at_nat @ P )
% 5.44/5.61 = ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_cong
% 5.44/5.61 thf(fact_67_Collect__cong,axiom,
% 5.44/5.61 ! [P: complex > $o,Q: complex > $o] :
% 5.44/5.61 ( ! [X5: complex] :
% 5.44/5.61 ( ( P @ X5 )
% 5.44/5.61 = ( Q @ X5 ) )
% 5.44/5.61 => ( ( collect_complex @ P )
% 5.44/5.61 = ( collect_complex @ Q ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_cong
% 5.44/5.61 thf(fact_68_Collect__cong,axiom,
% 5.44/5.61 ! [P: real > $o,Q: real > $o] :
% 5.44/5.61 ( ! [X5: real] :
% 5.44/5.61 ( ( P @ X5 )
% 5.44/5.61 = ( Q @ X5 ) )
% 5.44/5.61 => ( ( collect_real @ P )
% 5.44/5.61 = ( collect_real @ Q ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_cong
% 5.44/5.61 thf(fact_69_Collect__cong,axiom,
% 5.44/5.61 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.44/5.61 ( ! [X5: list_nat] :
% 5.44/5.61 ( ( P @ X5 )
% 5.44/5.61 = ( Q @ X5 ) )
% 5.44/5.61 => ( ( collect_list_nat @ P )
% 5.44/5.61 = ( collect_list_nat @ Q ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_cong
% 5.44/5.61 thf(fact_70_Collect__cong,axiom,
% 5.44/5.61 ! [P: nat > $o,Q: nat > $o] :
% 5.44/5.61 ( ! [X5: nat] :
% 5.44/5.61 ( ( P @ X5 )
% 5.44/5.61 = ( Q @ X5 ) )
% 5.44/5.61 => ( ( collect_nat @ P )
% 5.44/5.61 = ( collect_nat @ Q ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Collect_cong
% 5.44/5.61 thf(fact_71__C5_OIH_C_I2_J,axiom,
% 5.44/5.61 ! [X: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ summary @ X ) @ m ) ).
% 5.44/5.61
% 5.44/5.61 % "5.IH"(2)
% 5.44/5.61 thf(fact_72__092_060open_062invar__vebt_A_ItreeList_A_B_Asummin_J_An_092_060close_062,axiom,
% 5.44/5.61 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ summin ) @ na ).
% 5.44/5.61
% 5.44/5.61 % \<open>invar_vebt (treeList ! summin) n\<close>
% 5.44/5.61 thf(fact_73__092_060open_062both__member__options_Asummary_A_Ihigh_Ama_An_J_092_060close_062,axiom,
% 5.44/5.61 vEBT_V8194947554948674370ptions @ summary @ ( vEBT_VEBT_high @ ma @ na ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>both_member_options summary (high ma n)\<close>
% 5.44/5.61 thf(fact_74_numeral__le__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_le_iff
% 5.44/5.61 thf(fact_75_numeral__le__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_le_iff
% 5.44/5.61 thf(fact_76_numeral__le__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_le_iff
% 5.44/5.61 thf(fact_77_numeral__le__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_le_iff
% 5.44/5.61 thf(fact_78_numeral__less__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_less_iff
% 5.44/5.61 thf(fact_79_numeral__less__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_less_iff
% 5.44/5.61 thf(fact_80_numeral__less__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_less_iff
% 5.44/5.61 thf(fact_81_numeral__less__iff,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_less_iff
% 5.44/5.61 thf(fact_82_mult__numeral__left__semiring__numeral,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: extended_enat] :
% 5.44/5.61 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W ) @ Z ) )
% 5.44/5.61 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_left_semiring_numeral
% 5.44/5.61 thf(fact_83_mult__numeral__left__semiring__numeral,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: complex] :
% 5.44/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.44/5.61 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_left_semiring_numeral
% 5.44/5.61 thf(fact_84_mult__numeral__left__semiring__numeral,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: real] :
% 5.44/5.61 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.44/5.61 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_left_semiring_numeral
% 5.44/5.61 thf(fact_85_mult__numeral__left__semiring__numeral,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.44/5.61 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_left_semiring_numeral
% 5.44/5.61 thf(fact_86_mult__numeral__left__semiring__numeral,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: int] :
% 5.44/5.61 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.44/5.61 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_left_semiring_numeral
% 5.44/5.61 thf(fact_87_numeral__times__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_times_numeral
% 5.44/5.61 thf(fact_88_numeral__times__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.61 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_times_numeral
% 5.44/5.61 thf(fact_89_numeral__times__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_times_numeral
% 5.44/5.61 thf(fact_90_numeral__times__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_times_numeral
% 5.44/5.61 thf(fact_91_numeral__times__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_times_numeral
% 5.44/5.61 thf(fact_92_add__numeral__left,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: extended_enat] :
% 5.44/5.61 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W ) @ Z ) )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_numeral_left
% 5.44/5.61 thf(fact_93_add__numeral__left,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: complex] :
% 5.44/5.61 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.44/5.61 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_numeral_left
% 5.44/5.61 thf(fact_94_add__numeral__left,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: real] :
% 5.44/5.61 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.44/5.61 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_numeral_left
% 5.44/5.61 thf(fact_95_add__numeral__left,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.44/5.61 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_numeral_left
% 5.44/5.61 thf(fact_96_add__numeral__left,axiom,
% 5.44/5.61 ! [V: num,W: num,Z: int] :
% 5.44/5.61 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.44/5.61 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_numeral_left
% 5.44/5.61 thf(fact_97_numeral__plus__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_numeral
% 5.44/5.61 thf(fact_98_numeral__plus__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.61 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_numeral
% 5.44/5.61 thf(fact_99_numeral__plus__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_numeral
% 5.44/5.61 thf(fact_100_numeral__plus__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_numeral
% 5.44/5.61 thf(fact_101_numeral__plus__numeral,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_numeral
% 5.44/5.61 thf(fact_102_num__double,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 5.44/5.61 = ( bit0 @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % num_double
% 5.44/5.61 thf(fact_103__C6_C,axiom,
% 5.44/5.61 ( ( ord_less_eq_nat @ mi @ ma )
% 5.44/5.61 & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "6"
% 5.44/5.61 thf(fact_104_distrib__right__numeral,axiom,
% 5.44/5.61 ! [A: extended_enat,B: extended_enat,V: num] :
% 5.44/5.61 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_right_numeral
% 5.44/5.61 thf(fact_105_distrib__right__numeral,axiom,
% 5.44/5.61 ! [A: complex,B: complex,V: num] :
% 5.44/5.61 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.44/5.61 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_right_numeral
% 5.44/5.61 thf(fact_106_distrib__right__numeral,axiom,
% 5.44/5.61 ! [A: real,B: real,V: num] :
% 5.44/5.61 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.61 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_right_numeral
% 5.44/5.61 thf(fact_107_distrib__right__numeral,axiom,
% 5.44/5.61 ! [A: nat,B: nat,V: num] :
% 5.44/5.61 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_right_numeral
% 5.44/5.61 thf(fact_108_distrib__right__numeral,axiom,
% 5.44/5.61 ! [A: int,B: int,V: num] :
% 5.44/5.61 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.61 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_right_numeral
% 5.44/5.61 thf(fact_109_distrib__left__numeral,axiom,
% 5.44/5.61 ! [V: num,B: extended_enat,C: extended_enat] :
% 5.44/5.61 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ B @ C ) )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_left_numeral
% 5.44/5.61 thf(fact_110_distrib__left__numeral,axiom,
% 5.44/5.61 ! [V: num,B: complex,C: complex] :
% 5.44/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.44/5.61 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_left_numeral
% 5.44/5.61 thf(fact_111_distrib__left__numeral,axiom,
% 5.44/5.61 ! [V: num,B: real,C: real] :
% 5.44/5.61 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.44/5.61 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_left_numeral
% 5.44/5.61 thf(fact_112_distrib__left__numeral,axiom,
% 5.44/5.61 ! [V: num,B: nat,C: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_left_numeral
% 5.44/5.61 thf(fact_113_distrib__left__numeral,axiom,
% 5.44/5.61 ! [V: num,B: int,C: int] :
% 5.44/5.61 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.44/5.61 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % distrib_left_numeral
% 5.44/5.61 thf(fact_114_le__divide__eq__numeral1_I1_J,axiom,
% 5.44/5.61 ! [A: real,B: real,W: num] :
% 5.44/5.61 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.61 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_divide_eq_numeral1(1)
% 5.44/5.61 thf(fact_115_divide__le__eq__numeral1_I1_J,axiom,
% 5.44/5.61 ! [B: real,W: num,A: real] :
% 5.44/5.61 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.44/5.61 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % divide_le_eq_numeral1(1)
% 5.44/5.61 thf(fact_116_yhelper,axiom,
% 5.44/5.61 ! [Y: nat] :
% 5.44/5.61 ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ Y @ na ) ) @ ( vEBT_VEBT_low @ Y @ na ) )
% 5.44/5.61 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.44/5.61 => ( ( ord_less_nat @ mi @ Y )
% 5.44/5.61 & ( ord_less_eq_nat @ Y @ ma )
% 5.44/5.61 & ( ord_less_nat @ ( vEBT_VEBT_low @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % yhelper
% 5.44/5.61 thf(fact_117__C7b_C,axiom,
% 5.44/5.61 ! [I: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.44/5.61 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.44/5.61 = I )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.44/5.61 & ! [Y2: nat] :
% 5.44/5.61 ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 5.44/5.61 = I )
% 5.44/5.61 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ mi @ Y2 )
% 5.44/5.61 & ( ord_less_eq_nat @ Y2 @ ma ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "7b"
% 5.44/5.61 thf(fact_118_allvalidinlist,axiom,
% 5.44/5.61 ! [X3: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ X3 @ na ) ) ).
% 5.44/5.61
% 5.44/5.61 % allvalidinlist
% 5.44/5.61 thf(fact_119__C111_C,axiom,
% 5.44/5.61 ! [I: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.44/5.61 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ I ) @ X4 ) )
% 5.44/5.61 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % "111"
% 5.44/5.61 thf(fact_120_div__mult2__numeral__eq,axiom,
% 5.44/5.61 ! [A: nat,K: num,L2: num] :
% 5.44/5.61 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 5.44/5.61 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_mult2_numeral_eq
% 5.44/5.61 thf(fact_121_div__mult2__numeral__eq,axiom,
% 5.44/5.61 ! [A: int,K: num,L2: num] :
% 5.44/5.61 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 5.44/5.61 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_mult2_numeral_eq
% 5.44/5.61 thf(fact_122_div__mult2__numeral__eq,axiom,
% 5.44/5.61 ! [A: code_integer,K: num,L2: num] :
% 5.44/5.61 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ L2 ) )
% 5.44/5.61 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_mult2_numeral_eq
% 5.44/5.61 thf(fact_123_div__le__dividend,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 5.44/5.61
% 5.44/5.61 % div_le_dividend
% 5.44/5.61 thf(fact_124_div__le__mono,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_le_mono
% 5.44/5.61 thf(fact_125_is__num__normalize_I1_J,axiom,
% 5.44/5.61 ! [A: complex,B: complex,C: complex] :
% 5.44/5.61 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.44/5.61 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % is_num_normalize(1)
% 5.44/5.61 thf(fact_126_is__num__normalize_I1_J,axiom,
% 5.44/5.61 ! [A: real,B: real,C: real] :
% 5.44/5.61 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.44/5.61 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % is_num_normalize(1)
% 5.44/5.61 thf(fact_127_is__num__normalize_I1_J,axiom,
% 5.44/5.61 ! [A: int,B: int,C: int] :
% 5.44/5.61 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.61 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % is_num_normalize(1)
% 5.44/5.61 thf(fact_128_times__div__less__eq__dividend,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 5.44/5.61
% 5.44/5.61 % times_div_less_eq_dividend
% 5.44/5.61 thf(fact_129_div__times__less__eq__dividend,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 5.44/5.61
% 5.44/5.61 % div_times_less_eq_dividend
% 5.44/5.61 thf(fact_130_div__mult2__eq,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.61 ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
% 5.44/5.61 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_mult2_eq
% 5.44/5.61 thf(fact_131_mult__numeral__1__right,axiom,
% 5.44/5.61 ! [A: extended_enat] :
% 5.44/5.61 ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1_right
% 5.44/5.61 thf(fact_132_mult__numeral__1__right,axiom,
% 5.44/5.61 ! [A: complex] :
% 5.44/5.61 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1_right
% 5.44/5.61 thf(fact_133_mult__numeral__1__right,axiom,
% 5.44/5.61 ! [A: real] :
% 5.44/5.61 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1_right
% 5.44/5.61 thf(fact_134_mult__numeral__1__right,axiom,
% 5.44/5.61 ! [A: nat] :
% 5.44/5.61 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1_right
% 5.44/5.61 thf(fact_135_mult__numeral__1__right,axiom,
% 5.44/5.61 ! [A: int] :
% 5.44/5.61 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1_right
% 5.44/5.61 thf(fact_136_mult__numeral__1,axiom,
% 5.44/5.61 ! [A: extended_enat] :
% 5.44/5.61 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1
% 5.44/5.61 thf(fact_137_mult__numeral__1,axiom,
% 5.44/5.61 ! [A: complex] :
% 5.44/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1
% 5.44/5.61 thf(fact_138_mult__numeral__1,axiom,
% 5.44/5.61 ! [A: real] :
% 5.44/5.61 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1
% 5.44/5.61 thf(fact_139_mult__numeral__1,axiom,
% 5.44/5.61 ! [A: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1
% 5.44/5.61 thf(fact_140_mult__numeral__1,axiom,
% 5.44/5.61 ! [A: int] :
% 5.44/5.61 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % mult_numeral_1
% 5.44/5.61 thf(fact_141_numeral__Bit0,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_Bit0
% 5.44/5.61 thf(fact_142_numeral__Bit0,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_Bit0
% 5.44/5.61 thf(fact_143_numeral__Bit0,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_Bit0
% 5.44/5.61 thf(fact_144_numeral__Bit0,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_Bit0
% 5.44/5.61 thf(fact_145_numeral__Bit0,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_Bit0
% 5.44/5.61 thf(fact_146_divide__numeral__1,axiom,
% 5.44/5.61 ! [A: real] :
% 5.44/5.61 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % divide_numeral_1
% 5.44/5.61 thf(fact_147_divide__numeral__1,axiom,
% 5.44/5.61 ! [A: complex] :
% 5.44/5.61 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % divide_numeral_1
% 5.44/5.61 thf(fact_148_less__mult__imp__div__less,axiom,
% 5.44/5.61 ! [M: nat,I2: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
% 5.44/5.61 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_mult_imp_div_less
% 5.44/5.61 thf(fact_149_numeral__Bit0__div__2,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_Bit0_div_2
% 5.44/5.61 thf(fact_150_numeral__Bit0__div__2,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_Bit0_div_2
% 5.44/5.61 thf(fact_151_numeral__Bit0__div__2,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_Bit0_div_2
% 5.44/5.61 thf(fact_152_left__add__twice,axiom,
% 5.44/5.61 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.61 ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_add_twice
% 5.44/5.61 thf(fact_153_left__add__twice,axiom,
% 5.44/5.61 ! [A: complex,B: complex] :
% 5.44/5.61 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.44/5.61 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_add_twice
% 5.44/5.61 thf(fact_154_left__add__twice,axiom,
% 5.44/5.61 ! [A: real,B: real] :
% 5.44/5.61 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.44/5.61 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_add_twice
% 5.44/5.61 thf(fact_155_left__add__twice,axiom,
% 5.44/5.61 ! [A: nat,B: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_add_twice
% 5.44/5.61 thf(fact_156_left__add__twice,axiom,
% 5.44/5.61 ! [A: int,B: int] :
% 5.44/5.61 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.44/5.61 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_add_twice
% 5.44/5.61 thf(fact_157_mult__2__right,axiom,
% 5.44/5.61 ! [Z: extended_enat] :
% 5.44/5.61 ( ( times_7803423173614009249d_enat @ Z @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2_right
% 5.44/5.61 thf(fact_158_mult__2__right,axiom,
% 5.44/5.61 ! [Z: complex] :
% 5.44/5.61 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2_right
% 5.44/5.61 thf(fact_159_mult__2__right,axiom,
% 5.44/5.61 ! [Z: real] :
% 5.44/5.61 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2_right
% 5.44/5.61 thf(fact_160_mult__2__right,axiom,
% 5.44/5.61 ! [Z: nat] :
% 5.44/5.61 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2_right
% 5.44/5.61 thf(fact_161_mult__2__right,axiom,
% 5.44/5.61 ! [Z: int] :
% 5.44/5.61 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2_right
% 5.44/5.61 thf(fact_162_mult__2,axiom,
% 5.44/5.61 ! [Z: extended_enat] :
% 5.44/5.61 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2
% 5.44/5.61 thf(fact_163_mult__2,axiom,
% 5.44/5.61 ! [Z: complex] :
% 5.44/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.44/5.61 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2
% 5.44/5.61 thf(fact_164_mult__2,axiom,
% 5.44/5.61 ! [Z: real] :
% 5.44/5.61 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.44/5.61 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2
% 5.44/5.61 thf(fact_165_mult__2,axiom,
% 5.44/5.61 ! [Z: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.44/5.61 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2
% 5.44/5.61 thf(fact_166_mult__2,axiom,
% 5.44/5.61 ! [Z: int] :
% 5.44/5.61 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.44/5.61 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_2
% 5.44/5.61 thf(fact_167_in__children__def,axiom,
% 5.44/5.61 ( vEBT_V5917875025757280293ildren
% 5.44/5.61 = ( ^ [N: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N ) ) @ ( vEBT_VEBT_low @ X2 @ N ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % in_children_def
% 5.44/5.61 thf(fact_168__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 5.44/5.61 ( ( mi != ma )
% 5.44/5.61 & ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>mi \<noteq> ma \<and> x < 2 ^ deg\<close>
% 5.44/5.61 thf(fact_169_valid__insert__both__member__options__pres,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % valid_insert_both_member_options_pres
% 5.44/5.61 thf(fact_170_valid__insert__both__member__options__add,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % valid_insert_both_member_options_add
% 5.44/5.61 thf(fact_171_set__swap,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.44/5.61 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_swap
% 5.44/5.61 thf(fact_172_set__swap,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_o,J: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.44/5.61 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_swap
% 5.44/5.61 thf(fact_173_set__swap,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_nat,J: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.44/5.61 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_swap
% 5.44/5.61 thf(fact_174_set__swap,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_int,J: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.44/5.61 = ( set_int2 @ Xs2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_swap
% 5.44/5.61 thf(fact_175_nth__list__update__eq,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 5.44/5.61 = X ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update_eq
% 5.44/5.61 thf(fact_176_nth__list__update__eq,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 5.44/5.61 = X ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update_eq
% 5.44/5.61 thf(fact_177_nth__list__update__eq,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 5.44/5.61 = X ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update_eq
% 5.44/5.61 thf(fact_178_nth__list__update__eq,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_int,X: int] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 5.44/5.61 = X ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update_eq
% 5.44/5.61 thf(fact_179_list__update__beyond,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 5.44/5.61 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.44/5.61 = Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_beyond
% 5.44/5.61 thf(fact_180_list__update__beyond,axiom,
% 5.44/5.61 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 5.44/5.61 => ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.44/5.61 = Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_beyond
% 5.44/5.61 thf(fact_181_list__update__beyond,axiom,
% 5.44/5.61 ! [Xs2: list_nat,I2: nat,X: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I2 )
% 5.44/5.61 => ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.44/5.61 = Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_beyond
% 5.44/5.61 thf(fact_182_list__update__beyond,axiom,
% 5.44/5.61 ! [Xs2: list_int,I2: nat,X: int] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 5.44/5.61 => ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.44/5.61 = Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_beyond
% 5.44/5.61 thf(fact_183_both__member__options__ding,axiom,
% 5.44/5.61 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 5.44/5.61 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.44/5.61 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % both_member_options_ding
% 5.44/5.61 thf(fact_184_sum__squares__bound,axiom,
% 5.44/5.61 ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % sum_squares_bound
% 5.44/5.61 thf(fact_185_set__n__deg__not__0,axiom,
% 5.44/5.61 ! [TreeList2: list_VEBT_VEBT,N2: nat,M: nat] :
% 5.44/5.61 ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.44/5.61 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.44/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_n_deg_not_0
% 5.44/5.61 thf(fact_186_power2__sum,axiom,
% 5.44/5.61 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.61 ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_sum
% 5.44/5.61 thf(fact_187_power2__sum,axiom,
% 5.44/5.61 ! [X: complex,Y: complex] :
% 5.44/5.61 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_sum
% 5.44/5.61 thf(fact_188_power2__sum,axiom,
% 5.44/5.61 ! [X: real,Y: real] :
% 5.44/5.61 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_sum
% 5.44/5.61 thf(fact_189_power2__sum,axiom,
% 5.44/5.61 ! [X: nat,Y: nat] :
% 5.44/5.61 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_sum
% 5.44/5.61 thf(fact_190_power2__sum,axiom,
% 5.44/5.61 ! [X: int,Y: int] :
% 5.44/5.61 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_sum
% 5.44/5.61 thf(fact_191_inrg,axiom,
% 5.44/5.61 ( ( ord_less_eq_nat @ mi @ xa )
% 5.44/5.61 & ( ord_less_eq_nat @ xa @ ma ) ) ).
% 5.44/5.61
% 5.44/5.61 % inrg
% 5.44/5.61 thf(fact_192_deg__deg__n,axiom,
% 5.44/5.61 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N2 )
% 5.44/5.61 => ( Deg = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % deg_deg_n
% 5.44/5.61 thf(fact_193__C11_C,axiom,
% 5.44/5.61 ord_less_eq_nat @ one_one_nat @ na ).
% 5.44/5.61
% 5.44/5.61 % "11"
% 5.44/5.61 thf(fact_194_xmi,axiom,
% 5.44/5.61 xa = mi ).
% 5.44/5.61
% 5.44/5.61 % xmi
% 5.44/5.61 thf(fact_195_list__update__overwrite,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.44/5.61 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 @ Y )
% 5.44/5.61 = ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ Y ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_overwrite
% 5.44/5.61 thf(fact_196__092_060open_062x_A_092_060noteq_062_Ami_A_092_060or_062_Ax_A_092_060noteq_062_Ama_092_060close_062,axiom,
% 5.44/5.61 ( ( xa != mi )
% 5.44/5.61 | ( xa != ma ) ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>x \<noteq> mi \<or> x \<noteq> ma\<close>
% 5.44/5.61 thf(fact_197_power__one,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( power_8040749407984259932d_enat @ one_on7984719198319812577d_enat @ N2 )
% 5.44/5.61 = one_on7984719198319812577d_enat ) ).
% 5.44/5.61
% 5.44/5.61 % power_one
% 5.44/5.61 thf(fact_198_power__one,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( power_power_nat @ one_one_nat @ N2 )
% 5.44/5.61 = one_one_nat ) ).
% 5.44/5.61
% 5.44/5.61 % power_one
% 5.44/5.61 thf(fact_199_power__one,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( power_power_real @ one_one_real @ N2 )
% 5.44/5.61 = one_one_real ) ).
% 5.44/5.61
% 5.44/5.61 % power_one
% 5.44/5.61 thf(fact_200_power__one,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( power_power_int @ one_one_int @ N2 )
% 5.44/5.61 = one_one_int ) ).
% 5.44/5.61
% 5.44/5.61 % power_one
% 5.44/5.61 thf(fact_201_power__one,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ one_one_complex @ N2 )
% 5.44/5.61 = one_one_complex ) ).
% 5.44/5.61
% 5.44/5.61 % power_one
% 5.44/5.61 thf(fact_202_power__one__right,axiom,
% 5.44/5.61 ! [A: nat] :
% 5.44/5.61 ( ( power_power_nat @ A @ one_one_nat )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % power_one_right
% 5.44/5.61 thf(fact_203_power__one__right,axiom,
% 5.44/5.61 ! [A: real] :
% 5.44/5.61 ( ( power_power_real @ A @ one_one_nat )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % power_one_right
% 5.44/5.61 thf(fact_204_power__one__right,axiom,
% 5.44/5.61 ! [A: int] :
% 5.44/5.61 ( ( power_power_int @ A @ one_one_nat )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % power_one_right
% 5.44/5.61 thf(fact_205_power__one__right,axiom,
% 5.44/5.61 ! [A: complex] :
% 5.44/5.61 ( ( power_power_complex @ A @ one_one_nat )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % power_one_right
% 5.44/5.61 thf(fact_206_length__list__update,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.44/5.61 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 5.44/5.61 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % length_list_update
% 5.44/5.61 thf(fact_207_length__list__update,axiom,
% 5.44/5.61 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.44/5.61 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 5.44/5.61 = ( size_size_list_o @ Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % length_list_update
% 5.44/5.61 thf(fact_208_length__list__update,axiom,
% 5.44/5.61 ! [Xs2: list_nat,I2: nat,X: nat] :
% 5.44/5.61 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) )
% 5.44/5.61 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % length_list_update
% 5.44/5.61 thf(fact_209_length__list__update,axiom,
% 5.44/5.61 ! [Xs2: list_int,I2: nat,X: int] :
% 5.44/5.61 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 5.44/5.61 = ( size_size_list_int @ Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % length_list_update
% 5.44/5.61 thf(fact_210_list__update__id,axiom,
% 5.44/5.61 ! [Xs2: list_nat,I2: nat] :
% 5.44/5.61 ( ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ I2 ) )
% 5.44/5.61 = Xs2 ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_id
% 5.44/5.61 thf(fact_211_list__update__id,axiom,
% 5.44/5.61 ! [Xs2: list_int,I2: nat] :
% 5.44/5.61 ( ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ I2 ) )
% 5.44/5.61 = Xs2 ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_id
% 5.44/5.61 thf(fact_212_list__update__id,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,I2: nat] :
% 5.44/5.61 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) )
% 5.44/5.61 = Xs2 ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_id
% 5.44/5.61 thf(fact_213_nth__list__update__neq,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,Xs2: list_nat,X: nat] :
% 5.44/5.61 ( ( I2 != J )
% 5.44/5.61 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update_neq
% 5.44/5.61 thf(fact_214_nth__list__update__neq,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,Xs2: list_int,X: int] :
% 5.44/5.61 ( ( I2 != J )
% 5.44/5.61 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = ( nth_int @ Xs2 @ J ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update_neq
% 5.44/5.61 thf(fact_215_nth__list__update__neq,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.44/5.61 ( ( I2 != J )
% 5.44/5.61 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update_neq
% 5.44/5.61 thf(fact_216_numeral__eq__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ( numera1916890842035813515d_enat @ N2 )
% 5.44/5.61 = one_on7984719198319812577d_enat )
% 5.44/5.61 = ( N2 = one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_one_iff
% 5.44/5.61 thf(fact_217_numeral__eq__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ( numera6690914467698888265omplex @ N2 )
% 5.44/5.61 = one_one_complex )
% 5.44/5.61 = ( N2 = one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_one_iff
% 5.44/5.61 thf(fact_218_numeral__eq__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ( numeral_numeral_real @ N2 )
% 5.44/5.61 = one_one_real )
% 5.44/5.61 = ( N2 = one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_one_iff
% 5.44/5.61 thf(fact_219_numeral__eq__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ( numeral_numeral_nat @ N2 )
% 5.44/5.61 = one_one_nat )
% 5.44/5.61 = ( N2 = one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_one_iff
% 5.44/5.61 thf(fact_220_numeral__eq__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ( numeral_numeral_int @ N2 )
% 5.44/5.61 = one_one_int )
% 5.44/5.61 = ( N2 = one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_eq_one_iff
% 5.44/5.61 thf(fact_221_one__eq__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( one_on7984719198319812577d_enat
% 5.44/5.61 = ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( one = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_eq_numeral_iff
% 5.44/5.61 thf(fact_222_one__eq__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( one_one_complex
% 5.44/5.61 = ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.61 = ( one = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_eq_numeral_iff
% 5.44/5.61 thf(fact_223_one__eq__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( one_one_real
% 5.44/5.61 = ( numeral_numeral_real @ N2 ) )
% 5.44/5.61 = ( one = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_eq_numeral_iff
% 5.44/5.61 thf(fact_224_one__eq__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( one_one_nat
% 5.44/5.61 = ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( one = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_eq_numeral_iff
% 5.44/5.61 thf(fact_225_one__eq__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( one_one_int
% 5.44/5.61 = ( numeral_numeral_int @ N2 ) )
% 5.44/5.61 = ( one = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_eq_numeral_iff
% 5.44/5.61 thf(fact_226_power__inject__exp,axiom,
% 5.44/5.61 ! [A: real,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.61 => ( ( ( power_power_real @ A @ M )
% 5.44/5.61 = ( power_power_real @ A @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_inject_exp
% 5.44/5.61 thf(fact_227_power__inject__exp,axiom,
% 5.44/5.61 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ( ( power_power_nat @ A @ M )
% 5.44/5.61 = ( power_power_nat @ A @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_inject_exp
% 5.44/5.61 thf(fact_228_power__inject__exp,axiom,
% 5.44/5.61 ! [A: int,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.44/5.61 => ( ( ( power_power_int @ A @ M )
% 5.44/5.61 = ( power_power_int @ A @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_inject_exp
% 5.44/5.61 thf(fact_229_power__mult__numeral,axiom,
% 5.44/5.61 ! [A: nat,M: num,N2: num] :
% 5.44/5.61 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult_numeral
% 5.44/5.61 thf(fact_230_power__mult__numeral,axiom,
% 5.44/5.61 ! [A: real,M: num,N2: num] :
% 5.44/5.61 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult_numeral
% 5.44/5.61 thf(fact_231_power__mult__numeral,axiom,
% 5.44/5.61 ! [A: int,M: num,N2: num] :
% 5.44/5.61 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult_numeral
% 5.44/5.61 thf(fact_232_power__mult__numeral,axiom,
% 5.44/5.61 ! [A: complex,M: num,N2: num] :
% 5.44/5.61 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult_numeral
% 5.44/5.61 thf(fact_233_power__strict__increasing__iff,axiom,
% 5.44/5.61 ! [B: real,X: nat,Y: nat] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.61 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.44/5.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_strict_increasing_iff
% 5.44/5.61 thf(fact_234_power__strict__increasing__iff,axiom,
% 5.44/5.61 ! [B: nat,X: nat,Y: nat] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ B )
% 5.44/5.61 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.44/5.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_strict_increasing_iff
% 5.44/5.61 thf(fact_235_power__strict__increasing__iff,axiom,
% 5.44/5.61 ! [B: int,X: nat,Y: nat] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ B )
% 5.44/5.61 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.44/5.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_strict_increasing_iff
% 5.44/5.61 thf(fact_236_power__add__numeral,axiom,
% 5.44/5.61 ! [A: complex,M: num,N2: num] :
% 5.44/5.61 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.44/5.61 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add_numeral
% 5.44/5.61 thf(fact_237_power__add__numeral,axiom,
% 5.44/5.61 ! [A: real,M: num,N2: num] :
% 5.44/5.61 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.44/5.61 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add_numeral
% 5.44/5.61 thf(fact_238_power__add__numeral,axiom,
% 5.44/5.61 ! [A: nat,M: num,N2: num] :
% 5.44/5.61 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.44/5.61 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add_numeral
% 5.44/5.61 thf(fact_239_power__add__numeral,axiom,
% 5.44/5.61 ! [A: int,M: num,N2: num] :
% 5.44/5.61 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.44/5.61 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add_numeral
% 5.44/5.61 thf(fact_240_power__add__numeral2,axiom,
% 5.44/5.61 ! [A: complex,M: num,N2: num,B: complex] :
% 5.44/5.61 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.44/5.61 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add_numeral2
% 5.44/5.61 thf(fact_241_power__add__numeral2,axiom,
% 5.44/5.61 ! [A: real,M: num,N2: num,B: real] :
% 5.44/5.61 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.44/5.61 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add_numeral2
% 5.44/5.61 thf(fact_242_power__add__numeral2,axiom,
% 5.44/5.61 ! [A: nat,M: num,N2: num,B: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.44/5.61 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add_numeral2
% 5.44/5.61 thf(fact_243_power__add__numeral2,axiom,
% 5.44/5.61 ! [A: int,M: num,N2: num,B: int] :
% 5.44/5.61 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.44/5.61 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add_numeral2
% 5.44/5.61 thf(fact_244_one__add__one,axiom,
% 5.44/5.61 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_add_one
% 5.44/5.61 thf(fact_245_one__add__one,axiom,
% 5.44/5.61 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.44/5.61 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_add_one
% 5.44/5.61 thf(fact_246_one__add__one,axiom,
% 5.44/5.61 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.44/5.61 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_add_one
% 5.44/5.61 thf(fact_247_one__add__one,axiom,
% 5.44/5.61 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.44/5.61 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_add_one
% 5.44/5.61 thf(fact_248_one__add__one,axiom,
% 5.44/5.61 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.44/5.61 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_add_one
% 5.44/5.61 thf(fact_249_power__increasing__iff,axiom,
% 5.44/5.61 ! [B: real,X: nat,Y: nat] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.61 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.44/5.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_increasing_iff
% 5.44/5.61 thf(fact_250_power__increasing__iff,axiom,
% 5.44/5.61 ! [B: nat,X: nat,Y: nat] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ B )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.44/5.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_increasing_iff
% 5.44/5.61 thf(fact_251_power__increasing__iff,axiom,
% 5.44/5.61 ! [B: int,X: nat,Y: nat] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ B )
% 5.44/5.61 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.44/5.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_increasing_iff
% 5.44/5.61 thf(fact_252_numeral__plus__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_one
% 5.44/5.61 thf(fact_253_numeral__plus__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 5.44/5.61 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_one
% 5.44/5.61 thf(fact_254_numeral__plus__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 5.44/5.61 = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_one
% 5.44/5.61 thf(fact_255_numeral__plus__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.44/5.61 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_one
% 5.44/5.61 thf(fact_256_numeral__plus__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.44/5.61 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_plus_one
% 5.44/5.61 thf(fact_257_one__plus__numeral,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral
% 5.44/5.61 thf(fact_258_one__plus__numeral,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.61 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral
% 5.44/5.61 thf(fact_259_one__plus__numeral,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral
% 5.44/5.61 thf(fact_260_one__plus__numeral,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral
% 5.44/5.61 thf(fact_261_one__plus__numeral,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral
% 5.44/5.61 thf(fact_262_numeral__le__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 5.44/5.61 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_le_one_iff
% 5.44/5.61 thf(fact_263_numeral__le__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 5.44/5.61 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_le_one_iff
% 5.44/5.61 thf(fact_264_numeral__le__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.44/5.61 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_le_one_iff
% 5.44/5.61 thf(fact_265_numeral__le__one__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.44/5.61 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_le_one_iff
% 5.44/5.61 thf(fact_266_one__less__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ one @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_less_numeral_iff
% 5.44/5.61 thf(fact_267_one__less__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ one @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_less_numeral_iff
% 5.44/5.61 thf(fact_268_one__less__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ one @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_less_numeral_iff
% 5.44/5.61 thf(fact_269_one__less__numeral__iff,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ one @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_less_numeral_iff
% 5.44/5.61 thf(fact_270_subset__code_I1_J,axiom,
% 5.44/5.61 ! [Xs2: list_complex,B2: set_complex] :
% 5.44/5.61 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B2 )
% 5.44/5.61 = ( ! [X2: complex] :
% 5.44/5.61 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.44/5.61 => ( member_complex @ X2 @ B2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % subset_code(1)
% 5.44/5.61 thf(fact_271_subset__code_I1_J,axiom,
% 5.44/5.61 ! [Xs2: list_P6011104703257516679at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.44/5.61 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ B2 )
% 5.44/5.61 = ( ! [X2: product_prod_nat_nat] :
% 5.44/5.61 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.44/5.61 => ( member8440522571783428010at_nat @ X2 @ B2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % subset_code(1)
% 5.44/5.61 thf(fact_272_subset__code_I1_J,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 5.44/5.61 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B2 )
% 5.44/5.61 = ( ! [X2: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.61 => ( member_VEBT_VEBT @ X2 @ B2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % subset_code(1)
% 5.44/5.61 thf(fact_273_subset__code_I1_J,axiom,
% 5.44/5.61 ! [Xs2: list_int,B2: set_int] :
% 5.44/5.61 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B2 )
% 5.44/5.61 = ( ! [X2: int] :
% 5.44/5.61 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.44/5.61 => ( member_int @ X2 @ B2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % subset_code(1)
% 5.44/5.61 thf(fact_274_subset__code_I1_J,axiom,
% 5.44/5.61 ! [Xs2: list_real,B2: set_real] :
% 5.44/5.61 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B2 )
% 5.44/5.61 = ( ! [X2: real] :
% 5.44/5.61 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.44/5.61 => ( member_real @ X2 @ B2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % subset_code(1)
% 5.44/5.61 thf(fact_275_subset__code_I1_J,axiom,
% 5.44/5.61 ! [Xs2: list_nat,B2: set_nat] :
% 5.44/5.61 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B2 )
% 5.44/5.61 = ( ! [X2: nat] :
% 5.44/5.61 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.44/5.61 => ( member_nat @ X2 @ B2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % subset_code(1)
% 5.44/5.61 thf(fact_276_L2__set__mult__ineq__lemma,axiom,
% 5.44/5.61 ! [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 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % L2_set_mult_ineq_lemma
% 5.44/5.61 thf(fact_277_add__One__commute,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( plus_plus_num @ one @ N2 )
% 5.44/5.61 = ( plus_plus_num @ N2 @ one ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_One_commute
% 5.44/5.61 thf(fact_278_le__num__One__iff,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_less_eq_num @ X @ one )
% 5.44/5.61 = ( X = one ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_num_One_iff
% 5.44/5.61 thf(fact_279_le__numeral__extra_I4_J,axiom,
% 5.44/5.61 ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat ).
% 5.44/5.61
% 5.44/5.61 % le_numeral_extra(4)
% 5.44/5.61 thf(fact_280_le__numeral__extra_I4_J,axiom,
% 5.44/5.61 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.44/5.61
% 5.44/5.61 % le_numeral_extra(4)
% 5.44/5.61 thf(fact_281_le__numeral__extra_I4_J,axiom,
% 5.44/5.61 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.44/5.61
% 5.44/5.61 % le_numeral_extra(4)
% 5.44/5.61 thf(fact_282_le__numeral__extra_I4_J,axiom,
% 5.44/5.61 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.44/5.61
% 5.44/5.61 % le_numeral_extra(4)
% 5.44/5.61 thf(fact_283_less__numeral__extra_I4_J,axiom,
% 5.44/5.61 ~ ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat ) ).
% 5.44/5.61
% 5.44/5.61 % less_numeral_extra(4)
% 5.44/5.61 thf(fact_284_less__numeral__extra_I4_J,axiom,
% 5.44/5.61 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.44/5.61
% 5.44/5.61 % less_numeral_extra(4)
% 5.44/5.61 thf(fact_285_less__numeral__extra_I4_J,axiom,
% 5.44/5.61 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.44/5.61
% 5.44/5.61 % less_numeral_extra(4)
% 5.44/5.61 thf(fact_286_less__numeral__extra_I4_J,axiom,
% 5.44/5.61 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.44/5.61
% 5.44/5.61 % less_numeral_extra(4)
% 5.44/5.61 thf(fact_287_one__le__power,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.44/5.61 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_le_power
% 5.44/5.61 thf(fact_288_one__le__power,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_le_power
% 5.44/5.61 thf(fact_289_one__le__power,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.44/5.61 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_le_power
% 5.44/5.61 thf(fact_290_left__right__inverse__power,axiom,
% 5.44/5.61 ! [X: extended_enat,Y: extended_enat,N2: nat] :
% 5.44/5.61 ( ( ( times_7803423173614009249d_enat @ X @ Y )
% 5.44/5.61 = one_on7984719198319812577d_enat )
% 5.44/5.61 => ( ( times_7803423173614009249d_enat @ ( power_8040749407984259932d_enat @ X @ N2 ) @ ( power_8040749407984259932d_enat @ Y @ N2 ) )
% 5.44/5.61 = one_on7984719198319812577d_enat ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_right_inverse_power
% 5.44/5.61 thf(fact_291_left__right__inverse__power,axiom,
% 5.44/5.61 ! [X: complex,Y: complex,N2: nat] :
% 5.44/5.61 ( ( ( times_times_complex @ X @ Y )
% 5.44/5.61 = one_one_complex )
% 5.44/5.61 => ( ( times_times_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.44/5.61 = one_one_complex ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_right_inverse_power
% 5.44/5.61 thf(fact_292_left__right__inverse__power,axiom,
% 5.44/5.61 ! [X: real,Y: real,N2: nat] :
% 5.44/5.61 ( ( ( times_times_real @ X @ Y )
% 5.44/5.61 = one_one_real )
% 5.44/5.61 => ( ( times_times_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.44/5.61 = one_one_real ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_right_inverse_power
% 5.44/5.61 thf(fact_293_left__right__inverse__power,axiom,
% 5.44/5.61 ! [X: nat,Y: nat,N2: nat] :
% 5.44/5.61 ( ( ( times_times_nat @ X @ Y )
% 5.44/5.61 = one_one_nat )
% 5.44/5.61 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 5.44/5.61 = one_one_nat ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_right_inverse_power
% 5.44/5.61 thf(fact_294_left__right__inverse__power,axiom,
% 5.44/5.61 ! [X: int,Y: int,N2: nat] :
% 5.44/5.61 ( ( ( times_times_int @ X @ Y )
% 5.44/5.61 = one_one_int )
% 5.44/5.61 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.44/5.61 = one_one_int ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_right_inverse_power
% 5.44/5.61 thf(fact_295_power__one__over,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N2 )
% 5.44/5.61 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_one_over
% 5.44/5.61 thf(fact_296_power__one__over,axiom,
% 5.44/5.61 ! [A: complex,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N2 )
% 5.44/5.61 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_one_over
% 5.44/5.61 thf(fact_297_set__update__subsetI,axiom,
% 5.44/5.61 ! [Xs2: list_complex,A2: set_complex,X: complex,I2: nat] :
% 5.44/5.61 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 5.44/5.61 => ( ( member_complex @ X @ A2 )
% 5.44/5.61 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_subsetI
% 5.44/5.61 thf(fact_298_set__update__subsetI,axiom,
% 5.44/5.61 ! [Xs2: list_P6011104703257516679at_nat,A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,I2: nat] :
% 5.44/5.61 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 5.44/5.61 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.44/5.61 => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_subsetI
% 5.44/5.61 thf(fact_299_set__update__subsetI,axiom,
% 5.44/5.61 ! [Xs2: list_int,A2: set_int,X: int,I2: nat] :
% 5.44/5.61 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 5.44/5.61 => ( ( member_int @ X @ A2 )
% 5.44/5.61 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_subsetI
% 5.44/5.61 thf(fact_300_set__update__subsetI,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I2: nat] :
% 5.44/5.61 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 5.44/5.61 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.44/5.61 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_subsetI
% 5.44/5.61 thf(fact_301_set__update__subsetI,axiom,
% 5.44/5.61 ! [Xs2: list_real,A2: set_real,X: real,I2: nat] :
% 5.44/5.61 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 5.44/5.61 => ( ( member_real @ X @ A2 )
% 5.44/5.61 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_subsetI
% 5.44/5.61 thf(fact_302_set__update__subsetI,axiom,
% 5.44/5.61 ! [Xs2: list_nat,A2: set_nat,X: nat,I2: nat] :
% 5.44/5.61 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 5.44/5.61 => ( ( member_nat @ X @ A2 )
% 5.44/5.61 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_subsetI
% 5.44/5.61 thf(fact_303_four__x__squared,axiom,
% 5.44/5.61 ! [X: real] :
% 5.44/5.61 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % four_x_squared
% 5.44/5.61 thf(fact_304_power__gt1__lemma,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.61 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_gt1_lemma
% 5.44/5.61 thf(fact_305_power__gt1__lemma,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_gt1_lemma
% 5.44/5.61 thf(fact_306_power__gt1__lemma,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.44/5.61 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_gt1_lemma
% 5.44/5.61 thf(fact_307_power__less__power__Suc,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.61 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_less_power_Suc
% 5.44/5.61 thf(fact_308_power__less__power__Suc,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_less_power_Suc
% 5.44/5.61 thf(fact_309_power__less__power__Suc,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.44/5.61 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_less_power_Suc
% 5.44/5.61 thf(fact_310_power__less__imp__less__exp,axiom,
% 5.44/5.61 ! [A: real,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.61 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 5.44/5.61 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_less_imp_less_exp
% 5.44/5.61 thf(fact_311_power__less__imp__less__exp,axiom,
% 5.44/5.61 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.44/5.61 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_less_imp_less_exp
% 5.44/5.61 thf(fact_312_power__less__imp__less__exp,axiom,
% 5.44/5.61 ! [A: int,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.44/5.61 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.44/5.61 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_less_imp_less_exp
% 5.44/5.61 thf(fact_313_power__strict__increasing,axiom,
% 5.44/5.61 ! [N2: nat,N3: nat,A: real] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ N3 )
% 5.44/5.61 => ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.61 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_strict_increasing
% 5.44/5.61 thf(fact_314_power__strict__increasing,axiom,
% 5.44/5.61 ! [N2: nat,N3: nat,A: nat] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ N3 )
% 5.44/5.61 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_strict_increasing
% 5.44/5.61 thf(fact_315_power__strict__increasing,axiom,
% 5.44/5.61 ! [N2: nat,N3: nat,A: int] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ N3 )
% 5.44/5.61 => ( ( ord_less_int @ one_one_int @ A )
% 5.44/5.61 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_strict_increasing
% 5.44/5.61 thf(fact_316_power__increasing,axiom,
% 5.44/5.61 ! [N2: nat,N3: nat,A: real] :
% 5.44/5.61 ( ( ord_less_eq_nat @ N2 @ N3 )
% 5.44/5.61 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.44/5.61 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_increasing
% 5.44/5.61 thf(fact_317_power__increasing,axiom,
% 5.44/5.61 ! [N2: nat,N3: nat,A: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ N2 @ N3 )
% 5.44/5.61 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_increasing
% 5.44/5.61 thf(fact_318_power__increasing,axiom,
% 5.44/5.61 ! [N2: nat,N3: nat,A: int] :
% 5.44/5.61 ( ( ord_less_eq_nat @ N2 @ N3 )
% 5.44/5.61 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.44/5.61 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_increasing
% 5.44/5.61 thf(fact_319_one__le__numeral,axiom,
% 5.44/5.61 ! [N2: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_le_numeral
% 5.44/5.61 thf(fact_320_one__le__numeral,axiom,
% 5.44/5.61 ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_le_numeral
% 5.44/5.61 thf(fact_321_one__le__numeral,axiom,
% 5.44/5.61 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_le_numeral
% 5.44/5.61 thf(fact_322_one__le__numeral,axiom,
% 5.44/5.61 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_le_numeral
% 5.44/5.61 thf(fact_323_not__numeral__less__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ).
% 5.44/5.61
% 5.44/5.61 % not_numeral_less_one
% 5.44/5.61 thf(fact_324_not__numeral__less__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 5.44/5.61
% 5.44/5.61 % not_numeral_less_one
% 5.44/5.61 thf(fact_325_not__numeral__less__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 5.44/5.61
% 5.44/5.61 % not_numeral_less_one
% 5.44/5.61 thf(fact_326_not__numeral__less__one,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 5.44/5.61
% 5.44/5.61 % not_numeral_less_one
% 5.44/5.61 thf(fact_327_numeral__One,axiom,
% 5.44/5.61 ( ( numera1916890842035813515d_enat @ one )
% 5.44/5.61 = one_on7984719198319812577d_enat ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_One
% 5.44/5.61 thf(fact_328_numeral__One,axiom,
% 5.44/5.61 ( ( numera6690914467698888265omplex @ one )
% 5.44/5.61 = one_one_complex ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_One
% 5.44/5.61 thf(fact_329_numeral__One,axiom,
% 5.44/5.61 ( ( numeral_numeral_real @ one )
% 5.44/5.61 = one_one_real ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_One
% 5.44/5.61 thf(fact_330_numeral__One,axiom,
% 5.44/5.61 ( ( numeral_numeral_nat @ one )
% 5.44/5.61 = one_one_nat ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_One
% 5.44/5.61 thf(fact_331_numeral__One,axiom,
% 5.44/5.61 ( ( numeral_numeral_int @ one )
% 5.44/5.61 = one_one_int ) ).
% 5.44/5.61
% 5.44/5.61 % numeral_One
% 5.44/5.61 thf(fact_332_one__plus__numeral__commute,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.44/5.61 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral_commute
% 5.44/5.61 thf(fact_333_one__plus__numeral__commute,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.44/5.61 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral_commute
% 5.44/5.61 thf(fact_334_one__plus__numeral__commute,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.44/5.61 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral_commute
% 5.44/5.61 thf(fact_335_one__plus__numeral__commute,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.44/5.61 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral_commute
% 5.44/5.61 thf(fact_336_one__plus__numeral__commute,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.44/5.61 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.44/5.61
% 5.44/5.61 % one_plus_numeral_commute
% 5.44/5.61 thf(fact_337_numerals_I1_J,axiom,
% 5.44/5.61 ( ( numeral_numeral_nat @ one )
% 5.44/5.61 = one_one_nat ) ).
% 5.44/5.61
% 5.44/5.61 % numerals(1)
% 5.44/5.61 thf(fact_338_power__le__imp__le__exp,axiom,
% 5.44/5.61 ! [A: real,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.61 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_le_imp_le_exp
% 5.44/5.61 thf(fact_339_power__le__imp__le__exp,axiom,
% 5.44/5.61 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_le_imp_le_exp
% 5.44/5.61 thf(fact_340_power__le__imp__le__exp,axiom,
% 5.44/5.61 ! [A: int,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.44/5.61 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_le_imp_le_exp
% 5.44/5.61 thf(fact_341_one__power2,axiom,
% 5.44/5.61 ( ( power_8040749407984259932d_enat @ one_on7984719198319812577d_enat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = one_on7984719198319812577d_enat ) ).
% 5.44/5.61
% 5.44/5.61 % one_power2
% 5.44/5.61 thf(fact_342_one__power2,axiom,
% 5.44/5.61 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = one_one_nat ) ).
% 5.44/5.61
% 5.44/5.61 % one_power2
% 5.44/5.61 thf(fact_343_one__power2,axiom,
% 5.44/5.61 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = one_one_real ) ).
% 5.44/5.61
% 5.44/5.61 % one_power2
% 5.44/5.61 thf(fact_344_one__power2,axiom,
% 5.44/5.61 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = one_one_int ) ).
% 5.44/5.61
% 5.44/5.61 % one_power2
% 5.44/5.61 thf(fact_345_one__power2,axiom,
% 5.44/5.61 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = one_one_complex ) ).
% 5.44/5.61
% 5.44/5.61 % one_power2
% 5.44/5.61 thf(fact_346_neq__if__length__neq,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.44/5.61 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.44/5.61 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.44/5.61 => ( Xs2 != Ys ) ) ).
% 5.44/5.61
% 5.44/5.61 % neq_if_length_neq
% 5.44/5.61 thf(fact_347_neq__if__length__neq,axiom,
% 5.44/5.61 ! [Xs2: list_o,Ys: list_o] :
% 5.44/5.61 ( ( ( size_size_list_o @ Xs2 )
% 5.44/5.61 != ( size_size_list_o @ Ys ) )
% 5.44/5.61 => ( Xs2 != Ys ) ) ).
% 5.44/5.61
% 5.44/5.61 % neq_if_length_neq
% 5.44/5.61 thf(fact_348_neq__if__length__neq,axiom,
% 5.44/5.61 ! [Xs2: list_nat,Ys: list_nat] :
% 5.44/5.61 ( ( ( size_size_list_nat @ Xs2 )
% 5.44/5.61 != ( size_size_list_nat @ Ys ) )
% 5.44/5.61 => ( Xs2 != Ys ) ) ).
% 5.44/5.61
% 5.44/5.61 % neq_if_length_neq
% 5.44/5.61 thf(fact_349_neq__if__length__neq,axiom,
% 5.44/5.61 ! [Xs2: list_int,Ys: list_int] :
% 5.44/5.61 ( ( ( size_size_list_int @ Xs2 )
% 5.44/5.61 != ( size_size_list_int @ Ys ) )
% 5.44/5.61 => ( Xs2 != Ys ) ) ).
% 5.44/5.61
% 5.44/5.61 % neq_if_length_neq
% 5.44/5.61 thf(fact_350_Ex__list__of__length,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ? [Xs3: list_VEBT_VEBT] :
% 5.44/5.61 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.44/5.61 = N2 ) ).
% 5.44/5.61
% 5.44/5.61 % Ex_list_of_length
% 5.44/5.61 thf(fact_351_Ex__list__of__length,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ? [Xs3: list_o] :
% 5.44/5.61 ( ( size_size_list_o @ Xs3 )
% 5.44/5.61 = N2 ) ).
% 5.44/5.61
% 5.44/5.61 % Ex_list_of_length
% 5.44/5.61 thf(fact_352_Ex__list__of__length,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ? [Xs3: list_nat] :
% 5.44/5.61 ( ( size_size_list_nat @ Xs3 )
% 5.44/5.61 = N2 ) ).
% 5.44/5.61
% 5.44/5.61 % Ex_list_of_length
% 5.44/5.61 thf(fact_353_Ex__list__of__length,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ? [Xs3: list_int] :
% 5.44/5.61 ( ( size_size_list_int @ Xs3 )
% 5.44/5.61 = N2 ) ).
% 5.44/5.61
% 5.44/5.61 % Ex_list_of_length
% 5.44/5.61 thf(fact_354_list__update__swap,axiom,
% 5.44/5.61 ! [I2: nat,I3: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT,X6: vEBT_VEBT] :
% 5.44/5.61 ( ( I2 != I3 )
% 5.44/5.61 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I3 @ X6 )
% 5.44/5.61 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I3 @ X6 ) @ I2 @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_swap
% 5.44/5.61 thf(fact_355_nat__1__add__1,axiom,
% 5.44/5.61 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.44/5.61 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_1_add_1
% 5.44/5.61 thf(fact_356_ex__power__ivl1,axiom,
% 5.44/5.61 ! [B: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.44/5.61 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.44/5.61 => ? [N4: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N4 ) @ K )
% 5.44/5.61 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % ex_power_ivl1
% 5.44/5.61 thf(fact_357_ex__power__ivl2,axiom,
% 5.44/5.61 ! [B: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.44/5.61 => ? [N4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( power_power_nat @ B @ N4 ) @ K )
% 5.44/5.61 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % ex_power_ivl2
% 5.44/5.61 thf(fact_358_power__commutes,axiom,
% 5.44/5.61 ! [A: complex,N2: nat] :
% 5.44/5.61 ( ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A )
% 5.44/5.61 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_commutes
% 5.44/5.61 thf(fact_359_power__commutes,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( times_times_real @ ( power_power_real @ A @ N2 ) @ A )
% 5.44/5.61 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_commutes
% 5.44/5.61 thf(fact_360_power__commutes,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
% 5.44/5.61 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_commutes
% 5.44/5.61 thf(fact_361_power__commutes,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( times_times_int @ ( power_power_int @ A @ N2 ) @ A )
% 5.44/5.61 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_commutes
% 5.44/5.61 thf(fact_362_power__mult__distrib,axiom,
% 5.44/5.61 ! [A: complex,B: complex,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N2 )
% 5.44/5.61 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult_distrib
% 5.44/5.61 thf(fact_363_power__mult__distrib,axiom,
% 5.44/5.61 ! [A: real,B: real,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N2 )
% 5.44/5.61 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult_distrib
% 5.44/5.61 thf(fact_364_power__mult__distrib,axiom,
% 5.44/5.61 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
% 5.44/5.61 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult_distrib
% 5.44/5.61 thf(fact_365_power__mult__distrib,axiom,
% 5.44/5.61 ! [A: int,B: int,N2: nat] :
% 5.44/5.61 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N2 )
% 5.44/5.61 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult_distrib
% 5.44/5.61 thf(fact_366_power__commuting__commutes,axiom,
% 5.44/5.61 ! [X: complex,Y: complex,N2: nat] :
% 5.44/5.61 ( ( ( times_times_complex @ X @ Y )
% 5.44/5.61 = ( times_times_complex @ Y @ X ) )
% 5.44/5.61 => ( ( times_times_complex @ ( power_power_complex @ X @ N2 ) @ Y )
% 5.44/5.61 = ( times_times_complex @ Y @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_commuting_commutes
% 5.44/5.61 thf(fact_367_power__commuting__commutes,axiom,
% 5.44/5.61 ! [X: real,Y: real,N2: nat] :
% 5.44/5.61 ( ( ( times_times_real @ X @ Y )
% 5.44/5.61 = ( times_times_real @ Y @ X ) )
% 5.44/5.61 => ( ( times_times_real @ ( power_power_real @ X @ N2 ) @ Y )
% 5.44/5.61 = ( times_times_real @ Y @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_commuting_commutes
% 5.44/5.61 thf(fact_368_power__commuting__commutes,axiom,
% 5.44/5.61 ! [X: nat,Y: nat,N2: nat] :
% 5.44/5.61 ( ( ( times_times_nat @ X @ Y )
% 5.44/5.61 = ( times_times_nat @ Y @ X ) )
% 5.44/5.61 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ Y )
% 5.44/5.61 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_commuting_commutes
% 5.44/5.61 thf(fact_369_power__commuting__commutes,axiom,
% 5.44/5.61 ! [X: int,Y: int,N2: nat] :
% 5.44/5.61 ( ( ( times_times_int @ X @ Y )
% 5.44/5.61 = ( times_times_int @ Y @ X ) )
% 5.44/5.61 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ Y )
% 5.44/5.61 = ( times_times_int @ Y @ ( power_power_int @ X @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_commuting_commutes
% 5.44/5.61 thf(fact_370_power__divide,axiom,
% 5.44/5.61 ! [A: real,B: real,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N2 )
% 5.44/5.61 = ( divide_divide_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_divide
% 5.44/5.61 thf(fact_371_power__divide,axiom,
% 5.44/5.61 ! [A: complex,B: complex,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N2 )
% 5.44/5.61 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_divide
% 5.44/5.61 thf(fact_372_power__mult,axiom,
% 5.44/5.61 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.61 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult
% 5.44/5.61 thf(fact_373_power__mult,axiom,
% 5.44/5.61 ! [A: real,M: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.61 = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult
% 5.44/5.61 thf(fact_374_power__mult,axiom,
% 5.44/5.61 ! [A: int,M: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.61 = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult
% 5.44/5.61 thf(fact_375_power__mult,axiom,
% 5.44/5.61 ! [A: complex,M: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.61 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_mult
% 5.44/5.61 thf(fact_376_length__induct,axiom,
% 5.44/5.61 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.44/5.61 ( ! [Xs3: list_VEBT_VEBT] :
% 5.44/5.61 ( ! [Ys2: list_VEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.44/5.61 => ( P @ Ys2 ) )
% 5.44/5.61 => ( P @ Xs3 ) )
% 5.44/5.61 => ( P @ Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % length_induct
% 5.44/5.61 thf(fact_377_length__induct,axiom,
% 5.44/5.61 ! [P: list_o > $o,Xs2: list_o] :
% 5.44/5.61 ( ! [Xs3: list_o] :
% 5.44/5.61 ( ! [Ys2: list_o] :
% 5.44/5.61 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.44/5.61 => ( P @ Ys2 ) )
% 5.44/5.61 => ( P @ Xs3 ) )
% 5.44/5.61 => ( P @ Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % length_induct
% 5.44/5.61 thf(fact_378_length__induct,axiom,
% 5.44/5.61 ! [P: list_nat > $o,Xs2: list_nat] :
% 5.44/5.61 ( ! [Xs3: list_nat] :
% 5.44/5.61 ( ! [Ys2: list_nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.44/5.61 => ( P @ Ys2 ) )
% 5.44/5.61 => ( P @ Xs3 ) )
% 5.44/5.61 => ( P @ Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % length_induct
% 5.44/5.61 thf(fact_379_length__induct,axiom,
% 5.44/5.61 ! [P: list_int > $o,Xs2: list_int] :
% 5.44/5.61 ( ! [Xs3: list_int] :
% 5.44/5.61 ( ! [Ys2: list_int] :
% 5.44/5.61 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.44/5.61 => ( P @ Ys2 ) )
% 5.44/5.61 => ( P @ Xs3 ) )
% 5.44/5.61 => ( P @ Xs2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % length_induct
% 5.44/5.61 thf(fact_380_power__add,axiom,
% 5.44/5.61 ! [A: complex,M: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.61 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add
% 5.44/5.61 thf(fact_381_power__add,axiom,
% 5.44/5.61 ! [A: real,M: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.61 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add
% 5.44/5.61 thf(fact_382_power__add,axiom,
% 5.44/5.61 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.61 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add
% 5.44/5.61 thf(fact_383_power__add,axiom,
% 5.44/5.61 ! [A: int,M: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.61 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_add
% 5.44/5.61 thf(fact_384_nth__equalityI,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.44/5.61 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.44/5.61 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.44/5.61 => ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 5.44/5.61 = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 5.44/5.61 => ( Xs2 = Ys ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_equalityI
% 5.44/5.61 thf(fact_385_nth__equalityI,axiom,
% 5.44/5.61 ! [Xs2: list_o,Ys: list_o] :
% 5.44/5.61 ( ( ( size_size_list_o @ Xs2 )
% 5.44/5.61 = ( size_size_list_o @ Ys ) )
% 5.44/5.61 => ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( ( nth_o @ Xs2 @ I4 )
% 5.44/5.61 = ( nth_o @ Ys @ I4 ) ) )
% 5.44/5.61 => ( Xs2 = Ys ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_equalityI
% 5.44/5.61 thf(fact_386_nth__equalityI,axiom,
% 5.44/5.61 ! [Xs2: list_nat,Ys: list_nat] :
% 5.44/5.61 ( ( ( size_size_list_nat @ Xs2 )
% 5.44/5.61 = ( size_size_list_nat @ Ys ) )
% 5.44/5.61 => ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( ( nth_nat @ Xs2 @ I4 )
% 5.44/5.61 = ( nth_nat @ Ys @ I4 ) ) )
% 5.44/5.61 => ( Xs2 = Ys ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_equalityI
% 5.44/5.61 thf(fact_387_nth__equalityI,axiom,
% 5.44/5.61 ! [Xs2: list_int,Ys: list_int] :
% 5.44/5.61 ( ( ( size_size_list_int @ Xs2 )
% 5.44/5.61 = ( size_size_list_int @ Ys ) )
% 5.44/5.61 => ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( ( nth_int @ Xs2 @ I4 )
% 5.44/5.61 = ( nth_int @ Ys @ I4 ) ) )
% 5.44/5.61 => ( Xs2 = Ys ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_equalityI
% 5.44/5.61 thf(fact_388_Skolem__list__nth,axiom,
% 5.44/5.61 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.44/5.61 ( ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ K )
% 5.44/5.61 => ? [X4: vEBT_VEBT] : ( P @ I5 @ X4 ) ) )
% 5.44/5.61 = ( ? [Xs: list_VEBT_VEBT] :
% 5.44/5.61 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.44/5.61 = K )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ K )
% 5.44/5.61 => ( P @ I5 @ ( nth_VEBT_VEBT @ Xs @ I5 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Skolem_list_nth
% 5.44/5.61 thf(fact_389_Skolem__list__nth,axiom,
% 5.44/5.61 ! [K: nat,P: nat > $o > $o] :
% 5.44/5.61 ( ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ K )
% 5.44/5.61 => ? [X4: $o] : ( P @ I5 @ X4 ) ) )
% 5.44/5.61 = ( ? [Xs: list_o] :
% 5.44/5.61 ( ( ( size_size_list_o @ Xs )
% 5.44/5.61 = K )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ K )
% 5.44/5.61 => ( P @ I5 @ ( nth_o @ Xs @ I5 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Skolem_list_nth
% 5.44/5.61 thf(fact_390_Skolem__list__nth,axiom,
% 5.44/5.61 ! [K: nat,P: nat > nat > $o] :
% 5.44/5.61 ( ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ K )
% 5.44/5.61 => ? [X4: nat] : ( P @ I5 @ X4 ) ) )
% 5.44/5.61 = ( ? [Xs: list_nat] :
% 5.44/5.61 ( ( ( size_size_list_nat @ Xs )
% 5.44/5.61 = K )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ K )
% 5.44/5.61 => ( P @ I5 @ ( nth_nat @ Xs @ I5 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Skolem_list_nth
% 5.44/5.61 thf(fact_391_Skolem__list__nth,axiom,
% 5.44/5.61 ! [K: nat,P: nat > int > $o] :
% 5.44/5.61 ( ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ K )
% 5.44/5.61 => ? [X4: int] : ( P @ I5 @ X4 ) ) )
% 5.44/5.61 = ( ? [Xs: list_int] :
% 5.44/5.61 ( ( ( size_size_list_int @ Xs )
% 5.44/5.61 = K )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ K )
% 5.44/5.61 => ( P @ I5 @ ( nth_int @ Xs @ I5 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Skolem_list_nth
% 5.44/5.61 thf(fact_392_list__eq__iff__nth__eq,axiom,
% 5.44/5.61 ( ( ^ [Y4: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y4 = Z2 ) )
% 5.44/5.61 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.44/5.61 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.44/5.61 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.44/5.61 => ( ( nth_VEBT_VEBT @ Xs @ I5 )
% 5.44/5.61 = ( nth_VEBT_VEBT @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_eq_iff_nth_eq
% 5.44/5.61 thf(fact_393_list__eq__iff__nth__eq,axiom,
% 5.44/5.61 ( ( ^ [Y4: list_o,Z2: list_o] : ( Y4 = Z2 ) )
% 5.44/5.61 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.44/5.61 ( ( ( size_size_list_o @ Xs )
% 5.44/5.61 = ( size_size_list_o @ Ys3 ) )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 5.44/5.61 => ( ( nth_o @ Xs @ I5 )
% 5.44/5.61 = ( nth_o @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_eq_iff_nth_eq
% 5.44/5.61 thf(fact_394_list__eq__iff__nth__eq,axiom,
% 5.44/5.61 ( ( ^ [Y4: list_nat,Z2: list_nat] : ( Y4 = Z2 ) )
% 5.44/5.61 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.44/5.61 ( ( ( size_size_list_nat @ Xs )
% 5.44/5.61 = ( size_size_list_nat @ Ys3 ) )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 5.44/5.61 => ( ( nth_nat @ Xs @ I5 )
% 5.44/5.61 = ( nth_nat @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_eq_iff_nth_eq
% 5.44/5.61 thf(fact_395_list__eq__iff__nth__eq,axiom,
% 5.44/5.61 ( ( ^ [Y4: list_int,Z2: list_int] : ( Y4 = Z2 ) )
% 5.44/5.61 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.44/5.61 ( ( ( size_size_list_int @ Xs )
% 5.44/5.61 = ( size_size_list_int @ Ys3 ) )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 5.44/5.61 => ( ( nth_int @ Xs @ I5 )
% 5.44/5.61 = ( nth_int @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_eq_iff_nth_eq
% 5.44/5.61 thf(fact_396_nth__mem,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_real] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.44/5.61 => ( member_real @ ( nth_real @ Xs2 @ N2 ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_mem
% 5.44/5.61 thf(fact_397_nth__mem,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_complex] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.44/5.61 => ( member_complex @ ( nth_complex @ Xs2 @ N2 ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_mem
% 5.44/5.61 thf(fact_398_nth__mem,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_P6011104703257516679at_nat] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.44/5.61 => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N2 ) @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_mem
% 5.44/5.61 thf(fact_399_nth__mem,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_VEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_mem
% 5.44/5.61 thf(fact_400_nth__mem,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_o] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( member_o @ ( nth_o @ Xs2 @ N2 ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_mem
% 5.44/5.61 thf(fact_401_nth__mem,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_nat] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( member_nat @ ( nth_nat @ Xs2 @ N2 ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_mem
% 5.44/5.61 thf(fact_402_nth__mem,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_int] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( member_int @ ( nth_int @ Xs2 @ N2 ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_mem
% 5.44/5.61 thf(fact_403_list__ball__nth,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_ball_nth
% 5.44/5.61 thf(fact_404_list__ball__nth,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_o,P: $o > $o] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( ! [X5: $o] :
% 5.44/5.61 ( ( member_o @ X5 @ ( set_o2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( P @ ( nth_o @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_ball_nth
% 5.44/5.61 thf(fact_405_list__ball__nth,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_nat,P: nat > $o] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( ! [X5: nat] :
% 5.44/5.61 ( ( member_nat @ X5 @ ( set_nat2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( P @ ( nth_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_ball_nth
% 5.44/5.61 thf(fact_406_list__ball__nth,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_int,P: int > $o] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( ! [X5: int] :
% 5.44/5.61 ( ( member_int @ X5 @ ( set_int2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X5 ) )
% 5.44/5.61 => ( P @ ( nth_int @ Xs2 @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_ball_nth
% 5.44/5.61 thf(fact_407_in__set__conv__nth,axiom,
% 5.44/5.61 ! [X: real,Xs2: list_real] :
% 5.44/5.61 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.44/5.61 = ( ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_real @ Xs2 ) )
% 5.44/5.61 & ( ( nth_real @ Xs2 @ I5 )
% 5.44/5.61 = X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % in_set_conv_nth
% 5.44/5.61 thf(fact_408_in__set__conv__nth,axiom,
% 5.44/5.61 ! [X: complex,Xs2: list_complex] :
% 5.44/5.61 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.44/5.61 = ( ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.44/5.61 & ( ( nth_complex @ Xs2 @ I5 )
% 5.44/5.61 = X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % in_set_conv_nth
% 5.44/5.61 thf(fact_409_in__set__conv__nth,axiom,
% 5.44/5.61 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.44/5.61 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.44/5.61 = ( ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.44/5.61 & ( ( nth_Pr7617993195940197384at_nat @ Xs2 @ I5 )
% 5.44/5.61 = X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % in_set_conv_nth
% 5.44/5.61 thf(fact_410_in__set__conv__nth,axiom,
% 5.44/5.61 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.61 = ( ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 & ( ( nth_VEBT_VEBT @ Xs2 @ I5 )
% 5.44/5.61 = X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % in_set_conv_nth
% 5.44/5.61 thf(fact_411_in__set__conv__nth,axiom,
% 5.44/5.61 ! [X: $o,Xs2: list_o] :
% 5.44/5.61 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.44/5.61 = ( ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 & ( ( nth_o @ Xs2 @ I5 )
% 5.44/5.61 = X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % in_set_conv_nth
% 5.44/5.61 thf(fact_412_in__set__conv__nth,axiom,
% 5.44/5.61 ! [X: nat,Xs2: list_nat] :
% 5.44/5.61 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.44/5.61 = ( ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 & ( ( nth_nat @ Xs2 @ I5 )
% 5.44/5.61 = X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % in_set_conv_nth
% 5.44/5.61 thf(fact_413_in__set__conv__nth,axiom,
% 5.44/5.61 ! [X: int,Xs2: list_int] :
% 5.44/5.61 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.44/5.61 = ( ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 & ( ( nth_int @ Xs2 @ I5 )
% 5.44/5.61 = X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % in_set_conv_nth
% 5.44/5.61 thf(fact_414_all__nth__imp__all__set,axiom,
% 5.44/5.61 ! [Xs2: list_real,P: real > $o,X: real] :
% 5.44/5.61 ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_real @ Xs2 @ I4 ) ) )
% 5.44/5.61 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_nth_imp_all_set
% 5.44/5.61 thf(fact_415_all__nth__imp__all__set,axiom,
% 5.44/5.61 ! [Xs2: list_complex,P: complex > $o,X: complex] :
% 5.44/5.61 ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_complex @ Xs2 @ I4 ) ) )
% 5.44/5.61 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_nth_imp_all_set
% 5.44/5.61 thf(fact_416_all__nth__imp__all__set,axiom,
% 5.44/5.61 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.44/5.61 ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I4 ) ) )
% 5.44/5.61 => ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.44/5.61 => ( P @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_nth_imp_all_set
% 5.44/5.61 thf(fact_417_all__nth__imp__all__set,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.44/5.61 ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) )
% 5.44/5.61 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_nth_imp_all_set
% 5.44/5.61 thf(fact_418_all__nth__imp__all__set,axiom,
% 5.44/5.61 ! [Xs2: list_o,P: $o > $o,X: $o] :
% 5.44/5.61 ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_o @ Xs2 @ I4 ) ) )
% 5.44/5.61 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_nth_imp_all_set
% 5.44/5.61 thf(fact_419_all__nth__imp__all__set,axiom,
% 5.44/5.61 ! [Xs2: list_nat,P: nat > $o,X: nat] :
% 5.44/5.61 ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_nat @ Xs2 @ I4 ) ) )
% 5.44/5.61 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_nth_imp_all_set
% 5.44/5.61 thf(fact_420_all__nth__imp__all__set,axiom,
% 5.44/5.61 ! [Xs2: list_int,P: int > $o,X: int] :
% 5.44/5.61 ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_int @ Xs2 @ I4 ) ) )
% 5.44/5.61 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_nth_imp_all_set
% 5.44/5.61 thf(fact_421_all__set__conv__all__nth,axiom,
% 5.44/5.61 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.44/5.61 ( ( ! [X2: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X2 ) ) )
% 5.44/5.61 = ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I5 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_set_conv_all_nth
% 5.44/5.61 thf(fact_422_all__set__conv__all__nth,axiom,
% 5.44/5.61 ! [Xs2: list_o,P: $o > $o] :
% 5.44/5.61 ( ( ! [X2: $o] :
% 5.44/5.61 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X2 ) ) )
% 5.44/5.61 = ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_o @ Xs2 @ I5 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_set_conv_all_nth
% 5.44/5.61 thf(fact_423_all__set__conv__all__nth,axiom,
% 5.44/5.61 ! [Xs2: list_nat,P: nat > $o] :
% 5.44/5.61 ( ( ! [X2: nat] :
% 5.44/5.61 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X2 ) ) )
% 5.44/5.61 = ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_nat @ Xs2 @ I5 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_set_conv_all_nth
% 5.44/5.61 thf(fact_424_all__set__conv__all__nth,axiom,
% 5.44/5.61 ! [Xs2: list_int,P: int > $o] :
% 5.44/5.61 ( ( ! [X2: int] :
% 5.44/5.61 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.44/5.61 => ( P @ X2 ) ) )
% 5.44/5.61 = ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( P @ ( nth_int @ Xs2 @ I5 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % all_set_conv_all_nth
% 5.44/5.61 thf(fact_425_set__update__memI,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_real,X: real] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.44/5.61 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_memI
% 5.44/5.61 thf(fact_426_set__update__memI,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_complex,X: complex] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.44/5.61 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_memI
% 5.44/5.61 thf(fact_427_set__update__memI,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.44/5.61 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_memI
% 5.44/5.61 thf(fact_428_set__update__memI,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_memI
% 5.44/5.61 thf(fact_429_set__update__memI,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_o,X: $o] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_memI
% 5.44/5.61 thf(fact_430_set__update__memI,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_nat,X: nat] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_memI
% 5.44/5.61 thf(fact_431_set__update__memI,axiom,
% 5.44/5.61 ! [N2: nat,Xs2: list_int,X: int] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_update_memI
% 5.44/5.61 thf(fact_432_nth__list__update,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( ( ( I2 = J )
% 5.44/5.61 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = X ) )
% 5.44/5.61 & ( ( I2 != J )
% 5.44/5.61 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update
% 5.44/5.61 thf(fact_433_nth__list__update,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_o,X: $o,J: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = ( ( ( I2 = J )
% 5.44/5.61 => X )
% 5.44/5.61 & ( ( I2 != J )
% 5.44/5.61 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update
% 5.44/5.61 thf(fact_434_nth__list__update,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_nat,J: nat,X: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( ( ( I2 = J )
% 5.44/5.61 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = X ) )
% 5.44/5.61 & ( ( I2 != J )
% 5.44/5.61 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update
% 5.44/5.61 thf(fact_435_nth__list__update,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_int,J: nat,X: int] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( ( ( I2 = J )
% 5.44/5.61 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = X ) )
% 5.44/5.61 & ( ( I2 != J )
% 5.44/5.61 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.44/5.61 = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nth_list_update
% 5.44/5.61 thf(fact_436_list__update__same__conv,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.44/5.61 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.44/5.61 = Xs2 )
% 5.44/5.61 = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.44/5.61 = X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_same_conv
% 5.44/5.61 thf(fact_437_list__update__same__conv,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.44/5.61 => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.44/5.61 = Xs2 )
% 5.44/5.61 = ( ( nth_o @ Xs2 @ I2 )
% 5.44/5.61 = X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_same_conv
% 5.44/5.61 thf(fact_438_list__update__same__conv,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.44/5.61 => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.44/5.61 = Xs2 )
% 5.44/5.61 = ( ( nth_nat @ Xs2 @ I2 )
% 5.44/5.61 = X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_same_conv
% 5.44/5.61 thf(fact_439_list__update__same__conv,axiom,
% 5.44/5.61 ! [I2: nat,Xs2: list_int,X: int] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.44/5.61 => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.44/5.61 = Xs2 )
% 5.44/5.61 = ( ( nth_int @ Xs2 @ I2 )
% 5.44/5.61 = X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % list_update_same_conv
% 5.44/5.61 thf(fact_440_power4__eq__xxxx,axiom,
% 5.44/5.61 ! [X: complex] :
% 5.44/5.61 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % power4_eq_xxxx
% 5.44/5.61 thf(fact_441_power4__eq__xxxx,axiom,
% 5.44/5.61 ! [X: real] :
% 5.44/5.61 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % power4_eq_xxxx
% 5.44/5.61 thf(fact_442_power4__eq__xxxx,axiom,
% 5.44/5.61 ! [X: nat] :
% 5.44/5.61 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % power4_eq_xxxx
% 5.44/5.61 thf(fact_443_power4__eq__xxxx,axiom,
% 5.44/5.61 ! [X: int] :
% 5.44/5.61 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % power4_eq_xxxx
% 5.44/5.61 thf(fact_444_power2__eq__square,axiom,
% 5.44/5.61 ! [A: complex] :
% 5.44/5.61 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( times_times_complex @ A @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_eq_square
% 5.44/5.61 thf(fact_445_power2__eq__square,axiom,
% 5.44/5.61 ! [A: real] :
% 5.44/5.61 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( times_times_real @ A @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_eq_square
% 5.44/5.61 thf(fact_446_power2__eq__square,axiom,
% 5.44/5.61 ! [A: nat] :
% 5.44/5.61 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( times_times_nat @ A @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_eq_square
% 5.44/5.61 thf(fact_447_power2__eq__square,axiom,
% 5.44/5.61 ! [A: int] :
% 5.44/5.61 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( times_times_int @ A @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_eq_square
% 5.44/5.61 thf(fact_448_power__even__eq,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_even_eq
% 5.44/5.61 thf(fact_449_power__even__eq,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_even_eq
% 5.44/5.61 thf(fact_450_power__even__eq,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_even_eq
% 5.44/5.61 thf(fact_451_power__even__eq,axiom,
% 5.44/5.61 ! [A: complex,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_even_eq
% 5.44/5.61 thf(fact_452_less__exp,axiom,
% 5.44/5.61 ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_exp
% 5.44/5.61 thf(fact_453_self__le__ge2__pow,axiom,
% 5.44/5.61 ! [K: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % self_le_ge2_pow
% 5.44/5.61 thf(fact_454_power2__nat__le__eq__le,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_nat_le_eq_le
% 5.44/5.61 thf(fact_455_power2__nat__le__imp__le,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % power2_nat_le_imp_le
% 5.44/5.61 thf(fact_456__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_061_A_Iif_Ax_A_061_Ami_Athen_Athe_A_Ivebt__mint_Asummary_J_A_K_A2_A_094_A_Ideg_Adiv_A2_J_A_L_Athe_A_Ivebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__mint_Asummary_J_J_J_Aelse_Ax_J_092_060close_062,axiom,
% 5.44/5.61 ( ( ( xa = mi )
% 5.44/5.61 => ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) )
% 5.44/5.61 & ( ( xa != mi )
% 5.44/5.61 => ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = xa ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>summin * 2 ^ n + lx = (if x = mi then the (vebt_mint summary) * 2 ^ (deg div 2) + the (vebt_mint (treeList ! the (vebt_mint summary))) else x)\<close>
% 5.44/5.61 thf(fact_457_semiring__norm_I69_J,axiom,
% 5.44/5.61 ! [M: num] :
% 5.44/5.61 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(69)
% 5.44/5.61 thf(fact_458_semiring__norm_I76_J,axiom,
% 5.44/5.61 ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(76)
% 5.44/5.61 thf(fact_459_semiring__norm_I2_J,axiom,
% 5.44/5.61 ( ( plus_plus_num @ one @ one )
% 5.44/5.61 = ( bit0 @ one ) ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(2)
% 5.44/5.61 thf(fact_460_post__member__pre__member,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 5.44/5.61 => ( ( vEBT_vebt_member @ T @ Y )
% 5.44/5.61 | ( X = Y ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % post_member_pre_member
% 5.44/5.61 thf(fact_461__092_060open_062vebt__member_Asummary_A_Ihigh_Ama_An_J_092_060close_062,axiom,
% 5.44/5.61 vEBT_vebt_member @ summary @ ( vEBT_VEBT_high @ ma @ na ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>vebt_member summary (high ma n)\<close>
% 5.44/5.61 thf(fact_462__092_060open_062vebt__member_A_ItreeList_A_B_Asummin_J_Alx_092_060close_062,axiom,
% 5.44/5.61 vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ summin ) @ lx ).
% 5.44/5.61
% 5.44/5.61 % \<open>vebt_member (treeList ! summin) lx\<close>
% 5.44/5.61 thf(fact_463_member__bound,axiom,
% 5.44/5.61 ! [Tree: vEBT_VEBT,X: nat,N2: nat] :
% 5.44/5.61 ( ( vEBT_vebt_member @ Tree @ X )
% 5.44/5.61 => ( ( vEBT_invar_vebt @ Tree @ N2 )
% 5.44/5.61 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % member_bound
% 5.44/5.61 thf(fact_464_dsimp,axiom,
% 5.44/5.61 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ xa @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.44/5.61 = ( vEBT_Node
% 5.44/5.61 @ ( some_P7363390416028606310at_nat
% 5.44/5.61 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 @ ( if_nat
% 5.44/5.61 @ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.44/5.61 = ma )
% 5.44/5.61 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.44/5.61 @ ma ) ) )
% 5.44/5.61 @ deg
% 5.44/5.61 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
% 5.44/5.61 @ summary ) ) ).
% 5.44/5.61
% 5.44/5.61 % dsimp
% 5.44/5.61 thf(fact_465_div__exp__eq,axiom,
% 5.44/5.61 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_exp_eq
% 5.44/5.61 thf(fact_466_div__exp__eq,axiom,
% 5.44/5.61 ! [A: int,M: nat,N2: nat] :
% 5.44/5.61 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_exp_eq
% 5.44/5.61 thf(fact_467_div__exp__eq,axiom,
% 5.44/5.61 ! [A: code_integer,M: nat,N2: nat] :
% 5.44/5.61 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.61 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_exp_eq
% 5.44/5.61 thf(fact_468_field__less__half__sum,axiom,
% 5.44/5.61 ! [X: real,Y: real] :
% 5.44/5.61 ( ( ord_less_real @ X @ Y )
% 5.44/5.61 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % field_less_half_sum
% 5.44/5.61 thf(fact_469_semiring__norm_I68_J,axiom,
% 5.44/5.61 ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(68)
% 5.44/5.61 thf(fact_470_min__Null__member,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,X: nat] :
% 5.44/5.61 ( ( vEBT_VEBT_minNull @ T )
% 5.44/5.61 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % min_Null_member
% 5.44/5.61 thf(fact_471_both__member__options__equiv__member,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.44/5.61 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % both_member_options_equiv_member
% 5.44/5.61 thf(fact_472_valid__member__both__member__options,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.44/5.61 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % valid_member_both_member_options
% 5.44/5.61 thf(fact_473_semiring__norm_I87_J,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ( bit0 @ M )
% 5.44/5.61 = ( bit0 @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(87)
% 5.44/5.61 thf(fact_474_real__divide__square__eq,axiom,
% 5.44/5.61 ! [R: real,A: real] :
% 5.44/5.61 ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 5.44/5.61 = ( divide_divide_real @ A @ R ) ) ).
% 5.44/5.61
% 5.44/5.61 % real_divide_square_eq
% 5.44/5.61 thf(fact_475_mi__eq__ma__no__ch,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.44/5.61 => ( ( Mi = Ma )
% 5.44/5.61 => ( ! [X3: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 5.44/5.61 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mi_eq_ma_no_ch
% 5.44/5.61 thf(fact_476_semiring__norm_I83_J,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( one
% 5.44/5.61 != ( bit0 @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(83)
% 5.44/5.61 thf(fact_477_semiring__norm_I85_J,axiom,
% 5.44/5.61 ! [M: num] :
% 5.44/5.61 ( ( bit0 @ M )
% 5.44/5.61 != one ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(85)
% 5.44/5.61 thf(fact_478_bits__div__by__1,axiom,
% 5.44/5.61 ! [A: nat] :
% 5.44/5.61 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % bits_div_by_1
% 5.44/5.61 thf(fact_479_bits__div__by__1,axiom,
% 5.44/5.61 ! [A: int] :
% 5.44/5.61 ( ( divide_divide_int @ A @ one_one_int )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % bits_div_by_1
% 5.44/5.61 thf(fact_480_bits__div__by__1,axiom,
% 5.44/5.61 ! [A: code_integer] :
% 5.44/5.61 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % bits_div_by_1
% 5.44/5.61 thf(fact_481_insert__simp__mima,axiom,
% 5.44/5.61 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ( X = Mi )
% 5.44/5.61 | ( X = Ma ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % insert_simp_mima
% 5.44/5.61 thf(fact_482_member__correct,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( vEBT_vebt_member @ T @ X )
% 5.44/5.61 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % member_correct
% 5.44/5.61 thf(fact_483_semiring__norm_I6_J,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(6)
% 5.44/5.61 thf(fact_484_semiring__norm_I13_J,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(13)
% 5.44/5.61 thf(fact_485_semiring__norm_I11_J,axiom,
% 5.44/5.61 ! [M: num] :
% 5.44/5.61 ( ( times_times_num @ M @ one )
% 5.44/5.61 = M ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(11)
% 5.44/5.61 thf(fact_486_semiring__norm_I12_J,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( times_times_num @ one @ N2 )
% 5.44/5.61 = N2 ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(12)
% 5.44/5.61 thf(fact_487_delt__out__of__range,axiom,
% 5.44/5.61 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ( ord_less_nat @ X @ Mi )
% 5.44/5.61 | ( ord_less_nat @ Ma @ X ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % delt_out_of_range
% 5.44/5.61 thf(fact_488_semiring__norm_I78_J,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(78)
% 5.44/5.61 thf(fact_489_semiring__norm_I71_J,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(71)
% 5.44/5.61 thf(fact_490_semiring__norm_I75_J,axiom,
% 5.44/5.61 ! [M: num] :
% 5.44/5.61 ~ ( ord_less_num @ M @ one ) ).
% 5.44/5.61
% 5.44/5.61 % semiring_norm(75)
% 5.44/5.61 thf(fact_491_mi__ma__2__deg,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 5.44/5.61 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.44/5.61 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mi_ma_2_deg
% 5.44/5.61 thf(fact_492_summaxma,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.44/5.61 => ( ( Mi != Ma )
% 5.44/5.61 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.44/5.61 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % summaxma
% 5.44/5.61 thf(fact_493_both__member__options__from__complete__tree__to__child,axiom,
% 5.44/5.61 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.44/5.61 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.61 | ( X = Mi )
% 5.44/5.61 | ( X = Ma ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % both_member_options_from_complete_tree_to_child
% 5.44/5.61 thf(fact_494__C10_C,axiom,
% 5.44/5.61 vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ deg ).
% 5.44/5.61
% 5.44/5.61 % "10"
% 5.44/5.61 thf(fact_495_member__inv,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.44/5.61 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 & ( ( X = Mi )
% 5.44/5.61 | ( X = Ma )
% 5.44/5.61 | ( ( ord_less_nat @ X @ Ma )
% 5.44/5.61 & ( ord_less_nat @ Mi @ X )
% 5.44/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.61 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % member_inv
% 5.44/5.61 thf(fact_496_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.44/5.61 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.44/5.61 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % both_member_options_from_chilf_to_complete_tree
% 5.44/5.61 thf(fact_497_del__x__not__mi__newnode__not__nil,axiom,
% 5.44/5.61 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ( ord_less_nat @ Mi @ X )
% 5.44/5.61 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.44/5.61 => ( ( Mi != Ma )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = H2 )
% 5.44/5.61 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = L2 )
% 5.44/5.61 => ( ( Newnode
% 5.44/5.61 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.61 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.44/5.61 => ( ( Newlist
% 5.44/5.61 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.44/5.61 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.61 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % del_x_not_mi_newnode_not_nil
% 5.44/5.61 thf(fact_498_del__x__mi__lets__in__not__minNull,axiom,
% 5.44/5.61 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.44/5.61 ( ( ( X = Mi )
% 5.44/5.61 & ( ord_less_nat @ X @ Ma ) )
% 5.44/5.61 => ( ( Mi != Ma )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = H2 )
% 5.44/5.61 => ( ( Xn
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.44/5.61 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = L2 )
% 5.44/5.61 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.61 => ( ( Newnode
% 5.44/5.61 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.61 => ( ( Newlist
% 5.44/5.61 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.44/5.61 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.44/5.61 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % del_x_mi_lets_in_not_minNull
% 5.44/5.61 thf(fact_499_xnin,axiom,
% 5.44/5.61 vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) ).
% 5.44/5.61
% 5.44/5.61 % xnin
% 5.44/5.61 thf(fact_500__092_060open_062Some_Asummin_A_061_Avebt__mint_Asummary_092_060close_062,axiom,
% 5.44/5.61 ( ( some_nat @ summin )
% 5.44/5.61 = ( vEBT_vebt_mint @ summary ) ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>Some summin = vebt_mint summary\<close>
% 5.44/5.61 thf(fact_501__092_060open_062Some_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_092_060close_062,axiom,
% 5.44/5.61 ( ( some_nat @ lx )
% 5.44/5.61 = ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ summin ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>Some lx = vebt_mint (treeList ! summin)\<close>
% 5.44/5.61 thf(fact_502_complete__real,axiom,
% 5.44/5.61 ! [S: set_real] :
% 5.44/5.61 ( ? [X3: real] : ( member_real @ X3 @ S )
% 5.44/5.61 => ( ? [Z3: real] :
% 5.44/5.61 ! [X5: real] :
% 5.44/5.61 ( ( member_real @ X5 @ S )
% 5.44/5.61 => ( ord_less_eq_real @ X5 @ Z3 ) )
% 5.44/5.61 => ? [Y5: real] :
% 5.44/5.61 ( ! [X3: real] :
% 5.44/5.61 ( ( member_real @ X3 @ S )
% 5.44/5.61 => ( ord_less_eq_real @ X3 @ Y5 ) )
% 5.44/5.61 & ! [Z3: real] :
% 5.44/5.61 ( ! [X5: real] :
% 5.44/5.61 ( ( member_real @ X5 @ S )
% 5.44/5.61 => ( ord_less_eq_real @ X5 @ Z3 ) )
% 5.44/5.61 => ( ord_less_eq_real @ Y5 @ Z3 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % complete_real
% 5.44/5.61 thf(fact_503_real__arch__pow,axiom,
% 5.44/5.61 ! [X: real,Y: real] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.61 => ? [N4: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N4 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % real_arch_pow
% 5.44/5.61 thf(fact_504_less__eq__real__def,axiom,
% 5.44/5.61 ( ord_less_eq_real
% 5.44/5.61 = ( ^ [X2: real,Y3: real] :
% 5.44/5.61 ( ( ord_less_real @ X2 @ Y3 )
% 5.44/5.61 | ( X2 = Y3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_eq_real_def
% 5.44/5.61 thf(fact_505_two__realpow__ge__one,axiom,
% 5.44/5.61 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % two_realpow_ge_one
% 5.44/5.61 thf(fact_506_left__add__mult__distrib,axiom,
% 5.44/5.61 ! [I2: nat,U: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_add_mult_distrib
% 5.44/5.61 thf(fact_507_field__sum__of__halves,axiom,
% 5.44/5.61 ! [X: real] :
% 5.44/5.61 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.61 = X ) ).
% 5.44/5.61
% 5.44/5.61 % field_sum_of_halves
% 5.44/5.61 thf(fact_508_invar__vebt_Ointros_I4_J,axiom,
% 5.44/5.61 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.44/5.61 ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.44/5.61 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.44/5.61 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.44/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ( M = N2 )
% 5.44/5.61 => ( ( Deg
% 5.44/5.61 = ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.61 => ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X4 ) )
% 5.44/5.61 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.44/5.61 => ( ( ( Mi = Ma )
% 5.44/5.61 => ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.44/5.61 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.44/5.61 => ( ( ( Mi != Ma )
% 5.44/5.61 => ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 5.44/5.61 = I4 )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 5.44/5.61 & ! [X5: nat] :
% 5.44/5.61 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 5.44/5.61 = I4 )
% 5.44/5.61 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ Mi @ X5 )
% 5.44/5.61 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % invar_vebt.intros(4)
% 5.44/5.61 thf(fact_509_nested__mint,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,Va: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 5.44/5.61 => ( ( N2
% 5.44/5.61 = ( suc @ ( suc @ Va ) ) )
% 5.44/5.61 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.44/5.61 => ( ( Ma != Mi )
% 5.44/5.61 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nested_mint
% 5.44/5.61 thf(fact_510_insert__simp__norm,axiom,
% 5.44/5.61 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.61 => ( ( ord_less_nat @ Mi @ X )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( X != Ma )
% 5.44/5.61 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % insert_simp_norm
% 5.44/5.61 thf(fact_511_insert__simp__excp,axiom,
% 5.44/5.61 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.61 => ( ( ord_less_nat @ X @ Mi )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( X != Ma )
% 5.44/5.61 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % insert_simp_excp
% 5.44/5.61 thf(fact_512_del__single__cont,axiom,
% 5.44/5.61 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ( X = Mi )
% 5.44/5.61 & ( X = Ma ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % del_single_cont
% 5.44/5.61 thf(fact_513_nat__mult__eq__1__iff,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ( times_times_nat @ M @ N2 )
% 5.44/5.61 = one_one_nat )
% 5.44/5.61 = ( ( M = one_one_nat )
% 5.44/5.61 & ( N2 = one_one_nat ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_mult_eq_1_iff
% 5.44/5.61 thf(fact_514_nat__1__eq__mult__iff,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( one_one_nat
% 5.44/5.61 = ( times_times_nat @ M @ N2 ) )
% 5.44/5.61 = ( ( M = one_one_nat )
% 5.44/5.61 & ( N2 = one_one_nat ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_1_eq_mult_iff
% 5.44/5.61 thf(fact_515_nat__add__left__cancel__le,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_add_left_cancel_le
% 5.44/5.61 thf(fact_516_nat__add__left__cancel__less,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.44/5.61 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_add_left_cancel_less
% 5.44/5.61 thf(fact_517_enat__ord__number_I1_J,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % enat_ord_number(1)
% 5.44/5.61 thf(fact_518_enat__ord__number_I2_J,axiom,
% 5.44/5.61 ! [M: num,N2: num] :
% 5.44/5.61 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.44/5.61 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % enat_ord_number(2)
% 5.44/5.61 thf(fact_519_even__odd__cases,axiom,
% 5.44/5.61 ! [X: nat] :
% 5.44/5.61 ( ! [N4: nat] :
% 5.44/5.61 ( X
% 5.44/5.61 != ( plus_plus_nat @ N4 @ N4 ) )
% 5.44/5.61 => ~ ! [N4: nat] :
% 5.44/5.61 ( X
% 5.44/5.61 != ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % even_odd_cases
% 5.44/5.61 thf(fact_520_deg__SUcn__Node,axiom,
% 5.44/5.61 ! [Tree: vEBT_VEBT,N2: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N2 ) ) )
% 5.44/5.61 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.44/5.61 ( Tree
% 5.44/5.61 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N2 ) ) @ TreeList3 @ S2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % deg_SUcn_Node
% 5.44/5.61 thf(fact_521_maxbmo,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,X: nat] :
% 5.44/5.61 ( ( ( vEBT_vebt_maxt @ T )
% 5.44/5.61 = ( some_nat @ X ) )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % maxbmo
% 5.44/5.61 thf(fact_522_power__shift,axiom,
% 5.44/5.61 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.61 ( ( ( power_power_nat @ X @ Y )
% 5.44/5.61 = Z )
% 5.44/5.61 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.44/5.61 = ( some_nat @ Z ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_shift
% 5.44/5.61 thf(fact_523__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062summin_O_ASome_Asummin_A_061_Avebt__mint_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.44/5.61 ~ ! [Summin: nat] :
% 5.44/5.61 ( ( some_nat @ Summin )
% 5.44/5.61 != ( vEBT_vebt_mint @ summary ) ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>\<And>thesis. (\<And>summin. Some summin = vebt_mint summary \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.44/5.61 thf(fact_524_mint__member,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,Maxi: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_mint @ T )
% 5.44/5.61 = ( some_nat @ Maxi ) )
% 5.44/5.61 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mint_member
% 5.44/5.61 thf(fact_525_maxt__member,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,Maxi: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_maxt @ T )
% 5.44/5.61 = ( some_nat @ Maxi ) )
% 5.44/5.61 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % maxt_member
% 5.44/5.61 thf(fact_526__C8_C,axiom,
% 5.44/5.61 ( ( suc @ na )
% 5.44/5.61 = m ) ).
% 5.44/5.61
% 5.44/5.61 % "8"
% 5.44/5.61 thf(fact_527_old_Onat_Oinject,axiom,
% 5.44/5.61 ! [Nat: nat,Nat2: nat] :
% 5.44/5.61 ( ( ( suc @ Nat )
% 5.44/5.61 = ( suc @ Nat2 ) )
% 5.44/5.61 = ( Nat = Nat2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % old.nat.inject
% 5.44/5.61 thf(fact_528_nat_Oinject,axiom,
% 5.44/5.61 ! [X22: nat,Y22: nat] :
% 5.44/5.61 ( ( ( suc @ X22 )
% 5.44/5.61 = ( suc @ Y22 ) )
% 5.44/5.61 = ( X22 = Y22 ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat.inject
% 5.44/5.61 thf(fact_529_VEBT_Oinject_I1_J,axiom,
% 5.44/5.61 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.44/5.61 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.44/5.61 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.44/5.61 = ( ( X11 = Y11 )
% 5.44/5.61 & ( X12 = Y12 )
% 5.44/5.61 & ( X13 = Y13 )
% 5.44/5.61 & ( X14 = Y14 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % VEBT.inject(1)
% 5.44/5.61 thf(fact_530_mint__corr__help,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,Mini: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_mint @ T )
% 5.44/5.61 = ( some_nat @ Mini ) )
% 5.44/5.61 => ( ( vEBT_vebt_member @ T @ X )
% 5.44/5.61 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mint_corr_help
% 5.44/5.61 thf(fact_531_maxt__corr__help,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,Maxi: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_maxt @ T )
% 5.44/5.61 = ( some_nat @ Maxi ) )
% 5.44/5.61 => ( ( vEBT_vebt_member @ T @ X )
% 5.44/5.61 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % maxt_corr_help
% 5.44/5.61 thf(fact_532__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lx_O_ASome_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.44/5.61 ~ ! [Lx: nat] :
% 5.44/5.61 ( ( some_nat @ Lx )
% 5.44/5.61 != ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ summin ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % \<open>\<And>thesis. (\<And>lx. Some lx = vebt_mint (treeList ! summin) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.44/5.61 thf(fact_533_lessI,axiom,
% 5.44/5.61 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % lessI
% 5.44/5.61 thf(fact_534_Suc__mono,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_mono
% 5.44/5.61 thf(fact_535_Suc__less__eq,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.44/5.61 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_less_eq
% 5.44/5.61 thf(fact_536_misiz,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,M: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( some_nat @ M )
% 5.44/5.61 = ( vEBT_vebt_mint @ T ) )
% 5.44/5.61 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % misiz
% 5.44/5.61 thf(fact_537_Suc__le__mono,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 5.44/5.61 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_le_mono
% 5.44/5.61 thf(fact_538_add__Suc__right,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 5.44/5.61 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_Suc_right
% 5.44/5.61 thf(fact_539_max__Suc__Suc,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.44/5.61 = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_Suc_Suc
% 5.44/5.61 thf(fact_540_max__number__of_I1_J,axiom,
% 5.44/5.61 ! [U: num,V: num] :
% 5.44/5.61 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.44/5.61 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.44/5.61 = ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.61 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.44/5.61 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.44/5.61 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_number_of(1)
% 5.44/5.61 thf(fact_541_max__number__of_I1_J,axiom,
% 5.44/5.61 ! [U: num,V: num] :
% 5.44/5.61 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.44/5.61 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.44/5.61 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.44/5.61 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_number_of(1)
% 5.44/5.61 thf(fact_542_max__number__of_I1_J,axiom,
% 5.44/5.61 ! [U: num,V: num] :
% 5.44/5.61 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.61 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.61 = ( numeral_numeral_real @ V ) ) )
% 5.44/5.61 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.61 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.61 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_number_of(1)
% 5.44/5.61 thf(fact_543_max__number__of_I1_J,axiom,
% 5.44/5.61 ! [U: num,V: num] :
% 5.44/5.61 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.44/5.61 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.44/5.61 = ( numeral_numeral_nat @ V ) ) )
% 5.44/5.61 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.44/5.61 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.44/5.61 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_number_of(1)
% 5.44/5.61 thf(fact_544_max__number__of_I1_J,axiom,
% 5.44/5.61 ! [U: num,V: num] :
% 5.44/5.61 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.61 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.61 = ( numeral_numeral_int @ V ) ) )
% 5.44/5.61 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.61 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.61 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_number_of(1)
% 5.44/5.61 thf(fact_545_max__0__1_I5_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 5.44/5.61 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(5)
% 5.44/5.61 thf(fact_546_max__0__1_I5_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(5)
% 5.44/5.61 thf(fact_547_max__0__1_I5_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.44/5.61 = ( numeral_numeral_real @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(5)
% 5.44/5.61 thf(fact_548_max__0__1_I5_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.44/5.61 = ( numeral_numeral_nat @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(5)
% 5.44/5.61 thf(fact_549_max__0__1_I5_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.44/5.61 = ( numeral_numeral_int @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(5)
% 5.44/5.61 thf(fact_550_max__0__1_I6_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 5.44/5.61 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(6)
% 5.44/5.61 thf(fact_551_max__0__1_I6_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 5.44/5.61 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(6)
% 5.44/5.61 thf(fact_552_max__0__1_I6_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 5.44/5.61 = ( numeral_numeral_real @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(6)
% 5.44/5.61 thf(fact_553_max__0__1_I6_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 5.44/5.61 = ( numeral_numeral_nat @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(6)
% 5.44/5.61 thf(fact_554_max__0__1_I6_J,axiom,
% 5.44/5.61 ! [X: num] :
% 5.44/5.61 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 5.44/5.61 = ( numeral_numeral_int @ X ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_0_1(6)
% 5.44/5.61 thf(fact_555_mult__Suc__right,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 5.44/5.61 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_Suc_right
% 5.44/5.61 thf(fact_556_Suc__numeral,axiom,
% 5.44/5.61 ! [N2: num] :
% 5.44/5.61 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.61 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_numeral
% 5.44/5.61 thf(fact_557_lesseq__shift,axiom,
% 5.44/5.61 ( ord_less_eq_nat
% 5.44/5.61 = ( ^ [X2: nat,Y3: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lesseq_shift
% 5.44/5.61 thf(fact_558_add__2__eq__Suc,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.61 = ( suc @ ( suc @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_2_eq_Suc
% 5.44/5.61 thf(fact_559_add__2__eq__Suc_H,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( suc @ ( suc @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_2_eq_Suc'
% 5.44/5.61 thf(fact_560_div2__Suc__Suc,axiom,
% 5.44/5.61 ! [M: nat] :
% 5.44/5.61 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.61 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div2_Suc_Suc
% 5.44/5.61 thf(fact_561_Suc__1,axiom,
% 5.44/5.61 ( ( suc @ one_one_nat )
% 5.44/5.61 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_1
% 5.44/5.61 thf(fact_562_n__not__Suc__n,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( N2
% 5.44/5.61 != ( suc @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % n_not_Suc_n
% 5.44/5.61 thf(fact_563_Suc__inject,axiom,
% 5.44/5.61 ! [X: nat,Y: nat] :
% 5.44/5.61 ( ( ( suc @ X )
% 5.44/5.61 = ( suc @ Y ) )
% 5.44/5.61 => ( X = Y ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_inject
% 5.44/5.61 thf(fact_564_enat__less__induct,axiom,
% 5.44/5.61 ! [P: extended_enat > $o,N2: extended_enat] :
% 5.44/5.61 ( ! [N4: extended_enat] :
% 5.44/5.61 ( ! [M2: extended_enat] :
% 5.44/5.61 ( ( ord_le72135733267957522d_enat @ M2 @ N4 )
% 5.44/5.61 => ( P @ M2 ) )
% 5.44/5.61 => ( P @ N4 ) )
% 5.44/5.61 => ( P @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % enat_less_induct
% 5.44/5.61 thf(fact_565_nat__add__max__left,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 5.44/5.61 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N2 @ Q2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_add_max_left
% 5.44/5.61 thf(fact_566_nat__add__max__right,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 5.44/5.61 = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_add_max_right
% 5.44/5.61 thf(fact_567_nat__mult__max__left,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 5.44/5.61 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_mult_max_left
% 5.44/5.61 thf(fact_568_nat__mult__max__right,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.61 ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 5.44/5.61 = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_mult_max_right
% 5.44/5.61 thf(fact_569_Nat_OlessE,axiom,
% 5.44/5.61 ! [I2: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ K )
% 5.44/5.61 => ( ( K
% 5.44/5.61 != ( suc @ I2 ) )
% 5.44/5.61 => ~ ! [J2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J2 )
% 5.44/5.61 => ( K
% 5.44/5.61 != ( suc @ J2 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Nat.lessE
% 5.44/5.61 thf(fact_570_Suc__lessD,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 5.44/5.61 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_lessD
% 5.44/5.61 thf(fact_571_Suc__lessE,axiom,
% 5.44/5.61 ! [I2: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 5.44/5.61 => ~ ! [J2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J2 )
% 5.44/5.61 => ( K
% 5.44/5.61 != ( suc @ J2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_lessE
% 5.44/5.61 thf(fact_572_Suc__lessI,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ( ( ( suc @ M )
% 5.44/5.61 != N2 )
% 5.44/5.61 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_lessI
% 5.44/5.61 thf(fact_573_less__SucE,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.44/5.61 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ( M = N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_SucE
% 5.44/5.61 thf(fact_574_less__SucI,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_SucI
% 5.44/5.61 thf(fact_575_Ex__less__Suc,axiom,
% 5.44/5.61 ! [N2: nat,P: nat > $o] :
% 5.44/5.61 ( ( ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 5.44/5.61 & ( P @ I5 ) ) )
% 5.44/5.61 = ( ( P @ N2 )
% 5.44/5.61 | ? [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ N2 )
% 5.44/5.61 & ( P @ I5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Ex_less_Suc
% 5.44/5.61 thf(fact_576_less__Suc__eq,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.44/5.61 = ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 | ( M = N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_Suc_eq
% 5.44/5.61 thf(fact_577_not__less__eq,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 5.44/5.61 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_less_eq
% 5.44/5.61 thf(fact_578_All__less__Suc,axiom,
% 5.44/5.61 ! [N2: nat,P: nat > $o] :
% 5.44/5.61 ( ( ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 5.44/5.61 => ( P @ I5 ) ) )
% 5.44/5.61 = ( ( P @ N2 )
% 5.44/5.61 & ! [I5: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I5 @ N2 )
% 5.44/5.61 => ( P @ I5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % All_less_Suc
% 5.44/5.61 thf(fact_579_Suc__less__eq2,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.61 = ( ? [M3: nat] :
% 5.44/5.61 ( ( M
% 5.44/5.61 = ( suc @ M3 ) )
% 5.44/5.61 & ( ord_less_nat @ N2 @ M3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_less_eq2
% 5.44/5.61 thf(fact_580_less__antisym,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] :
% 5.44/5.61 ( ~ ( ord_less_nat @ N2 @ M )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.44/5.61 => ( M = N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_antisym
% 5.44/5.61 thf(fact_581_Suc__less__SucD,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.44/5.61 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_less_SucD
% 5.44/5.61 thf(fact_582_less__trans__Suc,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.61 => ( ( ord_less_nat @ J @ K )
% 5.44/5.61 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_trans_Suc
% 5.44/5.61 thf(fact_583_less__Suc__induct,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.61 => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 5.44/5.61 => ( ! [I4: nat,J2: nat,K2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ J2 )
% 5.44/5.61 => ( ( ord_less_nat @ J2 @ K2 )
% 5.44/5.61 => ( ( P @ I4 @ J2 )
% 5.44/5.61 => ( ( P @ J2 @ K2 )
% 5.44/5.61 => ( P @ I4 @ K2 ) ) ) ) )
% 5.44/5.61 => ( P @ I2 @ J ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_Suc_induct
% 5.44/5.61 thf(fact_584_strict__inc__induct,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,P: nat > $o] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.61 => ( ! [I4: nat] :
% 5.44/5.61 ( ( J
% 5.44/5.61 = ( suc @ I4 ) )
% 5.44/5.61 => ( P @ I4 ) )
% 5.44/5.61 => ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ J )
% 5.44/5.61 => ( ( P @ ( suc @ I4 ) )
% 5.44/5.61 => ( P @ I4 ) ) )
% 5.44/5.61 => ( P @ I2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % strict_inc_induct
% 5.44/5.61 thf(fact_585_not__less__less__Suc__eq,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] :
% 5.44/5.61 ( ~ ( ord_less_nat @ N2 @ M )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.44/5.61 = ( N2 = M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_less_less_Suc_eq
% 5.44/5.61 thf(fact_586_transitive__stepwise__le,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,R2: nat > nat > $o] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ! [X5: nat] : ( R2 @ X5 @ X5 )
% 5.44/5.61 => ( ! [X5: nat,Y5: nat,Z4: nat] :
% 5.44/5.61 ( ( R2 @ X5 @ Y5 )
% 5.44/5.61 => ( ( R2 @ Y5 @ Z4 )
% 5.44/5.61 => ( R2 @ X5 @ Z4 ) ) )
% 5.44/5.61 => ( ! [N4: nat] : ( R2 @ N4 @ ( suc @ N4 ) )
% 5.44/5.61 => ( R2 @ M @ N2 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % transitive_stepwise_le
% 5.44/5.61 thf(fact_587_nat__induct__at__least,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,P: nat > $o] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ( P @ M )
% 5.44/5.61 => ( ! [N4: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N4 )
% 5.44/5.61 => ( ( P @ N4 )
% 5.44/5.61 => ( P @ ( suc @ N4 ) ) ) )
% 5.44/5.61 => ( P @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_induct_at_least
% 5.44/5.61 thf(fact_588_full__nat__induct,axiom,
% 5.44/5.61 ! [P: nat > $o,N2: nat] :
% 5.44/5.61 ( ! [N4: nat] :
% 5.44/5.61 ( ! [M2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N4 )
% 5.44/5.61 => ( P @ M2 ) )
% 5.44/5.61 => ( P @ N4 ) )
% 5.44/5.61 => ( P @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % full_nat_induct
% 5.44/5.61 thf(fact_589_not__less__eq__eq,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_less_eq_eq
% 5.44/5.61 thf(fact_590_Suc__n__not__le__n,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_n_not_le_n
% 5.44/5.61 thf(fact_591_le__Suc__eq,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.61 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 | ( M
% 5.44/5.61 = ( suc @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_Suc_eq
% 5.44/5.61 thf(fact_592_Suc__le__D,axiom,
% 5.44/5.61 ! [N2: nat,M4: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M4 )
% 5.44/5.61 => ? [M5: nat] :
% 5.44/5.61 ( M4
% 5.44/5.61 = ( suc @ M5 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_le_D
% 5.44/5.61 thf(fact_593_le__SucI,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_SucI
% 5.44/5.61 thf(fact_594_le__SucE,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.61 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( M
% 5.44/5.61 = ( suc @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_SucE
% 5.44/5.61 thf(fact_595_Suc__leD,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_leD
% 5.44/5.61 thf(fact_596_nat__arith_Osuc1,axiom,
% 5.44/5.61 ! [A2: nat,K: nat,A: nat] :
% 5.44/5.61 ( ( A2
% 5.44/5.61 = ( plus_plus_nat @ K @ A ) )
% 5.44/5.61 => ( ( suc @ A2 )
% 5.44/5.61 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_arith.suc1
% 5.44/5.61 thf(fact_597_add__Suc,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.44/5.61 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_Suc
% 5.44/5.61 thf(fact_598_add__Suc__shift,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.44/5.61 = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_Suc_shift
% 5.44/5.61 thf(fact_599_Suc__mult__cancel1,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.44/5.61 = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.44/5.61 = ( M = N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_mult_cancel1
% 5.44/5.61 thf(fact_600_lift__Suc__mono__less,axiom,
% 5.44/5.61 ! [F: nat > extended_enat,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_le72135733267957522d_enat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_le72135733267957522d_enat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less
% 5.44/5.61 thf(fact_601_lift__Suc__mono__less,axiom,
% 5.44/5.61 ! [F: nat > real,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_real @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less
% 5.44/5.61 thf(fact_602_lift__Suc__mono__less,axiom,
% 5.44/5.61 ! [F: nat > num,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_num @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less
% 5.44/5.61 thf(fact_603_lift__Suc__mono__less,axiom,
% 5.44/5.61 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less
% 5.44/5.61 thf(fact_604_lift__Suc__mono__less,axiom,
% 5.44/5.61 ! [F: nat > int,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less
% 5.44/5.61 thf(fact_605_lift__Suc__mono__less__iff,axiom,
% 5.44/5.61 ! [F: nat > extended_enat,N2: nat,M: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_le72135733267957522d_enat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_le72135733267957522d_enat @ ( F @ N2 ) @ ( F @ M ) )
% 5.44/5.61 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less_iff
% 5.44/5.61 thf(fact_606_lift__Suc__mono__less__iff,axiom,
% 5.44/5.61 ! [F: nat > real,N2: nat,M: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 5.44/5.61 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less_iff
% 5.44/5.61 thf(fact_607_lift__Suc__mono__less__iff,axiom,
% 5.44/5.61 ! [F: nat > num,N2: nat,M: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_num @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 5.44/5.61 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less_iff
% 5.44/5.61 thf(fact_608_lift__Suc__mono__less__iff,axiom,
% 5.44/5.61 ! [F: nat > nat,N2: nat,M: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 5.44/5.61 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less_iff
% 5.44/5.61 thf(fact_609_lift__Suc__mono__less__iff,axiom,
% 5.44/5.61 ! [F: nat > int,N2: nat,M: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 5.44/5.61 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_less_iff
% 5.44/5.61 thf(fact_610_lift__Suc__antimono__le,axiom,
% 5.44/5.61 ! [F: nat > set_real,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_set_real @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_set_real @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_antimono_le
% 5.44/5.61 thf(fact_611_lift__Suc__antimono__le,axiom,
% 5.44/5.61 ! [F: nat > set_nat,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_antimono_le
% 5.44/5.61 thf(fact_612_lift__Suc__antimono__le,axiom,
% 5.44/5.61 ! [F: nat > num,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_antimono_le
% 5.44/5.61 thf(fact_613_lift__Suc__antimono__le,axiom,
% 5.44/5.61 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_antimono_le
% 5.44/5.61 thf(fact_614_lift__Suc__antimono__le,axiom,
% 5.44/5.61 ! [F: nat > int,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_antimono_le
% 5.44/5.61 thf(fact_615_lift__Suc__mono__le,axiom,
% 5.44/5.61 ! [F: nat > set_real,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_set_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_set_real @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_le
% 5.44/5.61 thf(fact_616_lift__Suc__mono__le,axiom,
% 5.44/5.61 ! [F: nat > set_nat,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_set_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_le
% 5.44/5.61 thf(fact_617_lift__Suc__mono__le,axiom,
% 5.44/5.61 ! [F: nat > num,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_num @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_le
% 5.44/5.61 thf(fact_618_lift__Suc__mono__le,axiom,
% 5.44/5.61 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_le
% 5.44/5.61 thf(fact_619_lift__Suc__mono__le,axiom,
% 5.44/5.61 ! [F: nat > int,N2: nat,N5: nat] :
% 5.44/5.61 ( ! [N4: nat] : ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.44/5.61 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % lift_Suc_mono_le
% 5.44/5.61 thf(fact_620_Suc__leI,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_leI
% 5.44/5.61 thf(fact_621_Suc__le__eq,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.44/5.61 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_le_eq
% 5.44/5.61 thf(fact_622_dec__induct,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,P: nat > $o] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ( P @ I2 )
% 5.44/5.61 => ( ! [N4: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ N4 )
% 5.44/5.61 => ( ( ord_less_nat @ N4 @ J )
% 5.44/5.61 => ( ( P @ N4 )
% 5.44/5.61 => ( P @ ( suc @ N4 ) ) ) ) )
% 5.44/5.61 => ( P @ J ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % dec_induct
% 5.44/5.61 thf(fact_623_inc__induct,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,P: nat > $o] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ( P @ J )
% 5.44/5.61 => ( ! [N4: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ N4 )
% 5.44/5.61 => ( ( ord_less_nat @ N4 @ J )
% 5.44/5.61 => ( ( P @ ( suc @ N4 ) )
% 5.44/5.61 => ( P @ N4 ) ) ) )
% 5.44/5.61 => ( P @ I2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % inc_induct
% 5.44/5.61 thf(fact_624_Suc__le__lessD,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.44/5.61 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_le_lessD
% 5.44/5.61 thf(fact_625_le__less__Suc__eq,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.44/5.61 = ( N2 = M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_less_Suc_eq
% 5.44/5.61 thf(fact_626_less__Suc__eq__le,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_Suc_eq_le
% 5.44/5.61 thf(fact_627_less__eq__Suc__le,axiom,
% 5.44/5.61 ( ord_less_nat
% 5.44/5.61 = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_eq_Suc_le
% 5.44/5.61 thf(fact_628_le__imp__less__Suc,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_imp_less_Suc
% 5.44/5.61 thf(fact_629_less__natE,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ~ ! [Q3: nat] :
% 5.44/5.61 ( N2
% 5.44/5.61 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_natE
% 5.44/5.61 thf(fact_630_less__add__Suc1,axiom,
% 5.44/5.61 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_add_Suc1
% 5.44/5.61 thf(fact_631_less__add__Suc2,axiom,
% 5.44/5.61 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_add_Suc2
% 5.44/5.61 thf(fact_632_less__iff__Suc__add,axiom,
% 5.44/5.61 ( ord_less_nat
% 5.44/5.61 = ( ^ [M6: nat,N: nat] :
% 5.44/5.61 ? [K3: nat] :
% 5.44/5.61 ( N
% 5.44/5.61 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_iff_Suc_add
% 5.44/5.61 thf(fact_633_less__imp__Suc__add,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ? [K2: nat] :
% 5.44/5.61 ( N2
% 5.44/5.61 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_imp_Suc_add
% 5.44/5.61 thf(fact_634_Suc__mult__less__cancel1,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.44/5.61 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_mult_less_cancel1
% 5.44/5.61 thf(fact_635_Suc__mult__le__cancel1,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.44/5.61 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_mult_le_cancel1
% 5.44/5.61 thf(fact_636_mult__Suc,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 5.44/5.61 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_Suc
% 5.44/5.61 thf(fact_637_Suc__eq__plus1__left,axiom,
% 5.44/5.61 ( suc
% 5.44/5.61 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_eq_plus1_left
% 5.44/5.61 thf(fact_638_plus__1__eq__Suc,axiom,
% 5.44/5.61 ( ( plus_plus_nat @ one_one_nat )
% 5.44/5.61 = suc ) ).
% 5.44/5.61
% 5.44/5.61 % plus_1_eq_Suc
% 5.44/5.61 thf(fact_639_Suc__eq__plus1,axiom,
% 5.44/5.61 ( suc
% 5.44/5.61 = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_eq_plus1
% 5.44/5.61 thf(fact_640_power__Suc,axiom,
% 5.44/5.61 ! [A: complex,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 5.44/5.61 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_Suc
% 5.44/5.61 thf(fact_641_power__Suc,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.44/5.61 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_Suc
% 5.44/5.61 thf(fact_642_power__Suc,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.44/5.61 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_Suc
% 5.44/5.61 thf(fact_643_power__Suc,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.44/5.61 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_Suc
% 5.44/5.61 thf(fact_644_power__Suc2,axiom,
% 5.44/5.61 ! [A: complex,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 5.44/5.61 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_Suc2
% 5.44/5.61 thf(fact_645_power__Suc2,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.44/5.61 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_Suc2
% 5.44/5.61 thf(fact_646_power__Suc2,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.44/5.61 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_Suc2
% 5.44/5.61 thf(fact_647_power__Suc2,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.44/5.61 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_Suc2
% 5.44/5.61 thf(fact_648_Suc__div__le__mono,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_div_le_mono
% 5.44/5.61 thf(fact_649_power__gt1,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.61 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_gt1
% 5.44/5.61 thf(fact_650_power__gt1,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.44/5.61 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_gt1
% 5.44/5.61 thf(fact_651_power__gt1,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.44/5.61 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_gt1
% 5.44/5.61 thf(fact_652_nat__neq__iff,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( M != N2 )
% 5.44/5.61 = ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_neq_iff
% 5.44/5.61 thf(fact_653_less__not__refl,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.44/5.61
% 5.44/5.61 % less_not_refl
% 5.44/5.61 thf(fact_654_less__not__refl2,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ M )
% 5.44/5.61 => ( M != N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_not_refl2
% 5.44/5.61 thf(fact_655_less__not__refl3,axiom,
% 5.44/5.61 ! [S3: nat,T: nat] :
% 5.44/5.61 ( ( ord_less_nat @ S3 @ T )
% 5.44/5.61 => ( S3 != T ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_not_refl3
% 5.44/5.61 thf(fact_656_less__irrefl__nat,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.44/5.61
% 5.44/5.61 % less_irrefl_nat
% 5.44/5.61 thf(fact_657_nat__less__induct,axiom,
% 5.44/5.61 ! [P: nat > $o,N2: nat] :
% 5.44/5.61 ( ! [N4: nat] :
% 5.44/5.61 ( ! [M2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M2 @ N4 )
% 5.44/5.61 => ( P @ M2 ) )
% 5.44/5.61 => ( P @ N4 ) )
% 5.44/5.61 => ( P @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_less_induct
% 5.44/5.61 thf(fact_658_infinite__descent,axiom,
% 5.44/5.61 ! [P: nat > $o,N2: nat] :
% 5.44/5.61 ( ! [N4: nat] :
% 5.44/5.61 ( ~ ( P @ N4 )
% 5.44/5.61 => ? [M2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M2 @ N4 )
% 5.44/5.61 & ~ ( P @ M2 ) ) )
% 5.44/5.61 => ( P @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % infinite_descent
% 5.44/5.61 thf(fact_659_linorder__neqE__nat,axiom,
% 5.44/5.61 ! [X: nat,Y: nat] :
% 5.44/5.61 ( ( X != Y )
% 5.44/5.61 => ( ~ ( ord_less_nat @ X @ Y )
% 5.44/5.61 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % linorder_neqE_nat
% 5.44/5.61 thf(fact_660_Nat_Oex__has__greatest__nat,axiom,
% 5.44/5.61 ! [P: nat > $o,K: nat,B: nat] :
% 5.44/5.61 ( ( P @ K )
% 5.44/5.61 => ( ! [Y5: nat] :
% 5.44/5.61 ( ( P @ Y5 )
% 5.44/5.61 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.44/5.61 => ? [X5: nat] :
% 5.44/5.61 ( ( P @ X5 )
% 5.44/5.61 & ! [Y2: nat] :
% 5.44/5.61 ( ( P @ Y2 )
% 5.44/5.61 => ( ord_less_eq_nat @ Y2 @ X5 ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Nat.ex_has_greatest_nat
% 5.44/5.61 thf(fact_661_nat__le__linear,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_le_linear
% 5.44/5.61 thf(fact_662_le__antisym,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.61 => ( M = N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_antisym
% 5.44/5.61 thf(fact_663_eq__imp__le,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( M = N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % eq_imp_le
% 5.44/5.61 thf(fact_664_le__trans,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ( ord_less_eq_nat @ J @ K )
% 5.44/5.61 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_trans
% 5.44/5.61 thf(fact_665_le__refl,axiom,
% 5.44/5.61 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 5.44/5.61
% 5.44/5.61 % le_refl
% 5.44/5.61 thf(fact_666_size__neq__size__imp__neq,axiom,
% 5.44/5.61 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 5.44/5.61 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 5.44/5.61 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 5.44/5.61 => ( X != Y ) ) ).
% 5.44/5.61
% 5.44/5.61 % size_neq_size_imp_neq
% 5.44/5.61 thf(fact_667_size__neq__size__imp__neq,axiom,
% 5.44/5.61 ! [X: list_o,Y: list_o] :
% 5.44/5.61 ( ( ( size_size_list_o @ X )
% 5.44/5.61 != ( size_size_list_o @ Y ) )
% 5.44/5.61 => ( X != Y ) ) ).
% 5.44/5.61
% 5.44/5.61 % size_neq_size_imp_neq
% 5.44/5.61 thf(fact_668_size__neq__size__imp__neq,axiom,
% 5.44/5.61 ! [X: list_nat,Y: list_nat] :
% 5.44/5.61 ( ( ( size_size_list_nat @ X )
% 5.44/5.61 != ( size_size_list_nat @ Y ) )
% 5.44/5.61 => ( X != Y ) ) ).
% 5.44/5.61
% 5.44/5.61 % size_neq_size_imp_neq
% 5.44/5.61 thf(fact_669_size__neq__size__imp__neq,axiom,
% 5.44/5.61 ! [X: list_int,Y: list_int] :
% 5.44/5.61 ( ( ( size_size_list_int @ X )
% 5.44/5.61 != ( size_size_list_int @ Y ) )
% 5.44/5.61 => ( X != Y ) ) ).
% 5.44/5.61
% 5.44/5.61 % size_neq_size_imp_neq
% 5.44/5.61 thf(fact_670_size__neq__size__imp__neq,axiom,
% 5.44/5.61 ! [X: num,Y: num] :
% 5.44/5.61 ( ( ( size_size_num @ X )
% 5.44/5.61 != ( size_size_num @ Y ) )
% 5.44/5.61 => ( X != Y ) ) ).
% 5.44/5.61
% 5.44/5.61 % size_neq_size_imp_neq
% 5.44/5.61 thf(fact_671_div__nat__eqI,axiom,
% 5.44/5.61 ! [N2: nat,Q2: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q2 ) @ M )
% 5.44/5.61 => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q2 ) ) )
% 5.44/5.61 => ( ( divide_divide_nat @ M @ N2 )
% 5.44/5.61 = Q2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % div_nat_eqI
% 5.44/5.61 thf(fact_672_Suc__nat__number__of__add,axiom,
% 5.44/5.61 ! [V: num,N2: nat] :
% 5.44/5.61 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 5.44/5.61 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_nat_number_of_add
% 5.44/5.61 thf(fact_673_invar__vebt_Ointros_I3_J,axiom,
% 5.44/5.61 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.44/5.61 ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.44/5.61 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.44/5.61 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.44/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ( M
% 5.44/5.61 = ( suc @ N2 ) )
% 5.44/5.61 => ( ( Deg
% 5.44/5.61 = ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.61 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.44/5.61 => ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % invar_vebt.intros(3)
% 5.44/5.61 thf(fact_674_power__odd__eq,axiom,
% 5.44/5.61 ! [A: complex,N2: nat] :
% 5.44/5.61 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.61 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_odd_eq
% 5.44/5.61 thf(fact_675_power__odd__eq,axiom,
% 5.44/5.61 ! [A: real,N2: nat] :
% 5.44/5.61 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.61 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_odd_eq
% 5.44/5.61 thf(fact_676_power__odd__eq,axiom,
% 5.44/5.61 ! [A: nat,N2: nat] :
% 5.44/5.61 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.61 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_odd_eq
% 5.44/5.61 thf(fact_677_power__odd__eq,axiom,
% 5.44/5.61 ! [A: int,N2: nat] :
% 5.44/5.61 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.61 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_odd_eq
% 5.44/5.61 thf(fact_678_nat__less__le,axiom,
% 5.44/5.61 ( ord_less_nat
% 5.44/5.61 = ( ^ [M6: nat,N: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.61 & ( M6 != N ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_less_le
% 5.44/5.61 thf(fact_679_less__imp__le__nat,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_imp_le_nat
% 5.44/5.61 thf(fact_680_le__eq__less__or__eq,axiom,
% 5.44/5.61 ( ord_less_eq_nat
% 5.44/5.61 = ( ^ [M6: nat,N: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M6 @ N )
% 5.44/5.61 | ( M6 = N ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_eq_less_or_eq
% 5.44/5.61 thf(fact_681_less__or__eq__imp__le,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 | ( M = N2 ) )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_or_eq_imp_le
% 5.44/5.61 thf(fact_682_le__neq__implies__less,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ( M != N2 )
% 5.44/5.61 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_neq_implies_less
% 5.44/5.61 thf(fact_683_less__mono__imp__le__mono,axiom,
% 5.44/5.61 ! [F: nat > nat,I2: nat,J: nat] :
% 5.44/5.61 ( ! [I4: nat,J2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ J2 )
% 5.44/5.61 => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_mono_imp_le_mono
% 5.44/5.61 thf(fact_684_add__lessD1,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.44/5.61 => ( ord_less_nat @ I2 @ K ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_lessD1
% 5.44/5.61 thf(fact_685_add__less__mono,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.61 => ( ( ord_less_nat @ K @ L2 )
% 5.44/5.61 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_less_mono
% 5.44/5.61 thf(fact_686_not__add__less1,axiom,
% 5.44/5.61 ! [I2: nat,J: nat] :
% 5.44/5.61 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 5.44/5.61
% 5.44/5.61 % not_add_less1
% 5.44/5.61 thf(fact_687_not__add__less2,axiom,
% 5.44/5.61 ! [J: nat,I2: nat] :
% 5.44/5.61 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 5.44/5.61
% 5.44/5.61 % not_add_less2
% 5.44/5.61 thf(fact_688_add__less__mono1,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_less_mono1
% 5.44/5.61 thf(fact_689_trans__less__add1,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % trans_less_add1
% 5.44/5.61 thf(fact_690_trans__less__add2,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % trans_less_add2
% 5.44/5.61 thf(fact_691_less__add__eq__less,axiom,
% 5.44/5.61 ! [K: nat,L2: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ K @ L2 )
% 5.44/5.61 => ( ( ( plus_plus_nat @ M @ L2 )
% 5.44/5.61 = ( plus_plus_nat @ K @ N2 ) )
% 5.44/5.61 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_add_eq_less
% 5.44/5.61 thf(fact_692_add__leE,axiom,
% 5.44/5.61 ! [M: nat,K: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.44/5.61 => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_leE
% 5.44/5.61 thf(fact_693_le__add1,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_add1
% 5.44/5.61 thf(fact_694_le__add2,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_add2
% 5.44/5.61 thf(fact_695_add__leD1,axiom,
% 5.44/5.61 ! [M: nat,K: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_leD1
% 5.44/5.61 thf(fact_696_add__leD2,axiom,
% 5.44/5.61 ! [M: nat,K: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_leD2
% 5.44/5.61 thf(fact_697_le__Suc__ex,axiom,
% 5.44/5.61 ! [K: nat,L2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ L2 )
% 5.44/5.61 => ? [N4: nat] :
% 5.44/5.61 ( L2
% 5.44/5.61 = ( plus_plus_nat @ K @ N4 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_Suc_ex
% 5.44/5.61 thf(fact_698_add__le__mono,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.44/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_le_mono
% 5.44/5.61 thf(fact_699_add__le__mono1,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_le_mono1
% 5.44/5.61 thf(fact_700_trans__le__add1,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % trans_le_add1
% 5.44/5.61 thf(fact_701_trans__le__add2,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % trans_le_add2
% 5.44/5.61 thf(fact_702_nat__le__iff__add,axiom,
% 5.44/5.61 ( ord_less_eq_nat
% 5.44/5.61 = ( ^ [M6: nat,N: nat] :
% 5.44/5.61 ? [K3: nat] :
% 5.44/5.61 ( N
% 5.44/5.61 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % nat_le_iff_add
% 5.44/5.61 thf(fact_703_le__cube,axiom,
% 5.44/5.61 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_cube
% 5.44/5.61 thf(fact_704_le__square,axiom,
% 5.44/5.61 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_square
% 5.44/5.61 thf(fact_705_mult__le__mono,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.44/5.61 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_le_mono
% 5.44/5.61 thf(fact_706_mult__le__mono1,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_le_mono1
% 5.44/5.61 thf(fact_707_mult__le__mono2,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.61 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_le_mono2
% 5.44/5.61 thf(fact_708_add__mult__distrib,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,K: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_mult_distrib
% 5.44/5.61 thf(fact_709_add__mult__distrib2,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.61 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_mult_distrib2
% 5.44/5.61 thf(fact_710_nat__mult__1,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( times_times_nat @ one_one_nat @ N2 )
% 5.44/5.61 = N2 ) ).
% 5.44/5.61
% 5.44/5.61 % nat_mult_1
% 5.44/5.61 thf(fact_711_nat__mult__1__right,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( times_times_nat @ N2 @ one_one_nat )
% 5.44/5.61 = N2 ) ).
% 5.44/5.61
% 5.44/5.61 % nat_mult_1_right
% 5.44/5.61 thf(fact_712_invar__vebt_Ointros_I2_J,axiom,
% 5.44/5.61 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.44/5.61 ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.44/5.61 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.44/5.61 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.44/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ( M = N2 )
% 5.44/5.61 => ( ( Deg
% 5.44/5.61 = ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.61 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.44/5.61 => ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % invar_vebt.intros(2)
% 5.44/5.61 thf(fact_713_mono__nat__linear__lb,axiom,
% 5.44/5.61 ! [F: nat > nat,M: nat,K: nat] :
% 5.44/5.61 ( ! [M5: nat,N4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M5 @ N4 )
% 5.44/5.61 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N4 ) ) )
% 5.44/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mono_nat_linear_lb
% 5.44/5.61 thf(fact_714_invar__vebt_Ointros_I5_J,axiom,
% 5.44/5.61 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.44/5.61 ( ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.44/5.61 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.44/5.61 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.44/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ( M
% 5.44/5.61 = ( suc @ N2 ) )
% 5.44/5.61 => ( ( Deg
% 5.44/5.61 = ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.61 => ( ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X4 ) )
% 5.44/5.61 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.44/5.61 => ( ( ( Mi = Ma )
% 5.44/5.61 => ! [X5: vEBT_VEBT] :
% 5.44/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.61 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 5.44/5.61 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.44/5.61 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.44/5.61 => ( ( ( Mi != Ma )
% 5.44/5.61 => ! [I4: nat] :
% 5.44/5.61 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.61 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 5.44/5.61 = I4 )
% 5.44/5.61 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 5.44/5.61 & ! [X5: nat] :
% 5.44/5.61 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 5.44/5.61 = I4 )
% 5.44/5.61 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 5.44/5.61 => ( ( ord_less_nat @ Mi @ X5 )
% 5.44/5.61 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 5.44/5.61 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % invar_vebt.intros(5)
% 5.44/5.61 thf(fact_715_maxt__corr,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_maxt @ T )
% 5.44/5.61 = ( some_nat @ X ) )
% 5.44/5.61 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % maxt_corr
% 5.44/5.61 thf(fact_716_maxt__sound,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.44/5.61 => ( ( vEBT_vebt_maxt @ T )
% 5.44/5.61 = ( some_nat @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % maxt_sound
% 5.44/5.61 thf(fact_717_mint__sound,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.44/5.61 => ( ( vEBT_vebt_mint @ T )
% 5.44/5.61 = ( some_nat @ X ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mint_sound
% 5.44/5.61 thf(fact_718_mint__corr,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_mint @ T )
% 5.44/5.61 = ( some_nat @ X ) )
% 5.44/5.61 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mint_corr
% 5.44/5.61 thf(fact_719_set__vebt__set__vebt_H__valid,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( vEBT_set_vebt @ T )
% 5.44/5.61 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % set_vebt_set_vebt'_valid
% 5.44/5.61 thf(fact_720_pred__max,axiom,
% 5.44/5.61 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( ord_less_nat @ Ma @ X )
% 5.44/5.61 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( some_nat @ Ma ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % pred_max
% 5.44/5.61 thf(fact_721_succ__min,axiom,
% 5.44/5.61 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( ord_less_nat @ X @ Mi )
% 5.44/5.61 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( some_nat @ Mi ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % succ_min
% 5.44/5.61 thf(fact_722_greater__shift,axiom,
% 5.44/5.61 ( ord_less_nat
% 5.44/5.61 = ( ^ [Y3: nat,X2: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % greater_shift
% 5.44/5.61 thf(fact_723_less__shift,axiom,
% 5.44/5.61 ( ord_less_nat
% 5.44/5.61 = ( ^ [X2: nat,Y3: nat] : ( vEBT_VEBT_less @ ( some_nat @ X2 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_shift
% 5.44/5.61 thf(fact_724_helpyd,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.44/5.61 = ( some_nat @ Y ) )
% 5.44/5.61 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % helpyd
% 5.44/5.61 thf(fact_725_helpypredd,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.44/5.61 = ( some_nat @ Y ) )
% 5.44/5.61 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % helpypredd
% 5.44/5.61 thf(fact_726_succ__member,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.44/5.61 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.44/5.61 = ( ( vEBT_vebt_member @ T @ Y )
% 5.44/5.61 & ( ord_less_nat @ X @ Y )
% 5.44/5.61 & ! [Z5: nat] :
% 5.44/5.61 ( ( ( vEBT_vebt_member @ T @ Z5 )
% 5.44/5.61 & ( ord_less_nat @ X @ Z5 ) )
% 5.44/5.61 => ( ord_less_eq_nat @ Y @ Z5 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % succ_member
% 5.44/5.61 thf(fact_727_pred__member,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.44/5.61 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.44/5.61 = ( ( vEBT_vebt_member @ T @ Y )
% 5.44/5.61 & ( ord_less_nat @ Y @ X )
% 5.44/5.61 & ! [Z5: nat] :
% 5.44/5.61 ( ( ( vEBT_vebt_member @ T @ Z5 )
% 5.44/5.61 & ( ord_less_nat @ Z5 @ X ) )
% 5.44/5.61 => ( ord_less_eq_nat @ Z5 @ Y ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % pred_member
% 5.44/5.61 thf(fact_728_pred__corr,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Px: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.44/5.61 = ( some_nat @ Px ) )
% 5.44/5.61 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % pred_corr
% 5.44/5.61 thf(fact_729_succ__corr,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.44/5.61 = ( some_nat @ Sx ) )
% 5.44/5.61 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % succ_corr
% 5.44/5.61 thf(fact_730_pred__correct,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.44/5.61 = ( some_nat @ Sx ) )
% 5.44/5.61 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % pred_correct
% 5.44/5.61 thf(fact_731_succ__correct,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.61 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.44/5.61 = ( some_nat @ Sx ) )
% 5.44/5.61 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % succ_correct
% 5.44/5.61 thf(fact_732_local_Opower__def,axiom,
% 5.44/5.61 ( vEBT_VEBT_power
% 5.44/5.61 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.44/5.61
% 5.44/5.61 % local.power_def
% 5.44/5.61 thf(fact_733_mintlistlength,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 5.44/5.61 => ( ( Mi != Ma )
% 5.44/5.61 => ( ( ord_less_nat @ Mi @ Ma )
% 5.44/5.61 & ? [M5: nat] :
% 5.44/5.61 ( ( ( some_nat @ M5 )
% 5.44/5.61 = ( vEBT_vebt_mint @ Summary ) )
% 5.44/5.61 & ( ord_less_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mintlistlength
% 5.44/5.61 thf(fact_734_succ__list__to__short,axiom,
% 5.44/5.61 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.61 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = none_nat ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % succ_list_to_short
% 5.44/5.61 thf(fact_735_pred__list__to__short,axiom,
% 5.44/5.61 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.61 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.61 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = none_nat ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % pred_list_to_short
% 5.44/5.61 thf(fact_736_option_Ocollapse,axiom,
% 5.44/5.61 ! [Option: option4927543243414619207at_nat] :
% 5.44/5.61 ( ( Option != none_P5556105721700978146at_nat )
% 5.44/5.61 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.44/5.61 = Option ) ) ).
% 5.44/5.61
% 5.44/5.61 % option.collapse
% 5.44/5.61 thf(fact_737_option_Ocollapse,axiom,
% 5.44/5.61 ! [Option: option_nat] :
% 5.44/5.61 ( ( Option != none_nat )
% 5.44/5.61 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.44/5.61 = Option ) ) ).
% 5.44/5.61
% 5.44/5.61 % option.collapse
% 5.44/5.61 thf(fact_738_option_Ocollapse,axiom,
% 5.44/5.61 ! [Option: option_num] :
% 5.44/5.61 ( ( Option != none_num )
% 5.44/5.61 => ( ( some_num @ ( the_num @ Option ) )
% 5.44/5.61 = Option ) ) ).
% 5.44/5.61
% 5.44/5.61 % option.collapse
% 5.44/5.61 thf(fact_739_vebt__insert_Osimps_I4_J,axiom,
% 5.44/5.61 ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.44/5.61 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 5.44/5.61
% 5.44/5.61 % vebt_insert.simps(4)
% 5.44/5.61 thf(fact_740_vebt__maxt_Osimps_I3_J,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.44/5.61 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.44/5.61 = ( some_nat @ Ma ) ) ).
% 5.44/5.61
% 5.44/5.61 % vebt_maxt.simps(3)
% 5.44/5.61 thf(fact_741_vebt__mint_Osimps_I3_J,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.44/5.61 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.44/5.61 = ( some_nat @ Mi ) ) ).
% 5.44/5.61
% 5.44/5.61 % vebt_mint.simps(3)
% 5.44/5.61 thf(fact_742_not__None__eq,axiom,
% 5.44/5.61 ! [X: option4927543243414619207at_nat] :
% 5.44/5.61 ( ( X != none_P5556105721700978146at_nat )
% 5.44/5.61 = ( ? [Y3: product_prod_nat_nat] :
% 5.44/5.61 ( X
% 5.44/5.61 = ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_None_eq
% 5.44/5.61 thf(fact_743_not__None__eq,axiom,
% 5.44/5.61 ! [X: option_nat] :
% 5.44/5.61 ( ( X != none_nat )
% 5.44/5.61 = ( ? [Y3: nat] :
% 5.44/5.61 ( X
% 5.44/5.61 = ( some_nat @ Y3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_None_eq
% 5.44/5.61 thf(fact_744_not__None__eq,axiom,
% 5.44/5.61 ! [X: option_num] :
% 5.44/5.61 ( ( X != none_num )
% 5.44/5.61 = ( ? [Y3: num] :
% 5.44/5.61 ( X
% 5.44/5.61 = ( some_num @ Y3 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_None_eq
% 5.44/5.61 thf(fact_745_not__Some__eq,axiom,
% 5.44/5.61 ! [X: option4927543243414619207at_nat] :
% 5.44/5.61 ( ( ! [Y3: product_prod_nat_nat] :
% 5.44/5.61 ( X
% 5.44/5.61 != ( some_P7363390416028606310at_nat @ Y3 ) ) )
% 5.44/5.61 = ( X = none_P5556105721700978146at_nat ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_Some_eq
% 5.44/5.61 thf(fact_746_not__Some__eq,axiom,
% 5.44/5.61 ! [X: option_nat] :
% 5.44/5.61 ( ( ! [Y3: nat] :
% 5.44/5.61 ( X
% 5.44/5.61 != ( some_nat @ Y3 ) ) )
% 5.44/5.61 = ( X = none_nat ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_Some_eq
% 5.44/5.61 thf(fact_747_not__Some__eq,axiom,
% 5.44/5.61 ! [X: option_num] :
% 5.44/5.61 ( ( ! [Y3: num] :
% 5.44/5.61 ( X
% 5.44/5.61 != ( some_num @ Y3 ) ) )
% 5.44/5.61 = ( X = none_num ) ) ).
% 5.44/5.61
% 5.44/5.61 % not_Some_eq
% 5.44/5.61 thf(fact_748_max__less__iff__conj,axiom,
% 5.44/5.61 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.44/5.61 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.44/5.61 = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 5.44/5.61 & ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_less_iff_conj
% 5.44/5.61 thf(fact_749_max__less__iff__conj,axiom,
% 5.44/5.61 ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 5.44/5.61 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y ) @ Z )
% 5.44/5.61 = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 5.44/5.61 & ( ord_le72135733267957522d_enat @ Y @ Z ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_less_iff_conj
% 5.44/5.61 thf(fact_750_max__less__iff__conj,axiom,
% 5.44/5.61 ! [X: real,Y: real,Z: real] :
% 5.44/5.61 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.44/5.61 = ( ( ord_less_real @ X @ Z )
% 5.44/5.61 & ( ord_less_real @ Y @ Z ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_less_iff_conj
% 5.44/5.61 thf(fact_751_max__less__iff__conj,axiom,
% 5.44/5.61 ! [X: num,Y: num,Z: num] :
% 5.44/5.61 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 5.44/5.61 = ( ( ord_less_num @ X @ Z )
% 5.44/5.61 & ( ord_less_num @ Y @ Z ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_less_iff_conj
% 5.44/5.61 thf(fact_752_max__less__iff__conj,axiom,
% 5.44/5.61 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.61 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 5.44/5.61 = ( ( ord_less_nat @ X @ Z )
% 5.44/5.61 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_less_iff_conj
% 5.44/5.61 thf(fact_753_max__less__iff__conj,axiom,
% 5.44/5.61 ! [X: int,Y: int,Z: int] :
% 5.44/5.61 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.44/5.61 = ( ( ord_less_int @ X @ Z )
% 5.44/5.61 & ( ord_less_int @ Y @ Z ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max_less_iff_conj
% 5.44/5.61 thf(fact_754_max_Oabsorb4,axiom,
% 5.44/5.61 ! [A: code_integer,B: code_integer] :
% 5.44/5.61 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.44/5.61 => ( ( ord_max_Code_integer @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb4
% 5.44/5.61 thf(fact_755_max_Oabsorb4,axiom,
% 5.44/5.61 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.61 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.61 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb4
% 5.44/5.61 thf(fact_756_max_Oabsorb4,axiom,
% 5.44/5.61 ! [A: real,B: real] :
% 5.44/5.61 ( ( ord_less_real @ A @ B )
% 5.44/5.61 => ( ( ord_max_real @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb4
% 5.44/5.61 thf(fact_757_max_Oabsorb4,axiom,
% 5.44/5.61 ! [A: num,B: num] :
% 5.44/5.61 ( ( ord_less_num @ A @ B )
% 5.44/5.61 => ( ( ord_max_num @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb4
% 5.44/5.61 thf(fact_758_max_Oabsorb4,axiom,
% 5.44/5.61 ! [A: nat,B: nat] :
% 5.44/5.61 ( ( ord_less_nat @ A @ B )
% 5.44/5.61 => ( ( ord_max_nat @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb4
% 5.44/5.61 thf(fact_759_max_Oabsorb4,axiom,
% 5.44/5.61 ! [A: int,B: int] :
% 5.44/5.61 ( ( ord_less_int @ A @ B )
% 5.44/5.61 => ( ( ord_max_int @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb4
% 5.44/5.61 thf(fact_760_minminNull,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT] :
% 5.44/5.61 ( ( ( vEBT_vebt_mint @ T )
% 5.44/5.61 = none_nat )
% 5.44/5.61 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.44/5.61
% 5.44/5.61 % minminNull
% 5.44/5.61 thf(fact_761_minNullmin,axiom,
% 5.44/5.61 ! [T: vEBT_VEBT] :
% 5.44/5.61 ( ( vEBT_VEBT_minNull @ T )
% 5.44/5.61 => ( ( vEBT_vebt_mint @ T )
% 5.44/5.61 = none_nat ) ) ).
% 5.44/5.61
% 5.44/5.61 % minNullmin
% 5.44/5.61 thf(fact_762_option_Oinject,axiom,
% 5.44/5.61 ! [X22: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 5.44/5.61 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.44/5.61 = ( some_P7363390416028606310at_nat @ Y22 ) )
% 5.44/5.61 = ( X22 = Y22 ) ) ).
% 5.44/5.61
% 5.44/5.61 % option.inject
% 5.44/5.61 thf(fact_763_option_Oinject,axiom,
% 5.44/5.61 ! [X22: nat,Y22: nat] :
% 5.44/5.61 ( ( ( some_nat @ X22 )
% 5.44/5.61 = ( some_nat @ Y22 ) )
% 5.44/5.61 = ( X22 = Y22 ) ) ).
% 5.44/5.61
% 5.44/5.61 % option.inject
% 5.44/5.61 thf(fact_764_option_Oinject,axiom,
% 5.44/5.61 ! [X22: num,Y22: num] :
% 5.44/5.61 ( ( ( some_num @ X22 )
% 5.44/5.61 = ( some_num @ Y22 ) )
% 5.44/5.61 = ( X22 = Y22 ) ) ).
% 5.44/5.61
% 5.44/5.61 % option.inject
% 5.44/5.61 thf(fact_765_max_Oright__idem,axiom,
% 5.44/5.61 ! [A: nat,B: nat] :
% 5.44/5.61 ( ( ord_max_nat @ ( ord_max_nat @ A @ B ) @ B )
% 5.44/5.61 = ( ord_max_nat @ A @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.right_idem
% 5.44/5.61 thf(fact_766_max_Oright__idem,axiom,
% 5.44/5.61 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.61 ( ( ord_ma741700101516333627d_enat @ ( ord_ma741700101516333627d_enat @ A @ B ) @ B )
% 5.44/5.61 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.right_idem
% 5.44/5.61 thf(fact_767_max_Oright__idem,axiom,
% 5.44/5.61 ! [A: int,B: int] :
% 5.44/5.61 ( ( ord_max_int @ ( ord_max_int @ A @ B ) @ B )
% 5.44/5.61 = ( ord_max_int @ A @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.right_idem
% 5.44/5.61 thf(fact_768_max_Oright__idem,axiom,
% 5.44/5.61 ! [A: code_integer,B: code_integer] :
% 5.44/5.61 ( ( ord_max_Code_integer @ ( ord_max_Code_integer @ A @ B ) @ B )
% 5.44/5.61 = ( ord_max_Code_integer @ A @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.right_idem
% 5.44/5.61 thf(fact_769_max_Oleft__idem,axiom,
% 5.44/5.61 ! [A: nat,B: nat] :
% 5.44/5.61 ( ( ord_max_nat @ A @ ( ord_max_nat @ A @ B ) )
% 5.44/5.61 = ( ord_max_nat @ A @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.left_idem
% 5.44/5.61 thf(fact_770_max_Oleft__idem,axiom,
% 5.44/5.61 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.61 ( ( ord_ma741700101516333627d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.44/5.61 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.left_idem
% 5.44/5.61 thf(fact_771_max_Oleft__idem,axiom,
% 5.44/5.61 ! [A: int,B: int] :
% 5.44/5.61 ( ( ord_max_int @ A @ ( ord_max_int @ A @ B ) )
% 5.44/5.61 = ( ord_max_int @ A @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.left_idem
% 5.44/5.61 thf(fact_772_max_Oleft__idem,axiom,
% 5.44/5.61 ! [A: code_integer,B: code_integer] :
% 5.44/5.61 ( ( ord_max_Code_integer @ A @ ( ord_max_Code_integer @ A @ B ) )
% 5.44/5.61 = ( ord_max_Code_integer @ A @ B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.left_idem
% 5.44/5.61 thf(fact_773_max_Oidem,axiom,
% 5.44/5.61 ! [A: nat] :
% 5.44/5.61 ( ( ord_max_nat @ A @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % max.idem
% 5.44/5.61 thf(fact_774_max_Oidem,axiom,
% 5.44/5.61 ! [A: extended_enat] :
% 5.44/5.61 ( ( ord_ma741700101516333627d_enat @ A @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % max.idem
% 5.44/5.61 thf(fact_775_max_Oidem,axiom,
% 5.44/5.61 ! [A: int] :
% 5.44/5.61 ( ( ord_max_int @ A @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % max.idem
% 5.44/5.61 thf(fact_776_max_Oidem,axiom,
% 5.44/5.61 ! [A: code_integer] :
% 5.44/5.61 ( ( ord_max_Code_integer @ A @ A )
% 5.44/5.61 = A ) ).
% 5.44/5.61
% 5.44/5.61 % max.idem
% 5.44/5.61 thf(fact_777_power__minus__is__div,axiom,
% 5.44/5.61 ! [B: nat,A: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.61 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.44/5.61 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % power_minus_is_div
% 5.44/5.61 thf(fact_778_geqmaxNone,axiom,
% 5.44/5.61 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.61 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 5.44/5.61 => ( ( ord_less_eq_nat @ Ma @ X )
% 5.44/5.61 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.61 = none_nat ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % geqmaxNone
% 5.44/5.61 thf(fact_779_Suc__diff__diff,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,K: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 5.44/5.61 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_diff_diff
% 5.44/5.61 thf(fact_780_diff__Suc__Suc,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.44/5.61 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_Suc_Suc
% 5.44/5.61 thf(fact_781_max_Obounded__iff,axiom,
% 5.44/5.61 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.44/5.61 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.44/5.61 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.44/5.61 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.bounded_iff
% 5.44/5.61 thf(fact_782_max_Obounded__iff,axiom,
% 5.44/5.61 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.44/5.61 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.44/5.61 = ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.44/5.61 & ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.bounded_iff
% 5.44/5.61 thf(fact_783_max_Obounded__iff,axiom,
% 5.44/5.61 ! [B: num,C: num,A: num] :
% 5.44/5.61 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.44/5.61 = ( ( ord_less_eq_num @ B @ A )
% 5.44/5.61 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.bounded_iff
% 5.44/5.61 thf(fact_784_max_Obounded__iff,axiom,
% 5.44/5.61 ! [B: nat,C: nat,A: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.44/5.61 = ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.61 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.bounded_iff
% 5.44/5.61 thf(fact_785_max_Obounded__iff,axiom,
% 5.44/5.61 ! [B: int,C: int,A: int] :
% 5.44/5.61 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.44/5.61 = ( ( ord_less_eq_int @ B @ A )
% 5.44/5.61 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.bounded_iff
% 5.44/5.61 thf(fact_786_max_Oabsorb2,axiom,
% 5.44/5.61 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.61 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.61 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb2
% 5.44/5.61 thf(fact_787_max_Oabsorb2,axiom,
% 5.44/5.61 ! [A: code_integer,B: code_integer] :
% 5.44/5.61 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.44/5.61 => ( ( ord_max_Code_integer @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb2
% 5.44/5.61 thf(fact_788_max_Oabsorb2,axiom,
% 5.44/5.61 ! [A: num,B: num] :
% 5.44/5.61 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.61 => ( ( ord_max_num @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb2
% 5.44/5.61 thf(fact_789_max_Oabsorb2,axiom,
% 5.44/5.61 ! [A: nat,B: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.61 => ( ( ord_max_nat @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb2
% 5.44/5.61 thf(fact_790_max_Oabsorb2,axiom,
% 5.44/5.61 ! [A: int,B: int] :
% 5.44/5.61 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.61 => ( ( ord_max_int @ A @ B )
% 5.44/5.61 = B ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb2
% 5.44/5.61 thf(fact_791_max_Oabsorb1,axiom,
% 5.44/5.61 ! [B: extended_enat,A: extended_enat] :
% 5.44/5.61 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.44/5.61 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb1
% 5.44/5.61 thf(fact_792_max_Oabsorb1,axiom,
% 5.44/5.61 ! [B: code_integer,A: code_integer] :
% 5.44/5.61 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.44/5.61 => ( ( ord_max_Code_integer @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb1
% 5.44/5.61 thf(fact_793_max_Oabsorb1,axiom,
% 5.44/5.61 ! [B: num,A: num] :
% 5.44/5.61 ( ( ord_less_eq_num @ B @ A )
% 5.44/5.61 => ( ( ord_max_num @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb1
% 5.44/5.61 thf(fact_794_max_Oabsorb1,axiom,
% 5.44/5.61 ! [B: nat,A: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.61 => ( ( ord_max_nat @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb1
% 5.44/5.61 thf(fact_795_max_Oabsorb1,axiom,
% 5.44/5.61 ! [B: int,A: int] :
% 5.44/5.61 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.61 => ( ( ord_max_int @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb1
% 5.44/5.61 thf(fact_796_max_Oabsorb3,axiom,
% 5.44/5.61 ! [B: code_integer,A: code_integer] :
% 5.44/5.61 ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.44/5.61 => ( ( ord_max_Code_integer @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb3
% 5.44/5.61 thf(fact_797_max_Oabsorb3,axiom,
% 5.44/5.61 ! [B: extended_enat,A: extended_enat] :
% 5.44/5.61 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.44/5.61 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb3
% 5.44/5.61 thf(fact_798_max_Oabsorb3,axiom,
% 5.44/5.61 ! [B: real,A: real] :
% 5.44/5.61 ( ( ord_less_real @ B @ A )
% 5.44/5.61 => ( ( ord_max_real @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb3
% 5.44/5.61 thf(fact_799_max_Oabsorb3,axiom,
% 5.44/5.61 ! [B: num,A: num] :
% 5.44/5.61 ( ( ord_less_num @ B @ A )
% 5.44/5.61 => ( ( ord_max_num @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb3
% 5.44/5.61 thf(fact_800_max_Oabsorb3,axiom,
% 5.44/5.61 ! [B: nat,A: nat] :
% 5.44/5.61 ( ( ord_less_nat @ B @ A )
% 5.44/5.61 => ( ( ord_max_nat @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb3
% 5.44/5.61 thf(fact_801_max_Oabsorb3,axiom,
% 5.44/5.61 ! [B: int,A: int] :
% 5.44/5.61 ( ( ord_less_int @ B @ A )
% 5.44/5.61 => ( ( ord_max_int @ A @ B )
% 5.44/5.61 = A ) ) ).
% 5.44/5.61
% 5.44/5.61 % max.absorb3
% 5.44/5.61 thf(fact_802_diff__diff__cancel,axiom,
% 5.44/5.61 ! [I2: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.44/5.61 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I2 ) )
% 5.44/5.61 = I2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_diff_cancel
% 5.44/5.61 thf(fact_803_diff__diff__left,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.44/5.61 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_diff_left
% 5.44/5.61 thf(fact_804_left__diff__distrib__numeral,axiom,
% 5.44/5.61 ! [A: complex,B: complex,V: num] :
% 5.44/5.61 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.44/5.61 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_diff_distrib_numeral
% 5.44/5.61 thf(fact_805_left__diff__distrib__numeral,axiom,
% 5.44/5.61 ! [A: real,B: real,V: num] :
% 5.44/5.61 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.61 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_diff_distrib_numeral
% 5.44/5.61 thf(fact_806_left__diff__distrib__numeral,axiom,
% 5.44/5.61 ! [A: int,B: int,V: num] :
% 5.44/5.61 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.61 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % left_diff_distrib_numeral
% 5.44/5.61 thf(fact_807_right__diff__distrib__numeral,axiom,
% 5.44/5.61 ! [V: num,B: complex,C: complex] :
% 5.44/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.44/5.61 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % right_diff_distrib_numeral
% 5.44/5.61 thf(fact_808_right__diff__distrib__numeral,axiom,
% 5.44/5.61 ! [V: num,B: real,C: real] :
% 5.44/5.61 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.44/5.61 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % right_diff_distrib_numeral
% 5.44/5.61 thf(fact_809_right__diff__distrib__numeral,axiom,
% 5.44/5.61 ! [V: num,B: int,C: int] :
% 5.44/5.61 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.44/5.61 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % right_diff_distrib_numeral
% 5.44/5.61 thf(fact_810_Nat_Oadd__diff__assoc,axiom,
% 5.44/5.61 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.61 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.44/5.61 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Nat.add_diff_assoc
% 5.44/5.61 thf(fact_811_Nat_Oadd__diff__assoc2,axiom,
% 5.44/5.61 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.61 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.44/5.61 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Nat.add_diff_assoc2
% 5.44/5.61 thf(fact_812_Nat_Odiff__diff__right,axiom,
% 5.44/5.61 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.61 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.44/5.61 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Nat.diff_diff_right
% 5.44/5.61 thf(fact_813_diff__Suc__1,axiom,
% 5.44/5.61 ! [N2: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.44/5.61 = N2 ) ).
% 5.44/5.61
% 5.44/5.61 % diff_Suc_1
% 5.44/5.61 thf(fact_814_diff__Suc__diff__eq2,axiom,
% 5.44/5.61 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.61 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 5.44/5.61 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_Suc_diff_eq2
% 5.44/5.61 thf(fact_815_diff__Suc__diff__eq1,axiom,
% 5.44/5.61 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.61 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.44/5.61 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_Suc_diff_eq1
% 5.44/5.61 thf(fact_816_diff__commute,axiom,
% 5.44/5.61 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.44/5.61 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_commute
% 5.44/5.61 thf(fact_817_add__diff__add,axiom,
% 5.44/5.61 ! [A: complex,C: complex,B: complex,D: complex] :
% 5.44/5.61 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ D ) )
% 5.44/5.61 = ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ ( minus_minus_complex @ C @ D ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_diff_add
% 5.44/5.61 thf(fact_818_add__diff__add,axiom,
% 5.44/5.61 ! [A: real,C: real,B: real,D: real] :
% 5.44/5.61 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.44/5.61 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_diff_add
% 5.44/5.61 thf(fact_819_add__diff__add,axiom,
% 5.44/5.61 ! [A: int,C: int,B: int,D: int] :
% 5.44/5.61 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.44/5.61 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % add_diff_add
% 5.44/5.61 thf(fact_820_zero__induct__lemma,axiom,
% 5.44/5.61 ! [P: nat > $o,K: nat,I2: nat] :
% 5.44/5.61 ( ( P @ K )
% 5.44/5.61 => ( ! [N4: nat] :
% 5.44/5.61 ( ( P @ ( suc @ N4 ) )
% 5.44/5.61 => ( P @ N4 ) )
% 5.44/5.61 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % zero_induct_lemma
% 5.44/5.61 thf(fact_821_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.44/5.61 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.44/5.61 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.44/5.61 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % VEBT_internal.option_shift.simps(3)
% 5.44/5.61 thf(fact_822_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.44/5.61 ! [F: num > num > num,A: num,B: num] :
% 5.44/5.61 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.44/5.61 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % VEBT_internal.option_shift.simps(3)
% 5.44/5.61 thf(fact_823_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.44/5.61 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.44/5.61 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.44/5.61 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % VEBT_internal.option_shift.simps(3)
% 5.44/5.61 thf(fact_824_diff__less__mono2,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,L2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.61 => ( ( ord_less_nat @ M @ L2 )
% 5.44/5.61 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N2 ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_less_mono2
% 5.44/5.61 thf(fact_825_less__imp__diff__less,axiom,
% 5.44/5.61 ! [J: nat,K: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_nat @ J @ K )
% 5.44/5.61 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 5.44/5.61
% 5.44/5.61 % less_imp_diff_less
% 5.44/5.61 thf(fact_826_diff__le__mono2,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,L2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N2 ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_le_mono2
% 5.44/5.61 thf(fact_827_le__diff__iff_H,axiom,
% 5.44/5.61 ! [A: nat,C: nat,B: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ A @ C )
% 5.44/5.61 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.44/5.61 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_diff_iff'
% 5.44/5.61 thf(fact_828_diff__le__self,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 5.44/5.61
% 5.44/5.61 % diff_le_self
% 5.44/5.61 thf(fact_829_diff__le__mono,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,L2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.61 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N2 @ L2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_le_mono
% 5.44/5.61 thf(fact_830_Nat_Odiff__diff__eq,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ M )
% 5.44/5.61 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.61 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.44/5.61 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Nat.diff_diff_eq
% 5.44/5.61 thf(fact_831_le__diff__iff,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ M )
% 5.44/5.61 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.61 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.44/5.61 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % le_diff_iff
% 5.44/5.61 thf(fact_832_eq__diff__iff,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ M )
% 5.44/5.61 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.61 => ( ( ( minus_minus_nat @ M @ K )
% 5.44/5.61 = ( minus_minus_nat @ N2 @ K ) )
% 5.44/5.61 = ( M = N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % eq_diff_iff
% 5.44/5.61 thf(fact_833_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.44/5.61 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.44/5.61 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 5.44/5.61 = none_P5556105721700978146at_nat ) ).
% 5.44/5.61
% 5.44/5.61 % VEBT_internal.option_shift.simps(1)
% 5.44/5.61 thf(fact_834_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.44/5.61 ! [Uu: num > num > num,Uv: option_num] :
% 5.44/5.61 ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 5.44/5.61 = none_num ) ).
% 5.44/5.61
% 5.44/5.61 % VEBT_internal.option_shift.simps(1)
% 5.44/5.61 thf(fact_835_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.44/5.61 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.44/5.61 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 5.44/5.61 = none_nat ) ).
% 5.44/5.61
% 5.44/5.61 % VEBT_internal.option_shift.simps(1)
% 5.44/5.61 thf(fact_836_Nat_Odiff__cancel,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.44/5.61 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % Nat.diff_cancel
% 5.44/5.61 thf(fact_837_diff__cancel2,axiom,
% 5.44/5.61 ! [M: nat,K: nat,N2: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.44/5.61 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_cancel2
% 5.44/5.61 thf(fact_838_diff__add__inverse,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 5.44/5.61 = M ) ).
% 5.44/5.61
% 5.44/5.61 % diff_add_inverse
% 5.44/5.61 thf(fact_839_diff__add__inverse2,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] :
% 5.44/5.61 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 5.44/5.61 = M ) ).
% 5.44/5.61
% 5.44/5.61 % diff_add_inverse2
% 5.44/5.61 thf(fact_840_diff__mult__distrib,axiom,
% 5.44/5.61 ! [M: nat,N2: nat,K: nat] :
% 5.44/5.61 ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 5.44/5.61 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_mult_distrib
% 5.44/5.61 thf(fact_841_diff__mult__distrib2,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.61 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_mult_distrib2
% 5.44/5.61 thf(fact_842_mult__diff__mult,axiom,
% 5.44/5.61 ! [X: complex,Y: complex,A: complex,B: complex] :
% 5.44/5.61 ( ( minus_minus_complex @ ( times_times_complex @ X @ Y ) @ ( times_times_complex @ A @ B ) )
% 5.44/5.61 = ( plus_plus_complex @ ( times_times_complex @ X @ ( minus_minus_complex @ Y @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X @ A ) @ B ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_diff_mult
% 5.44/5.61 thf(fact_843_mult__diff__mult,axiom,
% 5.44/5.61 ! [X: real,Y: real,A: real,B: real] :
% 5.44/5.61 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 5.44/5.61 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_diff_mult
% 5.44/5.61 thf(fact_844_mult__diff__mult,axiom,
% 5.44/5.61 ! [X: int,Y: int,A: int,B: int] :
% 5.44/5.61 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 5.44/5.61 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % mult_diff_mult
% 5.44/5.61 thf(fact_845_diff__less__Suc,axiom,
% 5.44/5.61 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 5.44/5.61
% 5.44/5.61 % diff_less_Suc
% 5.44/5.61 thf(fact_846_Suc__diff__Suc,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_nat @ N2 @ M )
% 5.44/5.61 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.61 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_diff_Suc
% 5.44/5.61 thf(fact_847_Suc__diff__le,axiom,
% 5.44/5.61 ! [N2: nat,M: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.61 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.44/5.61 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.61
% 5.44/5.61 % Suc_diff_le
% 5.44/5.61 thf(fact_848_less__diff__iff,axiom,
% 5.44/5.61 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.61 ( ( ord_less_eq_nat @ K @ M )
% 5.44/5.61 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.61 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.44/5.61 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_diff_iff
% 5.44/5.62 thf(fact_849_diff__less__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_nat @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_nat @ C @ A )
% 5.44/5.62 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_less_mono
% 5.44/5.62 thf(fact_850_less__diff__conv,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.62 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.44/5.62 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_diff_conv
% 5.44/5.62 thf(fact_851_add__diff__inverse__nat,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ~ ( ord_less_nat @ M @ N2 )
% 5.44/5.62 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.62 = M ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_inverse_nat
% 5.44/5.62 thf(fact_852_le__diff__conv,axiom,
% 5.44/5.62 ! [J: nat,K: nat,I2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.44/5.62 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_diff_conv
% 5.44/5.62 thf(fact_853_Nat_Ole__diff__conv2,axiom,
% 5.44/5.62 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.62 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.44/5.62 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % Nat.le_diff_conv2
% 5.44/5.62 thf(fact_854_Nat_Odiff__add__assoc,axiom,
% 5.44/5.62 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.62 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.44/5.62 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % Nat.diff_add_assoc
% 5.44/5.62 thf(fact_855_Nat_Odiff__add__assoc2,axiom,
% 5.44/5.62 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.62 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 5.44/5.62 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % Nat.diff_add_assoc2
% 5.44/5.62 thf(fact_856_Nat_Ole__imp__diff__is__add,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.62 => ( ( ( minus_minus_nat @ J @ I2 )
% 5.44/5.62 = K )
% 5.44/5.62 = ( J
% 5.44/5.62 = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % Nat.le_imp_diff_is_add
% 5.44/5.62 thf(fact_857_diff__Suc__eq__diff__pred,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.44/5.62 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_Suc_eq_diff_pred
% 5.44/5.62 thf(fact_858_nat__minus__add__max,axiom,
% 5.44/5.62 ! [N2: nat,M: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 5.44/5.62 = ( ord_max_nat @ N2 @ M ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_minus_add_max
% 5.44/5.62 thf(fact_859_vebt__mint_Osimps_I2_J,axiom,
% 5.44/5.62 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.44/5.62 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.44/5.62 = none_nat ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_mint.simps(2)
% 5.44/5.62 thf(fact_860_vebt__maxt_Osimps_I2_J,axiom,
% 5.44/5.62 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.44/5.62 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.44/5.62 = none_nat ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_maxt.simps(2)
% 5.44/5.62 thf(fact_861_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.44/5.62 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.44/5.62 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.44/5.62 = none_P5556105721700978146at_nat ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.simps(2)
% 5.44/5.62 thf(fact_862_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.44/5.62 ! [Uw: num > num > num,V: num] :
% 5.44/5.62 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.44/5.62 = none_num ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.simps(2)
% 5.44/5.62 thf(fact_863_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.44/5.62 ! [Uw: nat > nat > nat,V: nat] :
% 5.44/5.62 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.44/5.62 = none_nat ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.simps(2)
% 5.44/5.62 thf(fact_864_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.44/5.62 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 5.44/5.62 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 5.44/5.62 = Y )
% 5.44/5.62 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.44/5.62 => ( Y != none_P5556105721700978146at_nat ) )
% 5.44/5.62 => ( ( ? [V2: product_prod_nat_nat] :
% 5.44/5.62 ( Xa2
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.44/5.62 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.44/5.62 => ( Y != none_P5556105721700978146at_nat ) ) )
% 5.44/5.62 => ~ ! [A3: product_prod_nat_nat] :
% 5.44/5.62 ( ( Xa2
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.44/5.62 => ! [B3: product_prod_nat_nat] :
% 5.44/5.62 ( ( Xb
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.44/5.62 => ( Y
% 5.44/5.62 != ( some_P7363390416028606310at_nat @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.elims
% 5.44/5.62 thf(fact_865_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.44/5.62 ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y: option_num] :
% 5.44/5.62 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 5.44/5.62 = Y )
% 5.44/5.62 => ( ( ( Xa2 = none_num )
% 5.44/5.62 => ( Y != none_num ) )
% 5.44/5.62 => ( ( ? [V2: num] :
% 5.44/5.62 ( Xa2
% 5.44/5.62 = ( some_num @ V2 ) )
% 5.44/5.62 => ( ( Xb = none_num )
% 5.44/5.62 => ( Y != none_num ) ) )
% 5.44/5.62 => ~ ! [A3: num] :
% 5.44/5.62 ( ( Xa2
% 5.44/5.62 = ( some_num @ A3 ) )
% 5.44/5.62 => ! [B3: num] :
% 5.44/5.62 ( ( Xb
% 5.44/5.62 = ( some_num @ B3 ) )
% 5.44/5.62 => ( Y
% 5.44/5.62 != ( some_num @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.elims
% 5.44/5.62 thf(fact_866_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.44/5.62 ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y: option_nat] :
% 5.44/5.62 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 5.44/5.62 = Y )
% 5.44/5.62 => ( ( ( Xa2 = none_nat )
% 5.44/5.62 => ( Y != none_nat ) )
% 5.44/5.62 => ( ( ? [V2: nat] :
% 5.44/5.62 ( Xa2
% 5.44/5.62 = ( some_nat @ V2 ) )
% 5.44/5.62 => ( ( Xb = none_nat )
% 5.44/5.62 => ( Y != none_nat ) ) )
% 5.44/5.62 => ~ ! [A3: nat] :
% 5.44/5.62 ( ( Xa2
% 5.44/5.62 = ( some_nat @ A3 ) )
% 5.44/5.62 => ! [B3: nat] :
% 5.44/5.62 ( ( Xb
% 5.44/5.62 = ( some_nat @ B3 ) )
% 5.44/5.62 => ( Y
% 5.44/5.62 != ( some_nat @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.elims
% 5.44/5.62 thf(fact_867_less__diff__conv2,axiom,
% 5.44/5.62 ! [K: nat,J: nat,I2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ K @ J )
% 5.44/5.62 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.44/5.62 = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_diff_conv2
% 5.44/5.62 thf(fact_868_nat__eq__add__iff1,axiom,
% 5.44/5.62 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ J @ I2 )
% 5.44/5.62 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.44/5.62 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 5.44/5.62 = N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_eq_add_iff1
% 5.44/5.62 thf(fact_869_nat__eq__add__iff2,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.62 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.44/5.62 = ( M
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_eq_add_iff2
% 5.44/5.62 thf(fact_870_nat__le__add__iff1,axiom,
% 5.44/5.62 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ J @ I2 )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.44/5.62 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_le_add_iff1
% 5.44/5.62 thf(fact_871_nat__le__add__iff2,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.44/5.62 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_le_add_iff2
% 5.44/5.62 thf(fact_872_nat__diff__add__eq1,axiom,
% 5.44/5.62 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ J @ I2 )
% 5.44/5.62 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.44/5.62 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_diff_add_eq1
% 5.44/5.62 thf(fact_873_nat__diff__add__eq2,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.62 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.44/5.62 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_diff_add_eq2
% 5.44/5.62 thf(fact_874_max_Oleft__commute,axiom,
% 5.44/5.62 ! [B: nat,A: nat,C: nat] :
% 5.44/5.62 ( ( ord_max_nat @ B @ ( ord_max_nat @ A @ C ) )
% 5.44/5.62 = ( ord_max_nat @ A @ ( ord_max_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.left_commute
% 5.44/5.62 thf(fact_875_max_Oleft__commute,axiom,
% 5.44/5.62 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.44/5.62 ( ( ord_ma741700101516333627d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ C ) )
% 5.44/5.62 = ( ord_ma741700101516333627d_enat @ A @ ( ord_ma741700101516333627d_enat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.left_commute
% 5.44/5.62 thf(fact_876_max_Oleft__commute,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( ord_max_int @ B @ ( ord_max_int @ A @ C ) )
% 5.44/5.62 = ( ord_max_int @ A @ ( ord_max_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.left_commute
% 5.44/5.62 thf(fact_877_max_Oleft__commute,axiom,
% 5.44/5.62 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.62 ( ( ord_max_Code_integer @ B @ ( ord_max_Code_integer @ A @ C ) )
% 5.44/5.62 = ( ord_max_Code_integer @ A @ ( ord_max_Code_integer @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.left_commute
% 5.44/5.62 thf(fact_878_max_Ocommute,axiom,
% 5.44/5.62 ( ord_max_nat
% 5.44/5.62 = ( ^ [A4: nat,B4: nat] : ( ord_max_nat @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.commute
% 5.44/5.62 thf(fact_879_max_Ocommute,axiom,
% 5.44/5.62 ( ord_ma741700101516333627d_enat
% 5.44/5.62 = ( ^ [A4: extended_enat,B4: extended_enat] : ( ord_ma741700101516333627d_enat @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.commute
% 5.44/5.62 thf(fact_880_max_Ocommute,axiom,
% 5.44/5.62 ( ord_max_int
% 5.44/5.62 = ( ^ [A4: int,B4: int] : ( ord_max_int @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.commute
% 5.44/5.62 thf(fact_881_max_Ocommute,axiom,
% 5.44/5.62 ( ord_max_Code_integer
% 5.44/5.62 = ( ^ [A4: code_integer,B4: code_integer] : ( ord_max_Code_integer @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.commute
% 5.44/5.62 thf(fact_882_max_Oassoc,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_max_nat @ ( ord_max_nat @ A @ B ) @ C )
% 5.44/5.62 = ( ord_max_nat @ A @ ( ord_max_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.assoc
% 5.44/5.62 thf(fact_883_max_Oassoc,axiom,
% 5.44/5.62 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.62 ( ( ord_ma741700101516333627d_enat @ ( ord_ma741700101516333627d_enat @ A @ B ) @ C )
% 5.44/5.62 = ( ord_ma741700101516333627d_enat @ A @ ( ord_ma741700101516333627d_enat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.assoc
% 5.44/5.62 thf(fact_884_max_Oassoc,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_max_int @ ( ord_max_int @ A @ B ) @ C )
% 5.44/5.62 = ( ord_max_int @ A @ ( ord_max_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.assoc
% 5.44/5.62 thf(fact_885_max_Oassoc,axiom,
% 5.44/5.62 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.62 ( ( ord_max_Code_integer @ ( ord_max_Code_integer @ A @ B ) @ C )
% 5.44/5.62 = ( ord_max_Code_integer @ A @ ( ord_max_Code_integer @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.assoc
% 5.44/5.62 thf(fact_886_power2__commute,axiom,
% 5.44/5.62 ! [X: complex,Y: complex] :
% 5.44/5.62 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.62 = ( power_power_complex @ ( minus_minus_complex @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power2_commute
% 5.44/5.62 thf(fact_887_power2__commute,axiom,
% 5.44/5.62 ! [X: real,Y: real] :
% 5.44/5.62 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.62 = ( power_power_real @ ( minus_minus_real @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power2_commute
% 5.44/5.62 thf(fact_888_power2__commute,axiom,
% 5.44/5.62 ! [X: int,Y: int] :
% 5.44/5.62 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.62 = ( power_power_int @ ( minus_minus_int @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power2_commute
% 5.44/5.62 thf(fact_889_nat__less__add__iff1,axiom,
% 5.44/5.62 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ J @ I2 )
% 5.44/5.62 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.44/5.62 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_less_add_iff1
% 5.44/5.62 thf(fact_890_nat__less__add__iff2,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.62 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.44/5.62 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_less_add_iff2
% 5.44/5.62 thf(fact_891_diff__le__diff__pow,axiom,
% 5.44/5.62 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.44/5.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_le_diff_pow
% 5.44/5.62 thf(fact_892_power2__diff,axiom,
% 5.44/5.62 ! [X: complex,Y: complex] :
% 5.44/5.62 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.62 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power2_diff
% 5.44/5.62 thf(fact_893_power2__diff,axiom,
% 5.44/5.62 ! [X: real,Y: real] :
% 5.44/5.62 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.62 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power2_diff
% 5.44/5.62 thf(fact_894_power2__diff,axiom,
% 5.44/5.62 ! [X: int,Y: int] :
% 5.44/5.62 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.62 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power2_diff
% 5.44/5.62 thf(fact_895_max_OcoboundedI2,axiom,
% 5.44/5.62 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.44/5.62 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI2
% 5.44/5.62 thf(fact_896_max_OcoboundedI2,axiom,
% 5.44/5.62 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.62 ( ( ord_le3102999989581377725nteger @ C @ B )
% 5.44/5.62 => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI2
% 5.44/5.62 thf(fact_897_max_OcoboundedI2,axiom,
% 5.44/5.62 ! [C: num,B: num,A: num] :
% 5.44/5.62 ( ( ord_less_eq_num @ C @ B )
% 5.44/5.62 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI2
% 5.44/5.62 thf(fact_898_max_OcoboundedI2,axiom,
% 5.44/5.62 ! [C: nat,B: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ C @ B )
% 5.44/5.62 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI2
% 5.44/5.62 thf(fact_899_max_OcoboundedI2,axiom,
% 5.44/5.62 ! [C: int,B: int,A: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ C @ B )
% 5.44/5.62 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI2
% 5.44/5.62 thf(fact_900_max_OcoboundedI1,axiom,
% 5.44/5.62 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.44/5.62 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI1
% 5.44/5.62 thf(fact_901_max_OcoboundedI1,axiom,
% 5.44/5.62 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.62 ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.44/5.62 => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI1
% 5.44/5.62 thf(fact_902_max_OcoboundedI1,axiom,
% 5.44/5.62 ! [C: num,A: num,B: num] :
% 5.44/5.62 ( ( ord_less_eq_num @ C @ A )
% 5.44/5.62 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI1
% 5.44/5.62 thf(fact_903_max_OcoboundedI1,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ C @ A )
% 5.44/5.62 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI1
% 5.44/5.62 thf(fact_904_max_OcoboundedI1,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ C @ A )
% 5.44/5.62 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.coboundedI1
% 5.44/5.62 thf(fact_905_max_Oabsorb__iff2,axiom,
% 5.44/5.62 ( ord_le2932123472753598470d_enat
% 5.44/5.62 = ( ^ [A4: extended_enat,B4: extended_enat] :
% 5.44/5.62 ( ( ord_ma741700101516333627d_enat @ A4 @ B4 )
% 5.44/5.62 = B4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff2
% 5.44/5.62 thf(fact_906_max_Oabsorb__iff2,axiom,
% 5.44/5.62 ( ord_le3102999989581377725nteger
% 5.44/5.62 = ( ^ [A4: code_integer,B4: code_integer] :
% 5.44/5.62 ( ( ord_max_Code_integer @ A4 @ B4 )
% 5.44/5.62 = B4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff2
% 5.44/5.62 thf(fact_907_max_Oabsorb__iff2,axiom,
% 5.44/5.62 ( ord_less_eq_num
% 5.44/5.62 = ( ^ [A4: num,B4: num] :
% 5.44/5.62 ( ( ord_max_num @ A4 @ B4 )
% 5.44/5.62 = B4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff2
% 5.44/5.62 thf(fact_908_max_Oabsorb__iff2,axiom,
% 5.44/5.62 ( ord_less_eq_nat
% 5.44/5.62 = ( ^ [A4: nat,B4: nat] :
% 5.44/5.62 ( ( ord_max_nat @ A4 @ B4 )
% 5.44/5.62 = B4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff2
% 5.44/5.62 thf(fact_909_max_Oabsorb__iff2,axiom,
% 5.44/5.62 ( ord_less_eq_int
% 5.44/5.62 = ( ^ [A4: int,B4: int] :
% 5.44/5.62 ( ( ord_max_int @ A4 @ B4 )
% 5.44/5.62 = B4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff2
% 5.44/5.62 thf(fact_910_max_Oabsorb__iff1,axiom,
% 5.44/5.62 ( ord_le2932123472753598470d_enat
% 5.44/5.62 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.44/5.62 ( ( ord_ma741700101516333627d_enat @ A4 @ B4 )
% 5.44/5.62 = A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff1
% 5.44/5.62 thf(fact_911_max_Oabsorb__iff1,axiom,
% 5.44/5.62 ( ord_le3102999989581377725nteger
% 5.44/5.62 = ( ^ [B4: code_integer,A4: code_integer] :
% 5.44/5.62 ( ( ord_max_Code_integer @ A4 @ B4 )
% 5.44/5.62 = A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff1
% 5.44/5.62 thf(fact_912_max_Oabsorb__iff1,axiom,
% 5.44/5.62 ( ord_less_eq_num
% 5.44/5.62 = ( ^ [B4: num,A4: num] :
% 5.44/5.62 ( ( ord_max_num @ A4 @ B4 )
% 5.44/5.62 = A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff1
% 5.44/5.62 thf(fact_913_max_Oabsorb__iff1,axiom,
% 5.44/5.62 ( ord_less_eq_nat
% 5.44/5.62 = ( ^ [B4: nat,A4: nat] :
% 5.44/5.62 ( ( ord_max_nat @ A4 @ B4 )
% 5.44/5.62 = A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff1
% 5.44/5.62 thf(fact_914_max_Oabsorb__iff1,axiom,
% 5.44/5.62 ( ord_less_eq_int
% 5.44/5.62 = ( ^ [B4: int,A4: int] :
% 5.44/5.62 ( ( ord_max_int @ A4 @ B4 )
% 5.44/5.62 = A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.absorb_iff1
% 5.44/5.62 thf(fact_915_le__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 5.44/5.62 = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 5.44/5.62 | ( ord_le2932123472753598470d_enat @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_max_iff_disj
% 5.44/5.62 thf(fact_916_le__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.44/5.62 ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 5.44/5.62 = ( ( ord_le3102999989581377725nteger @ Z @ X )
% 5.44/5.62 | ( ord_le3102999989581377725nteger @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_max_iff_disj
% 5.44/5.62 thf(fact_917_le__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: num,X: num,Y: num] :
% 5.44/5.62 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 5.44/5.62 = ( ( ord_less_eq_num @ Z @ X )
% 5.44/5.62 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_max_iff_disj
% 5.44/5.62 thf(fact_918_le__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: nat,X: nat,Y: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 5.44/5.62 = ( ( ord_less_eq_nat @ Z @ X )
% 5.44/5.62 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_max_iff_disj
% 5.44/5.62 thf(fact_919_le__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: int,X: int,Y: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 5.44/5.62 = ( ( ord_less_eq_int @ Z @ X )
% 5.44/5.62 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_max_iff_disj
% 5.44/5.62 thf(fact_920_max_Ocobounded2,axiom,
% 5.44/5.62 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded2
% 5.44/5.62 thf(fact_921_max_Ocobounded2,axiom,
% 5.44/5.62 ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded2
% 5.44/5.62 thf(fact_922_max_Ocobounded2,axiom,
% 5.44/5.62 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded2
% 5.44/5.62 thf(fact_923_max_Ocobounded2,axiom,
% 5.44/5.62 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded2
% 5.44/5.62 thf(fact_924_max_Ocobounded2,axiom,
% 5.44/5.62 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded2
% 5.44/5.62 thf(fact_925_max_Ocobounded1,axiom,
% 5.44/5.62 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded1
% 5.44/5.62 thf(fact_926_max_Ocobounded1,axiom,
% 5.44/5.62 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded1
% 5.44/5.62 thf(fact_927_max_Ocobounded1,axiom,
% 5.44/5.62 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded1
% 5.44/5.62 thf(fact_928_max_Ocobounded1,axiom,
% 5.44/5.62 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded1
% 5.44/5.62 thf(fact_929_max_Ocobounded1,axiom,
% 5.44/5.62 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.cobounded1
% 5.44/5.62 thf(fact_930_max_Oorder__iff,axiom,
% 5.44/5.62 ( ord_le2932123472753598470d_enat
% 5.44/5.62 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.44/5.62 ( A4
% 5.44/5.62 = ( ord_ma741700101516333627d_enat @ A4 @ B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.order_iff
% 5.44/5.62 thf(fact_931_max_Oorder__iff,axiom,
% 5.44/5.62 ( ord_le3102999989581377725nteger
% 5.44/5.62 = ( ^ [B4: code_integer,A4: code_integer] :
% 5.44/5.62 ( A4
% 5.44/5.62 = ( ord_max_Code_integer @ A4 @ B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.order_iff
% 5.44/5.62 thf(fact_932_max_Oorder__iff,axiom,
% 5.44/5.62 ( ord_less_eq_num
% 5.44/5.62 = ( ^ [B4: num,A4: num] :
% 5.44/5.62 ( A4
% 5.44/5.62 = ( ord_max_num @ A4 @ B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.order_iff
% 5.44/5.62 thf(fact_933_max_Oorder__iff,axiom,
% 5.44/5.62 ( ord_less_eq_nat
% 5.44/5.62 = ( ^ [B4: nat,A4: nat] :
% 5.44/5.62 ( A4
% 5.44/5.62 = ( ord_max_nat @ A4 @ B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.order_iff
% 5.44/5.62 thf(fact_934_max_Oorder__iff,axiom,
% 5.44/5.62 ( ord_less_eq_int
% 5.44/5.62 = ( ^ [B4: int,A4: int] :
% 5.44/5.62 ( A4
% 5.44/5.62 = ( ord_max_int @ A4 @ B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.order_iff
% 5.44/5.62 thf(fact_935_max_OboundedI,axiom,
% 5.44/5.62 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.44/5.62 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.44/5.62 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedI
% 5.44/5.62 thf(fact_936_max_OboundedI,axiom,
% 5.44/5.62 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.62 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.44/5.62 => ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.44/5.62 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedI
% 5.44/5.62 thf(fact_937_max_OboundedI,axiom,
% 5.44/5.62 ! [B: num,A: num,C: num] :
% 5.44/5.62 ( ( ord_less_eq_num @ B @ A )
% 5.44/5.62 => ( ( ord_less_eq_num @ C @ A )
% 5.44/5.62 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedI
% 5.44/5.62 thf(fact_938_max_OboundedI,axiom,
% 5.44/5.62 ! [B: nat,A: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.62 => ( ( ord_less_eq_nat @ C @ A )
% 5.44/5.62 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedI
% 5.44/5.62 thf(fact_939_max_OboundedI,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.62 => ( ( ord_less_eq_int @ C @ A )
% 5.44/5.62 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedI
% 5.44/5.62 thf(fact_940_max_OboundedE,axiom,
% 5.44/5.62 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.44/5.62 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedE
% 5.44/5.62 thf(fact_941_max_OboundedE,axiom,
% 5.44/5.62 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.44/5.62 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.44/5.62 => ~ ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedE
% 5.44/5.62 thf(fact_942_max_OboundedE,axiom,
% 5.44/5.62 ! [B: num,C: num,A: num] :
% 5.44/5.62 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.44/5.62 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedE
% 5.44/5.62 thf(fact_943_max_OboundedE,axiom,
% 5.44/5.62 ! [B: nat,C: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.62 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedE
% 5.44/5.62 thf(fact_944_max_OboundedE,axiom,
% 5.44/5.62 ! [B: int,C: int,A: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.44/5.62 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.boundedE
% 5.44/5.62 thf(fact_945_max_OorderI,axiom,
% 5.44/5.62 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.44/5.62 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderI
% 5.44/5.62 thf(fact_946_max_OorderI,axiom,
% 5.44/5.62 ! [A: code_integer,B: code_integer] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( ord_max_Code_integer @ A @ B ) )
% 5.44/5.62 => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderI
% 5.44/5.62 thf(fact_947_max_OorderI,axiom,
% 5.44/5.62 ! [A: num,B: num] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( ord_max_num @ A @ B ) )
% 5.44/5.62 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderI
% 5.44/5.62 thf(fact_948_max_OorderI,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( ord_max_nat @ A @ B ) )
% 5.44/5.62 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderI
% 5.44/5.62 thf(fact_949_max_OorderI,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( ord_max_int @ A @ B ) )
% 5.44/5.62 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderI
% 5.44/5.62 thf(fact_950_max_OorderE,axiom,
% 5.44/5.62 ! [B: extended_enat,A: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.44/5.62 => ( A
% 5.44/5.62 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderE
% 5.44/5.62 thf(fact_951_max_OorderE,axiom,
% 5.44/5.62 ! [B: code_integer,A: code_integer] :
% 5.44/5.62 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.44/5.62 => ( A
% 5.44/5.62 = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderE
% 5.44/5.62 thf(fact_952_max_OorderE,axiom,
% 5.44/5.62 ! [B: num,A: num] :
% 5.44/5.62 ( ( ord_less_eq_num @ B @ A )
% 5.44/5.62 => ( A
% 5.44/5.62 = ( ord_max_num @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderE
% 5.44/5.62 thf(fact_953_max_OorderE,axiom,
% 5.44/5.62 ! [B: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.62 => ( A
% 5.44/5.62 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderE
% 5.44/5.62 thf(fact_954_max_OorderE,axiom,
% 5.44/5.62 ! [B: int,A: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.62 => ( A
% 5.44/5.62 = ( ord_max_int @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.orderE
% 5.44/5.62 thf(fact_955_max_Omono,axiom,
% 5.44/5.62 ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.44/5.62 => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 5.44/5.62 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.mono
% 5.44/5.62 thf(fact_956_max_Omono,axiom,
% 5.44/5.62 ! [C: code_integer,A: code_integer,D: code_integer,B: code_integer] :
% 5.44/5.62 ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.44/5.62 => ( ( ord_le3102999989581377725nteger @ D @ B )
% 5.44/5.62 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C @ D ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.mono
% 5.44/5.62 thf(fact_957_max_Omono,axiom,
% 5.44/5.62 ! [C: num,A: num,D: num,B: num] :
% 5.44/5.62 ( ( ord_less_eq_num @ C @ A )
% 5.44/5.62 => ( ( ord_less_eq_num @ D @ B )
% 5.44/5.62 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.mono
% 5.44/5.62 thf(fact_958_max_Omono,axiom,
% 5.44/5.62 ! [C: nat,A: nat,D: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ C @ A )
% 5.44/5.62 => ( ( ord_less_eq_nat @ D @ B )
% 5.44/5.62 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.mono
% 5.44/5.62 thf(fact_959_max_Omono,axiom,
% 5.44/5.62 ! [C: int,A: int,D: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ C @ A )
% 5.44/5.62 => ( ( ord_less_eq_int @ D @ B )
% 5.44/5.62 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.mono
% 5.44/5.62 thf(fact_960_less__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.44/5.62 ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 5.44/5.62 = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 5.44/5.62 | ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_max_iff_disj
% 5.44/5.62 thf(fact_961_less__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 5.44/5.62 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 5.44/5.62 = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 5.44/5.62 | ( ord_le72135733267957522d_enat @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_max_iff_disj
% 5.44/5.62 thf(fact_962_less__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: real,X: real,Y: real] :
% 5.44/5.62 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 5.44/5.62 = ( ( ord_less_real @ Z @ X )
% 5.44/5.62 | ( ord_less_real @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_max_iff_disj
% 5.44/5.62 thf(fact_963_less__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: num,X: num,Y: num] :
% 5.44/5.62 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 5.44/5.62 = ( ( ord_less_num @ Z @ X )
% 5.44/5.62 | ( ord_less_num @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_max_iff_disj
% 5.44/5.62 thf(fact_964_less__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: nat,X: nat,Y: nat] :
% 5.44/5.62 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 5.44/5.62 = ( ( ord_less_nat @ Z @ X )
% 5.44/5.62 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_max_iff_disj
% 5.44/5.62 thf(fact_965_less__max__iff__disj,axiom,
% 5.44/5.62 ! [Z: int,X: int,Y: int] :
% 5.44/5.62 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 5.44/5.62 = ( ( ord_less_int @ Z @ X )
% 5.44/5.62 | ( ord_less_int @ Z @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_max_iff_disj
% 5.44/5.62 thf(fact_966_max_Ostrict__boundedE,axiom,
% 5.44/5.62 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.44/5.62 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.44/5.62 => ~ ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_boundedE
% 5.44/5.62 thf(fact_967_max_Ostrict__boundedE,axiom,
% 5.44/5.62 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.44/5.62 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.44/5.62 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_boundedE
% 5.44/5.62 thf(fact_968_max_Ostrict__boundedE,axiom,
% 5.44/5.62 ! [B: real,C: real,A: real] :
% 5.44/5.62 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_less_real @ B @ A )
% 5.44/5.62 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_boundedE
% 5.44/5.62 thf(fact_969_max_Ostrict__boundedE,axiom,
% 5.44/5.62 ! [B: num,C: num,A: num] :
% 5.44/5.62 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_less_num @ B @ A )
% 5.44/5.62 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_boundedE
% 5.44/5.62 thf(fact_970_max_Ostrict__boundedE,axiom,
% 5.44/5.62 ! [B: nat,C: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_less_nat @ B @ A )
% 5.44/5.62 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_boundedE
% 5.44/5.62 thf(fact_971_max_Ostrict__boundedE,axiom,
% 5.44/5.62 ! [B: int,C: int,A: int] :
% 5.44/5.62 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.44/5.62 => ~ ( ( ord_less_int @ B @ A )
% 5.44/5.62 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_boundedE
% 5.44/5.62 thf(fact_972_max_Ostrict__order__iff,axiom,
% 5.44/5.62 ( ord_le6747313008572928689nteger
% 5.44/5.62 = ( ^ [B4: code_integer,A4: code_integer] :
% 5.44/5.62 ( ( A4
% 5.44/5.62 = ( ord_max_Code_integer @ A4 @ B4 ) )
% 5.44/5.62 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_order_iff
% 5.44/5.62 thf(fact_973_max_Ostrict__order__iff,axiom,
% 5.44/5.62 ( ord_le72135733267957522d_enat
% 5.44/5.62 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.44/5.62 ( ( A4
% 5.44/5.62 = ( ord_ma741700101516333627d_enat @ A4 @ B4 ) )
% 5.44/5.62 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_order_iff
% 5.44/5.62 thf(fact_974_max_Ostrict__order__iff,axiom,
% 5.44/5.62 ( ord_less_real
% 5.44/5.62 = ( ^ [B4: real,A4: real] :
% 5.44/5.62 ( ( A4
% 5.44/5.62 = ( ord_max_real @ A4 @ B4 ) )
% 5.44/5.62 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_order_iff
% 5.44/5.62 thf(fact_975_max_Ostrict__order__iff,axiom,
% 5.44/5.62 ( ord_less_num
% 5.44/5.62 = ( ^ [B4: num,A4: num] :
% 5.44/5.62 ( ( A4
% 5.44/5.62 = ( ord_max_num @ A4 @ B4 ) )
% 5.44/5.62 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_order_iff
% 5.44/5.62 thf(fact_976_max_Ostrict__order__iff,axiom,
% 5.44/5.62 ( ord_less_nat
% 5.44/5.62 = ( ^ [B4: nat,A4: nat] :
% 5.44/5.62 ( ( A4
% 5.44/5.62 = ( ord_max_nat @ A4 @ B4 ) )
% 5.44/5.62 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_order_iff
% 5.44/5.62 thf(fact_977_max_Ostrict__order__iff,axiom,
% 5.44/5.62 ( ord_less_int
% 5.44/5.62 = ( ^ [B4: int,A4: int] :
% 5.44/5.62 ( ( A4
% 5.44/5.62 = ( ord_max_int @ A4 @ B4 ) )
% 5.44/5.62 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_order_iff
% 5.44/5.62 thf(fact_978_max_Ostrict__coboundedI1,axiom,
% 5.44/5.62 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.62 ( ( ord_le6747313008572928689nteger @ C @ A )
% 5.44/5.62 => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI1
% 5.44/5.62 thf(fact_979_max_Ostrict__coboundedI1,axiom,
% 5.44/5.62 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.44/5.62 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.44/5.62 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI1
% 5.44/5.62 thf(fact_980_max_Ostrict__coboundedI1,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ C @ A )
% 5.44/5.62 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI1
% 5.44/5.62 thf(fact_981_max_Ostrict__coboundedI1,axiom,
% 5.44/5.62 ! [C: num,A: num,B: num] :
% 5.44/5.62 ( ( ord_less_num @ C @ A )
% 5.44/5.62 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI1
% 5.44/5.62 thf(fact_982_max_Ostrict__coboundedI1,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ C @ A )
% 5.44/5.62 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI1
% 5.44/5.62 thf(fact_983_max_Ostrict__coboundedI1,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ C @ A )
% 5.44/5.62 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI1
% 5.44/5.62 thf(fact_984_max_Ostrict__coboundedI2,axiom,
% 5.44/5.62 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.62 ( ( ord_le6747313008572928689nteger @ C @ B )
% 5.44/5.62 => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI2
% 5.44/5.62 thf(fact_985_max_Ostrict__coboundedI2,axiom,
% 5.44/5.62 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.44/5.62 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.44/5.62 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI2
% 5.44/5.62 thf(fact_986_max_Ostrict__coboundedI2,axiom,
% 5.44/5.62 ! [C: real,B: real,A: real] :
% 5.44/5.62 ( ( ord_less_real @ C @ B )
% 5.44/5.62 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI2
% 5.44/5.62 thf(fact_987_max_Ostrict__coboundedI2,axiom,
% 5.44/5.62 ! [C: num,B: num,A: num] :
% 5.44/5.62 ( ( ord_less_num @ C @ B )
% 5.44/5.62 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI2
% 5.44/5.62 thf(fact_988_max_Ostrict__coboundedI2,axiom,
% 5.44/5.62 ! [C: nat,B: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_nat @ C @ B )
% 5.44/5.62 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI2
% 5.44/5.62 thf(fact_989_max_Ostrict__coboundedI2,axiom,
% 5.44/5.62 ! [C: int,B: int,A: int] :
% 5.44/5.62 ( ( ord_less_int @ C @ B )
% 5.44/5.62 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max.strict_coboundedI2
% 5.44/5.62 thf(fact_990_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.44/5.62 ( ( ( X = none_P5556105721700978146at_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_991_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 5.44/5.62 ( ( ( X = none_P5556105721700978146at_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: product_prod_nat_nat,B3: nat] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_nat @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_992_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 5.44/5.62 ( ( ( X = none_P5556105721700978146at_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_num )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: product_prod_nat_nat,B3: num] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_num @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_993_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.44/5.62 ( ( ( X = none_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: nat,B3: product_prod_nat_nat] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_nat @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_994_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option_nat,P: option_nat > option_nat > $o,Y: option_nat] :
% 5.44/5.62 ( ( ( X = none_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: nat,B3: nat] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_nat @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_nat @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_995_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option_nat,P: option_nat > option_num > $o,Y: option_num] :
% 5.44/5.62 ( ( ( X = none_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_num )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: nat,B3: num] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_nat @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_num @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_996_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.44/5.62 ( ( ( X = none_num )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: num,B3: product_prod_nat_nat] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_num @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_997_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option_num,P: option_num > option_nat > $o,Y: option_nat] :
% 5.44/5.62 ( ( ( X = none_num )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_nat )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: num,B3: nat] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_num @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_nat @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_998_combine__options__cases,axiom,
% 5.44/5.62 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 5.44/5.62 ( ( ( X = none_num )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ( ( Y = none_num )
% 5.44/5.62 => ( P @ X @ Y ) )
% 5.44/5.62 => ( ! [A3: num,B3: num] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( some_num @ A3 ) )
% 5.44/5.62 => ( ( Y
% 5.44/5.62 = ( some_num @ B3 ) )
% 5.44/5.62 => ( P @ X @ Y ) ) )
% 5.44/5.62 => ( P @ X @ Y ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_options_cases
% 5.44/5.62 thf(fact_999_split__option__all,axiom,
% 5.44/5.62 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.44/5.62 ! [X7: option4927543243414619207at_nat] : ( P2 @ X7 ) )
% 5.44/5.62 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.44/5.62 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.44/5.62 & ! [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % split_option_all
% 5.44/5.62 thf(fact_1000_split__option__all,axiom,
% 5.44/5.62 ( ( ^ [P2: option_nat > $o] :
% 5.44/5.62 ! [X7: option_nat] : ( P2 @ X7 ) )
% 5.44/5.62 = ( ^ [P3: option_nat > $o] :
% 5.44/5.62 ( ( P3 @ none_nat )
% 5.44/5.62 & ! [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % split_option_all
% 5.44/5.62 thf(fact_1001_split__option__all,axiom,
% 5.44/5.62 ( ( ^ [P2: option_num > $o] :
% 5.44/5.62 ! [X7: option_num] : ( P2 @ X7 ) )
% 5.44/5.62 = ( ^ [P3: option_num > $o] :
% 5.44/5.62 ( ( P3 @ none_num )
% 5.44/5.62 & ! [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % split_option_all
% 5.44/5.62 thf(fact_1002_split__option__ex,axiom,
% 5.44/5.62 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.44/5.62 ? [X7: option4927543243414619207at_nat] : ( P2 @ X7 ) )
% 5.44/5.62 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.44/5.62 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.44/5.62 | ? [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % split_option_ex
% 5.44/5.62 thf(fact_1003_split__option__ex,axiom,
% 5.44/5.62 ( ( ^ [P2: option_nat > $o] :
% 5.44/5.62 ? [X7: option_nat] : ( P2 @ X7 ) )
% 5.44/5.62 = ( ^ [P3: option_nat > $o] :
% 5.44/5.62 ( ( P3 @ none_nat )
% 5.44/5.62 | ? [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % split_option_ex
% 5.44/5.62 thf(fact_1004_split__option__ex,axiom,
% 5.44/5.62 ( ( ^ [P2: option_num > $o] :
% 5.44/5.62 ? [X7: option_num] : ( P2 @ X7 ) )
% 5.44/5.62 = ( ^ [P3: option_num > $o] :
% 5.44/5.62 ( ( P3 @ none_num )
% 5.44/5.62 | ? [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % split_option_ex
% 5.44/5.62 thf(fact_1005_option_Oexhaust,axiom,
% 5.44/5.62 ! [Y: option4927543243414619207at_nat] :
% 5.44/5.62 ( ( Y != none_P5556105721700978146at_nat )
% 5.44/5.62 => ~ ! [X23: product_prod_nat_nat] :
% 5.44/5.62 ( Y
% 5.44/5.62 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.exhaust
% 5.44/5.62 thf(fact_1006_option_Oexhaust,axiom,
% 5.44/5.62 ! [Y: option_nat] :
% 5.44/5.62 ( ( Y != none_nat )
% 5.44/5.62 => ~ ! [X23: nat] :
% 5.44/5.62 ( Y
% 5.44/5.62 != ( some_nat @ X23 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.exhaust
% 5.44/5.62 thf(fact_1007_option_Oexhaust,axiom,
% 5.44/5.62 ! [Y: option_num] :
% 5.44/5.62 ( ( Y != none_num )
% 5.44/5.62 => ~ ! [X23: num] :
% 5.44/5.62 ( Y
% 5.44/5.62 != ( some_num @ X23 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.exhaust
% 5.44/5.62 thf(fact_1008_option_OdiscI,axiom,
% 5.44/5.62 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.44/5.62 ( ( Option
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.44/5.62 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.discI
% 5.44/5.62 thf(fact_1009_option_OdiscI,axiom,
% 5.44/5.62 ! [Option: option_nat,X22: nat] :
% 5.44/5.62 ( ( Option
% 5.44/5.62 = ( some_nat @ X22 ) )
% 5.44/5.62 => ( Option != none_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.discI
% 5.44/5.62 thf(fact_1010_option_OdiscI,axiom,
% 5.44/5.62 ! [Option: option_num,X22: num] :
% 5.44/5.62 ( ( Option
% 5.44/5.62 = ( some_num @ X22 ) )
% 5.44/5.62 => ( Option != none_num ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.discI
% 5.44/5.62 thf(fact_1011_option_Odistinct_I1_J,axiom,
% 5.44/5.62 ! [X22: product_prod_nat_nat] :
% 5.44/5.62 ( none_P5556105721700978146at_nat
% 5.44/5.62 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.distinct(1)
% 5.44/5.62 thf(fact_1012_option_Odistinct_I1_J,axiom,
% 5.44/5.62 ! [X22: nat] :
% 5.44/5.62 ( none_nat
% 5.44/5.62 != ( some_nat @ X22 ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.distinct(1)
% 5.44/5.62 thf(fact_1013_option_Odistinct_I1_J,axiom,
% 5.44/5.62 ! [X22: num] :
% 5.44/5.62 ( none_num
% 5.44/5.62 != ( some_num @ X22 ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.distinct(1)
% 5.44/5.62 thf(fact_1014_option_Osel,axiom,
% 5.44/5.62 ! [X22: product_prod_nat_nat] :
% 5.44/5.62 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.44/5.62 = X22 ) ).
% 5.44/5.62
% 5.44/5.62 % option.sel
% 5.44/5.62 thf(fact_1015_option_Osel,axiom,
% 5.44/5.62 ! [X22: nat] :
% 5.44/5.62 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.44/5.62 = X22 ) ).
% 5.44/5.62
% 5.44/5.62 % option.sel
% 5.44/5.62 thf(fact_1016_option_Osel,axiom,
% 5.44/5.62 ! [X22: num] :
% 5.44/5.62 ( ( the_num @ ( some_num @ X22 ) )
% 5.44/5.62 = X22 ) ).
% 5.44/5.62
% 5.44/5.62 % option.sel
% 5.44/5.62 thf(fact_1017_option_Oexpand,axiom,
% 5.44/5.62 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.44/5.62 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.44/5.62 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.44/5.62 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.44/5.62 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.44/5.62 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.44/5.62 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.44/5.62 => ( Option = Option2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.expand
% 5.44/5.62 thf(fact_1018_option_Oexpand,axiom,
% 5.44/5.62 ! [Option: option_nat,Option2: option_nat] :
% 5.44/5.62 ( ( ( Option = none_nat )
% 5.44/5.62 = ( Option2 = none_nat ) )
% 5.44/5.62 => ( ( ( Option != none_nat )
% 5.44/5.62 => ( ( Option2 != none_nat )
% 5.44/5.62 => ( ( the_nat @ Option )
% 5.44/5.62 = ( the_nat @ Option2 ) ) ) )
% 5.44/5.62 => ( Option = Option2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.expand
% 5.44/5.62 thf(fact_1019_option_Oexpand,axiom,
% 5.44/5.62 ! [Option: option_num,Option2: option_num] :
% 5.44/5.62 ( ( ( Option = none_num )
% 5.44/5.62 = ( Option2 = none_num ) )
% 5.44/5.62 => ( ( ( Option != none_num )
% 5.44/5.62 => ( ( Option2 != none_num )
% 5.44/5.62 => ( ( the_num @ Option )
% 5.44/5.62 = ( the_num @ Option2 ) ) ) )
% 5.44/5.62 => ( Option = Option2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.expand
% 5.44/5.62 thf(fact_1020_option_Oexhaust__sel,axiom,
% 5.44/5.62 ! [Option: option4927543243414619207at_nat] :
% 5.44/5.62 ( ( Option != none_P5556105721700978146at_nat )
% 5.44/5.62 => ( Option
% 5.44/5.62 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.exhaust_sel
% 5.44/5.62 thf(fact_1021_option_Oexhaust__sel,axiom,
% 5.44/5.62 ! [Option: option_nat] :
% 5.44/5.62 ( ( Option != none_nat )
% 5.44/5.62 => ( Option
% 5.44/5.62 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.exhaust_sel
% 5.44/5.62 thf(fact_1022_option_Oexhaust__sel,axiom,
% 5.44/5.62 ! [Option: option_num] :
% 5.44/5.62 ( ( Option != none_num )
% 5.44/5.62 => ( Option
% 5.44/5.62 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % option.exhaust_sel
% 5.44/5.62 thf(fact_1023_le__add__diff__inverse,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.62 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_diff_inverse
% 5.44/5.62 thf(fact_1024_le__add__diff__inverse,axiom,
% 5.44/5.62 ! [B: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.62 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_diff_inverse
% 5.44/5.62 thf(fact_1025_le__add__diff__inverse,axiom,
% 5.44/5.62 ! [B: int,A: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.62 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_diff_inverse
% 5.44/5.62 thf(fact_1026_le__add__diff__inverse2,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.62 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_diff_inverse2
% 5.44/5.62 thf(fact_1027_le__add__diff__inverse2,axiom,
% 5.44/5.62 ! [B: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.62 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_diff_inverse2
% 5.44/5.62 thf(fact_1028_le__add__diff__inverse2,axiom,
% 5.44/5.62 ! [B: int,A: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.62 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_diff_inverse2
% 5.44/5.62 thf(fact_1029_mul__def,axiom,
% 5.44/5.62 ( vEBT_VEBT_mul
% 5.44/5.62 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % mul_def
% 5.44/5.62 thf(fact_1030_add__def,axiom,
% 5.44/5.62 ( vEBT_VEBT_add
% 5.44/5.62 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_def
% 5.44/5.62 thf(fact_1031_Suc__double__not__eq__double,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.62 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.62
% 5.44/5.62 % Suc_double_not_eq_double
% 5.44/5.62 thf(fact_1032_double__not__eq__Suc__double,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.44/5.62 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % double_not_eq_Suc_double
% 5.44/5.62 thf(fact_1033_div__by__1,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_1
% 5.44/5.62 thf(fact_1034_div__by__1,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( divide_divide_real @ A @ one_one_real )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_1
% 5.44/5.62 thf(fact_1035_div__by__1,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( divide_divide_int @ A @ one_one_int )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_1
% 5.44/5.62 thf(fact_1036_div__by__1,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_1
% 5.44/5.62 thf(fact_1037_div__by__1,axiom,
% 5.44/5.62 ! [A: code_integer] :
% 5.44/5.62 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_1
% 5.44/5.62 thf(fact_1038_add__diff__cancel,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel
% 5.44/5.62 thf(fact_1039_add__diff__cancel,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel
% 5.44/5.62 thf(fact_1040_add__diff__cancel,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel
% 5.44/5.62 thf(fact_1041_diff__add__cancel,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_cancel
% 5.44/5.62 thf(fact_1042_diff__add__cancel,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_cancel
% 5.44/5.62 thf(fact_1043_diff__add__cancel,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_cancel
% 5.44/5.62 thf(fact_1044_add__diff__cancel__left,axiom,
% 5.44/5.62 ! [C: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ ( plus_plus_complex @ C @ A ) @ ( plus_plus_complex @ C @ B ) )
% 5.44/5.62 = ( minus_minus_complex @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_left
% 5.44/5.62 thf(fact_1045_add__diff__cancel__left,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.44/5.62 = ( minus_minus_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_left
% 5.44/5.62 thf(fact_1046_add__diff__cancel__left,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.44/5.62 = ( minus_minus_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_left
% 5.44/5.62 thf(fact_1047_add__diff__cancel__left,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.44/5.62 = ( minus_minus_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_left
% 5.44/5.62 thf(fact_1048_add__diff__cancel__left_H,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ A )
% 5.44/5.62 = B ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_left'
% 5.44/5.62 thf(fact_1049_add__diff__cancel__left_H,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.44/5.62 = B ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_left'
% 5.44/5.62 thf(fact_1050_add__diff__cancel__left_H,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.44/5.62 = B ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_left'
% 5.44/5.62 thf(fact_1051_add__diff__cancel__left_H,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.44/5.62 = B ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_left'
% 5.44/5.62 thf(fact_1052_add__shift,axiom,
% 5.44/5.62 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ X @ Y )
% 5.44/5.62 = Z )
% 5.44/5.62 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.44/5.62 = ( some_nat @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_shift
% 5.44/5.62 thf(fact_1053_mul__shift,axiom,
% 5.44/5.62 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.62 ( ( ( times_times_nat @ X @ Y )
% 5.44/5.62 = Z )
% 5.44/5.62 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.44/5.62 = ( some_nat @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mul_shift
% 5.44/5.62 thf(fact_1054_add__right__cancel,axiom,
% 5.44/5.62 ! [B: complex,A: complex,C: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ B @ A )
% 5.44/5.62 = ( plus_plus_complex @ C @ A ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_cancel
% 5.44/5.62 thf(fact_1055_add__right__cancel,axiom,
% 5.44/5.62 ! [B: real,A: real,C: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ B @ A )
% 5.44/5.62 = ( plus_plus_real @ C @ A ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_cancel
% 5.44/5.62 thf(fact_1056_add__right__cancel,axiom,
% 5.44/5.62 ! [B: nat,A: nat,C: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ B @ A )
% 5.44/5.62 = ( plus_plus_nat @ C @ A ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_cancel
% 5.44/5.62 thf(fact_1057_add__right__cancel,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ B @ A )
% 5.44/5.62 = ( plus_plus_int @ C @ A ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_cancel
% 5.44/5.62 thf(fact_1058_add__left__cancel,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ A @ B )
% 5.44/5.62 = ( plus_plus_complex @ A @ C ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_cancel
% 5.44/5.62 thf(fact_1059_add__left__cancel,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ A @ B )
% 5.44/5.62 = ( plus_plus_real @ A @ C ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_cancel
% 5.44/5.62 thf(fact_1060_add__left__cancel,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ A @ B )
% 5.44/5.62 = ( plus_plus_nat @ A @ C ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_cancel
% 5.44/5.62 thf(fact_1061_add__left__cancel,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ A @ B )
% 5.44/5.62 = ( plus_plus_int @ A @ C ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_cancel
% 5.44/5.62 thf(fact_1062_add__le__cancel__right,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.44/5.62 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_cancel_right
% 5.44/5.62 thf(fact_1063_add__le__cancel__right,axiom,
% 5.44/5.62 ! [A: nat,C: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.62 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_cancel_right
% 5.44/5.62 thf(fact_1064_add__le__cancel__right,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.44/5.62 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_cancel_right
% 5.44/5.62 thf(fact_1065_add__le__cancel__left,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.44/5.62 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_cancel_left
% 5.44/5.62 thf(fact_1066_add__le__cancel__left,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.44/5.62 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_cancel_left
% 5.44/5.62 thf(fact_1067_add__le__cancel__left,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.44/5.62 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_cancel_left
% 5.44/5.62 thf(fact_1068_add__less__cancel__right,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.44/5.62 = ( ord_less_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_cancel_right
% 5.44/5.62 thf(fact_1069_add__less__cancel__right,axiom,
% 5.44/5.62 ! [A: nat,C: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.62 = ( ord_less_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_cancel_right
% 5.44/5.62 thf(fact_1070_add__less__cancel__right,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.44/5.62 = ( ord_less_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_cancel_right
% 5.44/5.62 thf(fact_1071_add__less__cancel__left,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.44/5.62 = ( ord_less_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_cancel_left
% 5.44/5.62 thf(fact_1072_add__less__cancel__left,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.44/5.62 = ( ord_less_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_cancel_left
% 5.44/5.62 thf(fact_1073_add__less__cancel__left,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.44/5.62 = ( ord_less_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_cancel_left
% 5.44/5.62 thf(fact_1074_mult__1,axiom,
% 5.44/5.62 ! [A: extended_enat] :
% 5.44/5.62 ( ( times_7803423173614009249d_enat @ one_on7984719198319812577d_enat @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult_1
% 5.44/5.62 thf(fact_1075_mult__1,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( times_times_complex @ one_one_complex @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult_1
% 5.44/5.62 thf(fact_1076_mult__1,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( times_times_real @ one_one_real @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult_1
% 5.44/5.62 thf(fact_1077_mult__1,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( times_times_nat @ one_one_nat @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult_1
% 5.44/5.62 thf(fact_1078_mult__1,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( times_times_int @ one_one_int @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult_1
% 5.44/5.62 thf(fact_1079_mult_Oright__neutral,axiom,
% 5.44/5.62 ! [A: extended_enat] :
% 5.44/5.62 ( ( times_7803423173614009249d_enat @ A @ one_on7984719198319812577d_enat )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.right_neutral
% 5.44/5.62 thf(fact_1080_mult_Oright__neutral,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( times_times_complex @ A @ one_one_complex )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.right_neutral
% 5.44/5.62 thf(fact_1081_mult_Oright__neutral,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( times_times_real @ A @ one_one_real )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.right_neutral
% 5.44/5.62 thf(fact_1082_mult_Oright__neutral,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( times_times_nat @ A @ one_one_nat )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.right_neutral
% 5.44/5.62 thf(fact_1083_mult_Oright__neutral,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( times_times_int @ A @ one_one_int )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.right_neutral
% 5.44/5.62 thf(fact_1084_add__diff__cancel__right_H,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_right'
% 5.44/5.62 thf(fact_1085_add__diff__cancel__right_H,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_right'
% 5.44/5.62 thf(fact_1086_add__diff__cancel__right_H,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_right'
% 5.44/5.62 thf(fact_1087_add__diff__cancel__right_H,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_right'
% 5.44/5.62 thf(fact_1088_add__diff__cancel__right,axiom,
% 5.44/5.62 ! [A: complex,C: complex,B: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ C ) )
% 5.44/5.62 = ( minus_minus_complex @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_right
% 5.44/5.62 thf(fact_1089_add__diff__cancel__right,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.44/5.62 = ( minus_minus_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_right
% 5.44/5.62 thf(fact_1090_add__diff__cancel__right,axiom,
% 5.44/5.62 ! [A: nat,C: nat,B: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.62 = ( minus_minus_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_right
% 5.44/5.62 thf(fact_1091_add__diff__cancel__right,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.44/5.62 = ( minus_minus_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_cancel_right
% 5.44/5.62 thf(fact_1092_add__diff__assoc__enat,axiom,
% 5.44/5.62 ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 5.44/5.62 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 5.44/5.62 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_assoc_enat
% 5.44/5.62 thf(fact_1093_linorder__neqE__linordered__idom,axiom,
% 5.44/5.62 ! [X: real,Y: real] :
% 5.44/5.62 ( ( X != Y )
% 5.44/5.62 => ( ~ ( ord_less_real @ X @ Y )
% 5.44/5.62 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % linorder_neqE_linordered_idom
% 5.44/5.62 thf(fact_1094_linorder__neqE__linordered__idom,axiom,
% 5.44/5.62 ! [X: int,Y: int] :
% 5.44/5.62 ( ( X != Y )
% 5.44/5.62 => ( ~ ( ord_less_int @ X @ Y )
% 5.44/5.62 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % linorder_neqE_linordered_idom
% 5.44/5.62 thf(fact_1095_mult_Oleft__commute,axiom,
% 5.44/5.62 ! [B: complex,A: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ B @ ( times_times_complex @ A @ C ) )
% 5.44/5.62 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.left_commute
% 5.44/5.62 thf(fact_1096_mult_Oleft__commute,axiom,
% 5.44/5.62 ! [B: real,A: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.44/5.62 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.left_commute
% 5.44/5.62 thf(fact_1097_mult_Oleft__commute,axiom,
% 5.44/5.62 ! [B: nat,A: nat,C: nat] :
% 5.44/5.62 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.44/5.62 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.left_commute
% 5.44/5.62 thf(fact_1098_mult_Oleft__commute,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.44/5.62 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.left_commute
% 5.44/5.62 thf(fact_1099_mult_Ocommute,axiom,
% 5.44/5.62 ( times_times_complex
% 5.44/5.62 = ( ^ [A4: complex,B4: complex] : ( times_times_complex @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.commute
% 5.44/5.62 thf(fact_1100_mult_Ocommute,axiom,
% 5.44/5.62 ( times_times_real
% 5.44/5.62 = ( ^ [A4: real,B4: real] : ( times_times_real @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.commute
% 5.44/5.62 thf(fact_1101_mult_Ocommute,axiom,
% 5.44/5.62 ( times_times_nat
% 5.44/5.62 = ( ^ [A4: nat,B4: nat] : ( times_times_nat @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.commute
% 5.44/5.62 thf(fact_1102_mult_Ocommute,axiom,
% 5.44/5.62 ( times_times_int
% 5.44/5.62 = ( ^ [A4: int,B4: int] : ( times_times_int @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.commute
% 5.44/5.62 thf(fact_1103_mult_Oassoc,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.44/5.62 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.assoc
% 5.44/5.62 thf(fact_1104_mult_Oassoc,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.44/5.62 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.assoc
% 5.44/5.62 thf(fact_1105_mult_Oassoc,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.44/5.62 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.assoc
% 5.44/5.62 thf(fact_1106_mult_Oassoc,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.44/5.62 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult.assoc
% 5.44/5.62 thf(fact_1107_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.44/5.62 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ab_semigroup_mult_class.mult_ac(1)
% 5.44/5.62 thf(fact_1108_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.44/5.62 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ab_semigroup_mult_class.mult_ac(1)
% 5.44/5.62 thf(fact_1109_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.44/5.62 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ab_semigroup_mult_class.mult_ac(1)
% 5.44/5.62 thf(fact_1110_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.44/5.62 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ab_semigroup_mult_class.mult_ac(1)
% 5.44/5.62 thf(fact_1111_add__right__imp__eq,axiom,
% 5.44/5.62 ! [B: complex,A: complex,C: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ B @ A )
% 5.44/5.62 = ( plus_plus_complex @ C @ A ) )
% 5.44/5.62 => ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_imp_eq
% 5.44/5.62 thf(fact_1112_add__right__imp__eq,axiom,
% 5.44/5.62 ! [B: real,A: real,C: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ B @ A )
% 5.44/5.62 = ( plus_plus_real @ C @ A ) )
% 5.44/5.62 => ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_imp_eq
% 5.44/5.62 thf(fact_1113_add__right__imp__eq,axiom,
% 5.44/5.62 ! [B: nat,A: nat,C: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ B @ A )
% 5.44/5.62 = ( plus_plus_nat @ C @ A ) )
% 5.44/5.62 => ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_imp_eq
% 5.44/5.62 thf(fact_1114_add__right__imp__eq,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ B @ A )
% 5.44/5.62 = ( plus_plus_int @ C @ A ) )
% 5.44/5.62 => ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_imp_eq
% 5.44/5.62 thf(fact_1115_add__left__imp__eq,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ A @ B )
% 5.44/5.62 = ( plus_plus_complex @ A @ C ) )
% 5.44/5.62 => ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_imp_eq
% 5.44/5.62 thf(fact_1116_add__left__imp__eq,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ A @ B )
% 5.44/5.62 = ( plus_plus_real @ A @ C ) )
% 5.44/5.62 => ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_imp_eq
% 5.44/5.62 thf(fact_1117_add__left__imp__eq,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ A @ B )
% 5.44/5.62 = ( plus_plus_nat @ A @ C ) )
% 5.44/5.62 => ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_imp_eq
% 5.44/5.62 thf(fact_1118_add__left__imp__eq,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ A @ B )
% 5.44/5.62 = ( plus_plus_int @ A @ C ) )
% 5.44/5.62 => ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_imp_eq
% 5.44/5.62 thf(fact_1119_add_Oleft__commute,axiom,
% 5.44/5.62 ! [B: complex,A: complex,C: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ B @ ( plus_plus_complex @ A @ C ) )
% 5.44/5.62 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.left_commute
% 5.44/5.62 thf(fact_1120_add_Oleft__commute,axiom,
% 5.44/5.62 ! [B: real,A: real,C: real] :
% 5.44/5.62 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.44/5.62 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.left_commute
% 5.44/5.62 thf(fact_1121_add_Oleft__commute,axiom,
% 5.44/5.62 ! [B: nat,A: nat,C: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.44/5.62 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.left_commute
% 5.44/5.62 thf(fact_1122_add_Oleft__commute,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.44/5.62 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.left_commute
% 5.44/5.62 thf(fact_1123_add_Ocommute,axiom,
% 5.44/5.62 ( plus_plus_complex
% 5.44/5.62 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.commute
% 5.44/5.62 thf(fact_1124_add_Ocommute,axiom,
% 5.44/5.62 ( plus_plus_real
% 5.44/5.62 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.commute
% 5.44/5.62 thf(fact_1125_add_Ocommute,axiom,
% 5.44/5.62 ( plus_plus_nat
% 5.44/5.62 = ( ^ [A4: nat,B4: nat] : ( plus_plus_nat @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.commute
% 5.44/5.62 thf(fact_1126_add_Ocommute,axiom,
% 5.44/5.62 ( plus_plus_int
% 5.44/5.62 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ B4 @ A4 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.commute
% 5.44/5.62 thf(fact_1127_add_Oright__cancel,axiom,
% 5.44/5.62 ! [B: complex,A: complex,C: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ B @ A )
% 5.44/5.62 = ( plus_plus_complex @ C @ A ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.right_cancel
% 5.44/5.62 thf(fact_1128_add_Oright__cancel,axiom,
% 5.44/5.62 ! [B: real,A: real,C: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ B @ A )
% 5.44/5.62 = ( plus_plus_real @ C @ A ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.right_cancel
% 5.44/5.62 thf(fact_1129_add_Oright__cancel,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ B @ A )
% 5.44/5.62 = ( plus_plus_int @ C @ A ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.right_cancel
% 5.44/5.62 thf(fact_1130_add_Oleft__cancel,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ A @ B )
% 5.44/5.62 = ( plus_plus_complex @ A @ C ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.left_cancel
% 5.44/5.62 thf(fact_1131_add_Oleft__cancel,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ A @ B )
% 5.44/5.62 = ( plus_plus_real @ A @ C ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.left_cancel
% 5.44/5.62 thf(fact_1132_add_Oleft__cancel,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ A @ B )
% 5.44/5.62 = ( plus_plus_int @ A @ C ) )
% 5.44/5.62 = ( B = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.left_cancel
% 5.44/5.62 thf(fact_1133_add_Oassoc,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.assoc
% 5.44/5.62 thf(fact_1134_add_Oassoc,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.assoc
% 5.44/5.62 thf(fact_1135_add_Oassoc,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.assoc
% 5.44/5.62 thf(fact_1136_add_Oassoc,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add.assoc
% 5.44/5.62 thf(fact_1137_group__cancel_Oadd2,axiom,
% 5.44/5.62 ! [B2: complex,K: complex,B: complex,A: complex] :
% 5.44/5.62 ( ( B2
% 5.44/5.62 = ( plus_plus_complex @ K @ B ) )
% 5.44/5.62 => ( ( plus_plus_complex @ A @ B2 )
% 5.44/5.62 = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.add2
% 5.44/5.62 thf(fact_1138_group__cancel_Oadd2,axiom,
% 5.44/5.62 ! [B2: real,K: real,B: real,A: real] :
% 5.44/5.62 ( ( B2
% 5.44/5.62 = ( plus_plus_real @ K @ B ) )
% 5.44/5.62 => ( ( plus_plus_real @ A @ B2 )
% 5.44/5.62 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.add2
% 5.44/5.62 thf(fact_1139_group__cancel_Oadd2,axiom,
% 5.44/5.62 ! [B2: nat,K: nat,B: nat,A: nat] :
% 5.44/5.62 ( ( B2
% 5.44/5.62 = ( plus_plus_nat @ K @ B ) )
% 5.44/5.62 => ( ( plus_plus_nat @ A @ B2 )
% 5.44/5.62 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.add2
% 5.44/5.62 thf(fact_1140_group__cancel_Oadd2,axiom,
% 5.44/5.62 ! [B2: int,K: int,B: int,A: int] :
% 5.44/5.62 ( ( B2
% 5.44/5.62 = ( plus_plus_int @ K @ B ) )
% 5.44/5.62 => ( ( plus_plus_int @ A @ B2 )
% 5.44/5.62 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.add2
% 5.44/5.62 thf(fact_1141_group__cancel_Oadd1,axiom,
% 5.44/5.62 ! [A2: complex,K: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( A2
% 5.44/5.62 = ( plus_plus_complex @ K @ A ) )
% 5.44/5.62 => ( ( plus_plus_complex @ A2 @ B )
% 5.44/5.62 = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.add1
% 5.44/5.62 thf(fact_1142_group__cancel_Oadd1,axiom,
% 5.44/5.62 ! [A2: real,K: real,A: real,B: real] :
% 5.44/5.62 ( ( A2
% 5.44/5.62 = ( plus_plus_real @ K @ A ) )
% 5.44/5.62 => ( ( plus_plus_real @ A2 @ B )
% 5.44/5.62 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.add1
% 5.44/5.62 thf(fact_1143_group__cancel_Oadd1,axiom,
% 5.44/5.62 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( A2
% 5.44/5.62 = ( plus_plus_nat @ K @ A ) )
% 5.44/5.62 => ( ( plus_plus_nat @ A2 @ B )
% 5.44/5.62 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.add1
% 5.44/5.62 thf(fact_1144_group__cancel_Oadd1,axiom,
% 5.44/5.62 ! [A2: int,K: int,A: int,B: int] :
% 5.44/5.62 ( ( A2
% 5.44/5.62 = ( plus_plus_int @ K @ A ) )
% 5.44/5.62 => ( ( plus_plus_int @ A2 @ B )
% 5.44/5.62 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.add1
% 5.44/5.62 thf(fact_1145_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ( plus_plus_real @ I2 @ K )
% 5.44/5.62 = ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(4)
% 5.44/5.62 thf(fact_1146_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ( plus_plus_nat @ I2 @ K )
% 5.44/5.62 = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(4)
% 5.44/5.62 thf(fact_1147_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ( plus_plus_int @ I2 @ K )
% 5.44/5.62 = ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(4)
% 5.44/5.62 thf(fact_1148_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ab_semigroup_add_class.add_ac(1)
% 5.44/5.62 thf(fact_1149_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ab_semigroup_add_class.add_ac(1)
% 5.44/5.62 thf(fact_1150_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ab_semigroup_add_class.add_ac(1)
% 5.44/5.62 thf(fact_1151_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ab_semigroup_add_class.add_ac(1)
% 5.44/5.62 thf(fact_1152_one__reorient,axiom,
% 5.44/5.62 ! [X: extended_enat] :
% 5.44/5.62 ( ( one_on7984719198319812577d_enat = X )
% 5.44/5.62 = ( X = one_on7984719198319812577d_enat ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_reorient
% 5.44/5.62 thf(fact_1153_one__reorient,axiom,
% 5.44/5.62 ! [X: complex] :
% 5.44/5.62 ( ( one_one_complex = X )
% 5.44/5.62 = ( X = one_one_complex ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_reorient
% 5.44/5.62 thf(fact_1154_one__reorient,axiom,
% 5.44/5.62 ! [X: real] :
% 5.44/5.62 ( ( one_one_real = X )
% 5.44/5.62 = ( X = one_one_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_reorient
% 5.44/5.62 thf(fact_1155_one__reorient,axiom,
% 5.44/5.62 ! [X: nat] :
% 5.44/5.62 ( ( one_one_nat = X )
% 5.44/5.62 = ( X = one_one_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_reorient
% 5.44/5.62 thf(fact_1156_one__reorient,axiom,
% 5.44/5.62 ! [X: int] :
% 5.44/5.62 ( ( one_one_int = X )
% 5.44/5.62 = ( X = one_one_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_reorient
% 5.44/5.62 thf(fact_1157_add__le__imp__le__right,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.44/5.62 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_right
% 5.44/5.62 thf(fact_1158_add__le__imp__le__right,axiom,
% 5.44/5.62 ! [A: nat,C: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.62 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_right
% 5.44/5.62 thf(fact_1159_add__le__imp__le__right,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.44/5.62 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_right
% 5.44/5.62 thf(fact_1160_add__le__imp__le__left,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.44/5.62 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_left
% 5.44/5.62 thf(fact_1161_add__le__imp__le__left,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.44/5.62 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_left
% 5.44/5.62 thf(fact_1162_add__le__imp__le__left,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.44/5.62 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_left
% 5.44/5.62 thf(fact_1163_le__iff__add,axiom,
% 5.44/5.62 ( ord_less_eq_nat
% 5.44/5.62 = ( ^ [A4: nat,B4: nat] :
% 5.44/5.62 ? [C2: nat] :
% 5.44/5.62 ( B4
% 5.44/5.62 = ( plus_plus_nat @ A4 @ C2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_iff_add
% 5.44/5.62 thf(fact_1164_add__right__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.62 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_mono
% 5.44/5.62 thf(fact_1165_add__right__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_mono
% 5.44/5.62 thf(fact_1166_add__right__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.62 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_right_mono
% 5.44/5.62 thf(fact_1167_less__eqE,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ~ ! [C3: nat] :
% 5.44/5.62 ( B
% 5.44/5.62 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_eqE
% 5.44/5.62 thf(fact_1168_add__left__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.62 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_mono
% 5.44/5.62 thf(fact_1169_add__left__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_mono
% 5.44/5.62 thf(fact_1170_add__left__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.62 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_left_mono
% 5.44/5.62 thf(fact_1171_add__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_real @ C @ D )
% 5.44/5.62 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono
% 5.44/5.62 thf(fact_1172_add__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_nat @ C @ D )
% 5.44/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono
% 5.44/5.62 thf(fact_1173_add__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_int @ C @ D )
% 5.44/5.62 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono
% 5.44/5.62 thf(fact_1174_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.44/5.62 & ( ord_less_eq_real @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(1)
% 5.44/5.62 thf(fact_1175_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.62 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(1)
% 5.44/5.62 thf(fact_1176_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.62 & ( ord_less_eq_int @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(1)
% 5.44/5.62 thf(fact_1177_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( ord_less_eq_real @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(2)
% 5.44/5.62 thf(fact_1178_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(2)
% 5.44/5.62 thf(fact_1179_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( ord_less_eq_int @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(2)
% 5.44/5.62 thf(fact_1180_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(3)
% 5.44/5.62 thf(fact_1181_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(3)
% 5.44/5.62 thf(fact_1182_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_semiring(3)
% 5.44/5.62 thf(fact_1183_add__less__imp__less__right,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.44/5.62 => ( ord_less_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_imp_less_right
% 5.44/5.62 thf(fact_1184_add__less__imp__less__right,axiom,
% 5.44/5.62 ! [A: nat,C: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.62 => ( ord_less_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_imp_less_right
% 5.44/5.62 thf(fact_1185_add__less__imp__less__right,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.44/5.62 => ( ord_less_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_imp_less_right
% 5.44/5.62 thf(fact_1186_add__less__imp__less__left,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.44/5.62 => ( ord_less_real @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_imp_less_left
% 5.44/5.62 thf(fact_1187_add__less__imp__less__left,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.44/5.62 => ( ord_less_nat @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_imp_less_left
% 5.44/5.62 thf(fact_1188_add__less__imp__less__left,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.44/5.62 => ( ord_less_int @ A @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_imp_less_left
% 5.44/5.62 thf(fact_1189_add__strict__right__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_right_mono
% 5.44/5.62 thf(fact_1190_add__strict__right__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_nat @ A @ B )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_right_mono
% 5.44/5.62 thf(fact_1191_add__strict__right__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ B )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_right_mono
% 5.44/5.62 thf(fact_1192_add__strict__left__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_left_mono
% 5.44/5.62 thf(fact_1193_add__strict__left__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_nat @ A @ B )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_left_mono
% 5.44/5.62 thf(fact_1194_add__strict__left__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ B )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_left_mono
% 5.44/5.62 thf(fact_1195_add__strict__mono,axiom,
% 5.44/5.62 ! [A: extended_enat,B: extended_enat,C: extended_enat,D: extended_enat] :
% 5.44/5.62 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.62 => ( ( ord_le72135733267957522d_enat @ C @ D )
% 5.44/5.62 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ C ) @ ( plus_p3455044024723400733d_enat @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_mono
% 5.44/5.62 thf(fact_1196_add__strict__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ( ord_less_real @ C @ D )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_mono
% 5.44/5.62 thf(fact_1197_add__strict__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.62 ( ( ord_less_nat @ A @ B )
% 5.44/5.62 => ( ( ord_less_nat @ C @ D )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_mono
% 5.44/5.62 thf(fact_1198_add__strict__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ B )
% 5.44/5.62 => ( ( ord_less_int @ C @ D )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_strict_mono
% 5.44/5.62 thf(fact_1199_add__mono__thms__linordered__field_I1_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( ord_less_real @ I2 @ J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(1)
% 5.44/5.62 thf(fact_1200_add__mono__thms__linordered__field_I1_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( ord_less_nat @ I2 @ J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(1)
% 5.44/5.62 thf(fact_1201_add__mono__thms__linordered__field_I1_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( ord_less_int @ I2 @ J )
% 5.44/5.62 & ( K = L2 ) )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(1)
% 5.44/5.62 thf(fact_1202_add__mono__thms__linordered__field_I2_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( ord_less_real @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(2)
% 5.44/5.62 thf(fact_1203_add__mono__thms__linordered__field_I2_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( ord_less_nat @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(2)
% 5.44/5.62 thf(fact_1204_add__mono__thms__linordered__field_I2_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( I2 = J )
% 5.44/5.62 & ( ord_less_int @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(2)
% 5.44/5.62 thf(fact_1205_add__mono__thms__linordered__field_I5_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( ord_less_real @ I2 @ J )
% 5.44/5.62 & ( ord_less_real @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(5)
% 5.44/5.62 thf(fact_1206_add__mono__thms__linordered__field_I5_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( ord_less_nat @ I2 @ J )
% 5.44/5.62 & ( ord_less_nat @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(5)
% 5.44/5.62 thf(fact_1207_add__mono__thms__linordered__field_I5_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( ord_less_int @ I2 @ J )
% 5.44/5.62 & ( ord_less_int @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(5)
% 5.44/5.62 thf(fact_1208_diff__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,D: real,C: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_real @ D @ C )
% 5.44/5.62 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_mono
% 5.44/5.62 thf(fact_1209_diff__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,D: int,C: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_int @ D @ C )
% 5.44/5.62 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_mono
% 5.44/5.62 thf(fact_1210_diff__left__mono,axiom,
% 5.44/5.62 ! [B: real,A: real,C: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.62 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_left_mono
% 5.44/5.62 thf(fact_1211_diff__left__mono,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.62 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_left_mono
% 5.44/5.62 thf(fact_1212_diff__right__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.62 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_right_mono
% 5.44/5.62 thf(fact_1213_diff__right__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.62 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_right_mono
% 5.44/5.62 thf(fact_1214_diff__eq__diff__less__eq,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.62 ( ( ( minus_minus_real @ A @ B )
% 5.44/5.62 = ( minus_minus_real @ C @ D ) )
% 5.44/5.62 => ( ( ord_less_eq_real @ A @ B )
% 5.44/5.62 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_eq_diff_less_eq
% 5.44/5.62 thf(fact_1215_diff__eq__diff__less__eq,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.62 ( ( ( minus_minus_int @ A @ B )
% 5.44/5.62 = ( minus_minus_int @ C @ D ) )
% 5.44/5.62 => ( ( ord_less_eq_int @ A @ B )
% 5.44/5.62 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_eq_diff_less_eq
% 5.44/5.62 thf(fact_1216_diff__strict__right__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_strict_right_mono
% 5.44/5.62 thf(fact_1217_diff__strict__right__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ B )
% 5.44/5.62 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_strict_right_mono
% 5.44/5.62 thf(fact_1218_diff__strict__left__mono,axiom,
% 5.44/5.62 ! [B: real,A: real,C: real] :
% 5.44/5.62 ( ( ord_less_real @ B @ A )
% 5.44/5.62 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_strict_left_mono
% 5.44/5.62 thf(fact_1219_diff__strict__left__mono,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( ord_less_int @ B @ A )
% 5.44/5.62 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_strict_left_mono
% 5.44/5.62 thf(fact_1220_diff__eq__diff__less,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.62 ( ( ( minus_minus_real @ A @ B )
% 5.44/5.62 = ( minus_minus_real @ C @ D ) )
% 5.44/5.62 => ( ( ord_less_real @ A @ B )
% 5.44/5.62 = ( ord_less_real @ C @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_eq_diff_less
% 5.44/5.62 thf(fact_1221_diff__eq__diff__less,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.62 ( ( ( minus_minus_int @ A @ B )
% 5.44/5.62 = ( minus_minus_int @ C @ D ) )
% 5.44/5.62 => ( ( ord_less_int @ A @ B )
% 5.44/5.62 = ( ord_less_int @ C @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_eq_diff_less
% 5.44/5.62 thf(fact_1222_diff__strict__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,D: real,C: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ( ord_less_real @ D @ C )
% 5.44/5.62 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_strict_mono
% 5.44/5.62 thf(fact_1223_diff__strict__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,D: int,C: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ B )
% 5.44/5.62 => ( ( ord_less_int @ D @ C )
% 5.44/5.62 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_strict_mono
% 5.44/5.62 thf(fact_1224_combine__common__factor,axiom,
% 5.44/5.62 ! [A: complex,E: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ C ) )
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_common_factor
% 5.44/5.62 thf(fact_1225_combine__common__factor,axiom,
% 5.44/5.62 ! [A: real,E: real,B: real,C: real] :
% 5.44/5.62 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_common_factor
% 5.44/5.62 thf(fact_1226_combine__common__factor,axiom,
% 5.44/5.62 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_common_factor
% 5.44/5.62 thf(fact_1227_combine__common__factor,axiom,
% 5.44/5.62 ! [A: int,E: int,B: int,C: int] :
% 5.44/5.62 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % combine_common_factor
% 5.44/5.62 thf(fact_1228_distrib__right,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % distrib_right
% 5.44/5.62 thf(fact_1229_distrib__right,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % distrib_right
% 5.44/5.62 thf(fact_1230_distrib__right,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % distrib_right
% 5.44/5.62 thf(fact_1231_distrib__right,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % distrib_right
% 5.44/5.62 thf(fact_1232_distrib__left,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % distrib_left
% 5.44/5.62 thf(fact_1233_distrib__left,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % distrib_left
% 5.44/5.62 thf(fact_1234_distrib__left,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % distrib_left
% 5.44/5.62 thf(fact_1235_distrib__left,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % distrib_left
% 5.44/5.62 thf(fact_1236_comm__semiring__class_Odistrib,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % comm_semiring_class.distrib
% 5.44/5.62 thf(fact_1237_comm__semiring__class_Odistrib,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % comm_semiring_class.distrib
% 5.44/5.62 thf(fact_1238_comm__semiring__class_Odistrib,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % comm_semiring_class.distrib
% 5.44/5.62 thf(fact_1239_comm__semiring__class_Odistrib,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % comm_semiring_class.distrib
% 5.44/5.62 thf(fact_1240_ring__class_Oring__distribs_I1_J,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ring_class.ring_distribs(1)
% 5.44/5.62 thf(fact_1241_ring__class_Oring__distribs_I1_J,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ring_class.ring_distribs(1)
% 5.44/5.62 thf(fact_1242_ring__class_Oring__distribs_I1_J,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ring_class.ring_distribs(1)
% 5.44/5.62 thf(fact_1243_ring__class_Oring__distribs_I2_J,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ring_class.ring_distribs(2)
% 5.44/5.62 thf(fact_1244_ring__class_Oring__distribs_I2_J,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ring_class.ring_distribs(2)
% 5.44/5.62 thf(fact_1245_ring__class_Oring__distribs_I2_J,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ring_class.ring_distribs(2)
% 5.44/5.62 thf(fact_1246_mult_Ocomm__neutral,axiom,
% 5.44/5.62 ! [A: extended_enat] :
% 5.44/5.62 ( ( times_7803423173614009249d_enat @ A @ one_on7984719198319812577d_enat )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.comm_neutral
% 5.44/5.62 thf(fact_1247_mult_Ocomm__neutral,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( times_times_complex @ A @ one_one_complex )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.comm_neutral
% 5.44/5.62 thf(fact_1248_mult_Ocomm__neutral,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( times_times_real @ A @ one_one_real )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.comm_neutral
% 5.44/5.62 thf(fact_1249_mult_Ocomm__neutral,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( times_times_nat @ A @ one_one_nat )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.comm_neutral
% 5.44/5.62 thf(fact_1250_mult_Ocomm__neutral,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( times_times_int @ A @ one_one_int )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % mult.comm_neutral
% 5.44/5.62 thf(fact_1251_comm__monoid__mult__class_Omult__1,axiom,
% 5.44/5.62 ! [A: extended_enat] :
% 5.44/5.62 ( ( times_7803423173614009249d_enat @ one_on7984719198319812577d_enat @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % comm_monoid_mult_class.mult_1
% 5.44/5.62 thf(fact_1252_comm__monoid__mult__class_Omult__1,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( times_times_complex @ one_one_complex @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % comm_monoid_mult_class.mult_1
% 5.44/5.62 thf(fact_1253_comm__monoid__mult__class_Omult__1,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( times_times_real @ one_one_real @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % comm_monoid_mult_class.mult_1
% 5.44/5.62 thf(fact_1254_comm__monoid__mult__class_Omult__1,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( times_times_nat @ one_one_nat @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % comm_monoid_mult_class.mult_1
% 5.44/5.62 thf(fact_1255_comm__monoid__mult__class_Omult__1,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( times_times_int @ one_one_int @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % comm_monoid_mult_class.mult_1
% 5.44/5.62 thf(fact_1256_right__diff__distrib_H,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.44/5.62 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % right_diff_distrib'
% 5.44/5.62 thf(fact_1257_right__diff__distrib_H,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.44/5.62 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % right_diff_distrib'
% 5.44/5.62 thf(fact_1258_right__diff__distrib_H,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.44/5.62 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % right_diff_distrib'
% 5.44/5.62 thf(fact_1259_right__diff__distrib_H,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.44/5.62 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % right_diff_distrib'
% 5.44/5.62 thf(fact_1260_left__diff__distrib_H,axiom,
% 5.44/5.62 ! [B: complex,C: complex,A: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 5.44/5.62 = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % left_diff_distrib'
% 5.44/5.62 thf(fact_1261_left__diff__distrib_H,axiom,
% 5.44/5.62 ! [B: real,C: real,A: real] :
% 5.44/5.62 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.44/5.62 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % left_diff_distrib'
% 5.44/5.62 thf(fact_1262_left__diff__distrib_H,axiom,
% 5.44/5.62 ! [B: nat,C: nat,A: nat] :
% 5.44/5.62 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.44/5.62 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % left_diff_distrib'
% 5.44/5.62 thf(fact_1263_left__diff__distrib_H,axiom,
% 5.44/5.62 ! [B: int,C: int,A: int] :
% 5.44/5.62 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.44/5.62 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % left_diff_distrib'
% 5.44/5.62 thf(fact_1264_right__diff__distrib,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.44/5.62 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % right_diff_distrib
% 5.44/5.62 thf(fact_1265_right__diff__distrib,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.44/5.62 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % right_diff_distrib
% 5.44/5.62 thf(fact_1266_right__diff__distrib,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.44/5.62 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % right_diff_distrib
% 5.44/5.62 thf(fact_1267_left__diff__distrib,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % left_diff_distrib
% 5.44/5.62 thf(fact_1268_left__diff__distrib,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % left_diff_distrib
% 5.44/5.62 thf(fact_1269_left__diff__distrib,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % left_diff_distrib
% 5.44/5.62 thf(fact_1270_diff__diff__eq,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_diff_eq
% 5.44/5.62 thf(fact_1271_diff__diff__eq,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_diff_eq
% 5.44/5.62 thf(fact_1272_diff__diff__eq,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_diff_eq
% 5.44/5.62 thf(fact_1273_diff__diff__eq,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_diff_eq
% 5.44/5.62 thf(fact_1274_add__implies__diff,axiom,
% 5.44/5.62 ! [C: complex,B: complex,A: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ C @ B )
% 5.44/5.62 = A )
% 5.44/5.62 => ( C
% 5.44/5.62 = ( minus_minus_complex @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_implies_diff
% 5.44/5.62 thf(fact_1275_add__implies__diff,axiom,
% 5.44/5.62 ! [C: real,B: real,A: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ C @ B )
% 5.44/5.62 = A )
% 5.44/5.62 => ( C
% 5.44/5.62 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_implies_diff
% 5.44/5.62 thf(fact_1276_add__implies__diff,axiom,
% 5.44/5.62 ! [C: nat,B: nat,A: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ C @ B )
% 5.44/5.62 = A )
% 5.44/5.62 => ( C
% 5.44/5.62 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_implies_diff
% 5.44/5.62 thf(fact_1277_add__implies__diff,axiom,
% 5.44/5.62 ! [C: int,B: int,A: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ C @ B )
% 5.44/5.62 = A )
% 5.44/5.62 => ( C
% 5.44/5.62 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_implies_diff
% 5.44/5.62 thf(fact_1278_diff__add__eq__diff__diff__swap,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.44/5.62 = ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_eq_diff_diff_swap
% 5.44/5.62 thf(fact_1279_diff__add__eq__diff__diff__swap,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.44/5.62 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_eq_diff_diff_swap
% 5.44/5.62 thf(fact_1280_diff__add__eq__diff__diff__swap,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.44/5.62 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_eq_diff_diff_swap
% 5.44/5.62 thf(fact_1281_diff__add__eq,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_eq
% 5.44/5.62 thf(fact_1282_diff__add__eq,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_eq
% 5.44/5.62 thf(fact_1283_diff__add__eq,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_eq
% 5.44/5.62 thf(fact_1284_diff__diff__eq2,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.44/5.62 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_diff_eq2
% 5.44/5.62 thf(fact_1285_diff__diff__eq2,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.44/5.62 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_diff_eq2
% 5.44/5.62 thf(fact_1286_diff__diff__eq2,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.44/5.62 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_diff_eq2
% 5.44/5.62 thf(fact_1287_add__diff__eq,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.44/5.62 = ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_eq
% 5.44/5.62 thf(fact_1288_add__diff__eq,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.44/5.62 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_eq
% 5.44/5.62 thf(fact_1289_add__diff__eq,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.44/5.62 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_diff_eq
% 5.44/5.62 thf(fact_1290_eq__diff__eq,axiom,
% 5.44/5.62 ! [A: complex,C: complex,B: complex] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( minus_minus_complex @ C @ B ) )
% 5.44/5.62 = ( ( plus_plus_complex @ A @ B )
% 5.44/5.62 = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_diff_eq
% 5.44/5.62 thf(fact_1291_eq__diff__eq,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( minus_minus_real @ C @ B ) )
% 5.44/5.62 = ( ( plus_plus_real @ A @ B )
% 5.44/5.62 = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_diff_eq
% 5.44/5.62 thf(fact_1292_eq__diff__eq,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( minus_minus_int @ C @ B ) )
% 5.44/5.62 = ( ( plus_plus_int @ A @ B )
% 5.44/5.62 = C ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_diff_eq
% 5.44/5.62 thf(fact_1293_diff__eq__eq,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( ( minus_minus_complex @ A @ B )
% 5.44/5.62 = C )
% 5.44/5.62 = ( A
% 5.44/5.62 = ( plus_plus_complex @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_eq_eq
% 5.44/5.62 thf(fact_1294_diff__eq__eq,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ( minus_minus_real @ A @ B )
% 5.44/5.62 = C )
% 5.44/5.62 = ( A
% 5.44/5.62 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_eq_eq
% 5.44/5.62 thf(fact_1295_diff__eq__eq,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ( minus_minus_int @ A @ B )
% 5.44/5.62 = C )
% 5.44/5.62 = ( A
% 5.44/5.62 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_eq_eq
% 5.44/5.62 thf(fact_1296_group__cancel_Osub1,axiom,
% 5.44/5.62 ! [A2: complex,K: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( A2
% 5.44/5.62 = ( plus_plus_complex @ K @ A ) )
% 5.44/5.62 => ( ( minus_minus_complex @ A2 @ B )
% 5.44/5.62 = ( plus_plus_complex @ K @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.sub1
% 5.44/5.62 thf(fact_1297_group__cancel_Osub1,axiom,
% 5.44/5.62 ! [A2: real,K: real,A: real,B: real] :
% 5.44/5.62 ( ( A2
% 5.44/5.62 = ( plus_plus_real @ K @ A ) )
% 5.44/5.62 => ( ( minus_minus_real @ A2 @ B )
% 5.44/5.62 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.sub1
% 5.44/5.62 thf(fact_1298_group__cancel_Osub1,axiom,
% 5.44/5.62 ! [A2: int,K: int,A: int,B: int] :
% 5.44/5.62 ( ( A2
% 5.44/5.62 = ( plus_plus_int @ K @ A ) )
% 5.44/5.62 => ( ( minus_minus_int @ A2 @ B )
% 5.44/5.62 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % group_cancel.sub1
% 5.44/5.62 thf(fact_1299_max__add__distrib__right,axiom,
% 5.44/5.62 ! [X: real,Y: real,Z: real] :
% 5.44/5.62 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 5.44/5.62 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_add_distrib_right
% 5.44/5.62 thf(fact_1300_max__add__distrib__right,axiom,
% 5.44/5.62 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 5.44/5.62 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_add_distrib_right
% 5.44/5.62 thf(fact_1301_max__add__distrib__right,axiom,
% 5.44/5.62 ! [X: int,Y: int,Z: int] :
% 5.44/5.62 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 5.44/5.62 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_add_distrib_right
% 5.44/5.62 thf(fact_1302_max__add__distrib__right,axiom,
% 5.44/5.62 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.44/5.62 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 5.44/5.62 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_add_distrib_right
% 5.44/5.62 thf(fact_1303_max__add__distrib__left,axiom,
% 5.44/5.62 ! [X: real,Y: real,Z: real] :
% 5.44/5.62 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.44/5.62 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_add_distrib_left
% 5.44/5.62 thf(fact_1304_max__add__distrib__left,axiom,
% 5.44/5.62 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 5.44/5.62 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_add_distrib_left
% 5.44/5.62 thf(fact_1305_max__add__distrib__left,axiom,
% 5.44/5.62 ! [X: int,Y: int,Z: int] :
% 5.44/5.62 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.44/5.62 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_add_distrib_left
% 5.44/5.62 thf(fact_1306_max__add__distrib__left,axiom,
% 5.44/5.62 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.44/5.62 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.44/5.62 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_add_distrib_left
% 5.44/5.62 thf(fact_1307_max__diff__distrib__left,axiom,
% 5.44/5.62 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.44/5.62 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.44/5.62 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_diff_distrib_left
% 5.44/5.62 thf(fact_1308_max__diff__distrib__left,axiom,
% 5.44/5.62 ! [X: real,Y: real,Z: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.44/5.62 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_diff_distrib_left
% 5.44/5.62 thf(fact_1309_max__diff__distrib__left,axiom,
% 5.44/5.62 ! [X: int,Y: int,Z: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.44/5.62 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_diff_distrib_left
% 5.44/5.62 thf(fact_1310_add__less__le__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_real @ C @ D )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_le_mono
% 5.44/5.62 thf(fact_1311_add__less__le__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.62 ( ( ord_less_nat @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_nat @ C @ D )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_le_mono
% 5.44/5.62 thf(fact_1312_add__less__le__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_int @ C @ D )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_le_mono
% 5.44/5.62 thf(fact_1313_add__le__less__mono,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.62 => ( ( ord_less_real @ C @ D )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_less_mono
% 5.44/5.62 thf(fact_1314_add__le__less__mono,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( ord_less_nat @ C @ D )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_less_mono
% 5.44/5.62 thf(fact_1315_add__le__less__mono,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.62 => ( ( ord_less_int @ C @ D )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_less_mono
% 5.44/5.62 thf(fact_1316_add__mono__thms__linordered__field_I3_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( ord_less_real @ I2 @ J )
% 5.44/5.62 & ( ord_less_eq_real @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(3)
% 5.44/5.62 thf(fact_1317_add__mono__thms__linordered__field_I3_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( ord_less_nat @ I2 @ J )
% 5.44/5.62 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(3)
% 5.44/5.62 thf(fact_1318_add__mono__thms__linordered__field_I3_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( ord_less_int @ I2 @ J )
% 5.44/5.62 & ( ord_less_eq_int @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(3)
% 5.44/5.62 thf(fact_1319_add__mono__thms__linordered__field_I4_J,axiom,
% 5.44/5.62 ! [I2: real,J: real,K: real,L2: real] :
% 5.44/5.62 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.44/5.62 & ( ord_less_real @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(4)
% 5.44/5.62 thf(fact_1320_add__mono__thms__linordered__field_I4_J,axiom,
% 5.44/5.62 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.44/5.62 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.62 & ( ord_less_nat @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(4)
% 5.44/5.62 thf(fact_1321_add__mono__thms__linordered__field_I4_J,axiom,
% 5.44/5.62 ! [I2: int,J: int,K: int,L2: int] :
% 5.44/5.62 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.62 & ( ord_less_int @ K @ L2 ) )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono_thms_linordered_field(4)
% 5.44/5.62 thf(fact_1322_less__1__mult,axiom,
% 5.44/5.62 ! [M: real,N2: real] :
% 5.44/5.62 ( ( ord_less_real @ one_one_real @ M )
% 5.44/5.62 => ( ( ord_less_real @ one_one_real @ N2 )
% 5.44/5.62 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_1_mult
% 5.44/5.62 thf(fact_1323_less__1__mult,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ one_one_nat @ M )
% 5.44/5.62 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.44/5.62 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_1_mult
% 5.44/5.62 thf(fact_1324_less__1__mult,axiom,
% 5.44/5.62 ! [M: int,N2: int] :
% 5.44/5.62 ( ( ord_less_int @ one_one_int @ M )
% 5.44/5.62 => ( ( ord_less_int @ one_one_int @ N2 )
% 5.44/5.62 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_1_mult
% 5.44/5.62 thf(fact_1325_add__mono1,axiom,
% 5.44/5.62 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.62 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.62 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ B @ one_on7984719198319812577d_enat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono1
% 5.44/5.62 thf(fact_1326_add__mono1,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono1
% 5.44/5.62 thf(fact_1327_add__mono1,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ A @ B )
% 5.44/5.62 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono1
% 5.44/5.62 thf(fact_1328_add__mono1,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ B )
% 5.44/5.62 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_mono1
% 5.44/5.62 thf(fact_1329_less__add__one,axiom,
% 5.44/5.62 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_one
% 5.44/5.62 thf(fact_1330_less__add__one,axiom,
% 5.44/5.62 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_one
% 5.44/5.62 thf(fact_1331_less__add__one,axiom,
% 5.44/5.62 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_one
% 5.44/5.62 thf(fact_1332_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( ( minus_minus_nat @ B @ A )
% 5.44/5.62 = C )
% 5.44/5.62 = ( B
% 5.44/5.62 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.44/5.62 thf(fact_1333_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.44/5.62 = B ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.44/5.62 thf(fact_1334_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.44/5.62 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.44/5.62 thf(fact_1335_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.44/5.62 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.44/5.62 thf(fact_1336_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.44/5.62 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.44/5.62 thf(fact_1337_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.44/5.62 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.44/5.62 thf(fact_1338_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.44/5.62 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.44/5.62 thf(fact_1339_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.44/5.62 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.44/5.62 thf(fact_1340_le__add__diff,axiom,
% 5.44/5.62 ! [A: nat,B: nat,C: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_diff
% 5.44/5.62 thf(fact_1341_add__le__add__imp__diff__le,axiom,
% 5.44/5.62 ! [I2: real,K: real,N2: real,J: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 5.44/5.62 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 5.44/5.62 => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_add_imp_diff_le
% 5.44/5.62 thf(fact_1342_add__le__add__imp__diff__le,axiom,
% 5.44/5.62 ! [I2: nat,K: nat,N2: nat,J: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.44/5.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_add_imp_diff_le
% 5.44/5.62 thf(fact_1343_add__le__add__imp__diff__le,axiom,
% 5.44/5.62 ! [I2: int,K: int,N2: int,J: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.44/5.62 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.44/5.62 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_add_imp_diff_le
% 5.44/5.62 thf(fact_1344_diff__add,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.62 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.44/5.62 = B ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add
% 5.44/5.62 thf(fact_1345_add__le__imp__le__diff,axiom,
% 5.44/5.62 ! [I2: real,K: real,N2: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_diff
% 5.44/5.62 thf(fact_1346_add__le__imp__le__diff,axiom,
% 5.44/5.62 ! [I2: nat,K: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_diff
% 5.44/5.62 thf(fact_1347_add__le__imp__le__diff,axiom,
% 5.44/5.62 ! [I2: int,K: int,N2: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.44/5.62 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_imp_le_diff
% 5.44/5.62 thf(fact_1348_le__diff__eq,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.44/5.62 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_diff_eq
% 5.44/5.62 thf(fact_1349_le__diff__eq,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.44/5.62 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_diff_eq
% 5.44/5.62 thf(fact_1350_diff__le__eq,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.44/5.62 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_le_eq
% 5.44/5.62 thf(fact_1351_diff__le__eq,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.44/5.62 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_le_eq
% 5.44/5.62 thf(fact_1352_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ~ ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % linordered_semidom_class.add_diff_inverse
% 5.44/5.62 thf(fact_1353_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ~ ( ord_less_nat @ A @ B )
% 5.44/5.62 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % linordered_semidom_class.add_diff_inverse
% 5.44/5.62 thf(fact_1354_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ~ ( ord_less_int @ A @ B )
% 5.44/5.62 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % linordered_semidom_class.add_diff_inverse
% 5.44/5.62 thf(fact_1355_less__diff__eq,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.44/5.62 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_diff_eq
% 5.44/5.62 thf(fact_1356_less__diff__eq,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.44/5.62 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_diff_eq
% 5.44/5.62 thf(fact_1357_diff__less__eq,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.44/5.62 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_less_eq
% 5.44/5.62 thf(fact_1358_diff__less__eq,axiom,
% 5.44/5.62 ! [A: int,B: int,C: int] :
% 5.44/5.62 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.44/5.62 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_less_eq
% 5.44/5.62 thf(fact_1359_square__diff__square__factored,axiom,
% 5.44/5.62 ! [X: complex,Y: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ ( times_times_complex @ Y @ Y ) )
% 5.44/5.62 = ( times_times_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_complex @ X @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % square_diff_square_factored
% 5.44/5.62 thf(fact_1360_square__diff__square__factored,axiom,
% 5.44/5.62 ! [X: real,Y: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.44/5.62 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % square_diff_square_factored
% 5.44/5.62 thf(fact_1361_square__diff__square__factored,axiom,
% 5.44/5.62 ! [X: int,Y: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.44/5.62 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % square_diff_square_factored
% 5.44/5.62 thf(fact_1362_eq__add__iff2,axiom,
% 5.44/5.62 ! [A: complex,E: complex,C: complex,B: complex,D: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D ) )
% 5.44/5.62 = ( C
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E ) @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_add_iff2
% 5.44/5.62 thf(fact_1363_eq__add__iff2,axiom,
% 5.44/5.62 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.44/5.62 = ( C
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_add_iff2
% 5.44/5.62 thf(fact_1364_eq__add__iff2,axiom,
% 5.44/5.62 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.44/5.62 = ( C
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_add_iff2
% 5.44/5.62 thf(fact_1365_eq__add__iff1,axiom,
% 5.44/5.62 ! [A: complex,E: complex,C: complex,B: complex,D: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 5.44/5.62 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D ) )
% 5.44/5.62 = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E ) @ C )
% 5.44/5.62 = D ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_add_iff1
% 5.44/5.62 thf(fact_1366_eq__add__iff1,axiom,
% 5.44/5.62 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.44/5.62 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.44/5.62 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.44/5.62 = D ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_add_iff1
% 5.44/5.62 thf(fact_1367_eq__add__iff1,axiom,
% 5.44/5.62 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.44/5.62 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.44/5.62 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.44/5.62 = D ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_add_iff1
% 5.44/5.62 thf(fact_1368_ordered__ring__class_Ole__add__iff2,axiom,
% 5.44/5.62 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.44/5.62 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_ring_class.le_add_iff2
% 5.44/5.62 thf(fact_1369_ordered__ring__class_Ole__add__iff2,axiom,
% 5.44/5.62 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.44/5.62 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_ring_class.le_add_iff2
% 5.44/5.62 thf(fact_1370_ordered__ring__class_Ole__add__iff1,axiom,
% 5.44/5.62 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.44/5.62 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_ring_class.le_add_iff1
% 5.44/5.62 thf(fact_1371_ordered__ring__class_Ole__add__iff1,axiom,
% 5.44/5.62 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.44/5.62 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.44/5.62
% 5.44/5.62 % ordered_ring_class.le_add_iff1
% 5.44/5.62 thf(fact_1372_less__add__iff2,axiom,
% 5.44/5.62 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.44/5.62 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_iff2
% 5.44/5.62 thf(fact_1373_less__add__iff2,axiom,
% 5.44/5.62 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.44/5.62 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_iff2
% 5.44/5.62 thf(fact_1374_less__add__iff1,axiom,
% 5.44/5.62 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.44/5.62 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_iff1
% 5.44/5.62 thf(fact_1375_less__add__iff1,axiom,
% 5.44/5.62 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.44/5.62 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_iff1
% 5.44/5.62 thf(fact_1376_square__diff__one__factored,axiom,
% 5.44/5.62 ! [X: complex] :
% 5.44/5.62 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.44/5.62 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % square_diff_one_factored
% 5.44/5.62 thf(fact_1377_square__diff__one__factored,axiom,
% 5.44/5.62 ! [X: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.44/5.62 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % square_diff_one_factored
% 5.44/5.62 thf(fact_1378_square__diff__one__factored,axiom,
% 5.44/5.62 ! [X: int] :
% 5.44/5.62 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.44/5.62 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % square_diff_one_factored
% 5.44/5.62 thf(fact_1379_real__average__minus__first,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.44/5.62 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % real_average_minus_first
% 5.44/5.62 thf(fact_1380_real__average__minus__second,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.44/5.62 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % real_average_minus_second
% 5.44/5.62 thf(fact_1381_times__divide__eq__right,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.44/5.62 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % times_divide_eq_right
% 5.44/5.62 thf(fact_1382_times__divide__eq__right,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % times_divide_eq_right
% 5.44/5.62 thf(fact_1383_divide__divide__eq__right,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.44/5.62 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_divide_eq_right
% 5.44/5.62 thf(fact_1384_divide__divide__eq__right,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_divide_eq_right
% 5.44/5.62 thf(fact_1385_divide__divide__eq__left,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.44/5.62 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_divide_eq_left
% 5.44/5.62 thf(fact_1386_divide__divide__eq__left,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.44/5.62 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_divide_eq_left
% 5.44/5.62 thf(fact_1387_times__divide__eq__left,axiom,
% 5.44/5.62 ! [B: real,C: real,A: real] :
% 5.44/5.62 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.44/5.62 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % times_divide_eq_left
% 5.44/5.62 thf(fact_1388_times__divide__eq__left,axiom,
% 5.44/5.62 ! [B: complex,C: complex,A: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.44/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % times_divide_eq_left
% 5.44/5.62 thf(fact_1389_vebt__succ_Osimps_I3_J,axiom,
% 5.44/5.62 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.44/5.62 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.44/5.62 = none_nat ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_succ.simps(3)
% 5.44/5.62 thf(fact_1390_vebt__pred_Osimps_I4_J,axiom,
% 5.44/5.62 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.44/5.62 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.44/5.62 = none_nat ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_pred.simps(4)
% 5.44/5.62 thf(fact_1391_divmod__step__eq,axiom,
% 5.44/5.62 ! [L2: num,R: nat,Q2: nat] :
% 5.44/5.62 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 5.44/5.62 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.44/5.62 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 5.44/5.62 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 5.44/5.62 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.44/5.62 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divmod_step_eq
% 5.44/5.62 thf(fact_1392_divmod__step__eq,axiom,
% 5.44/5.62 ! [L2: num,R: int,Q2: int] :
% 5.44/5.62 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 5.44/5.62 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.44/5.62 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 5.44/5.62 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 5.44/5.62 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.44/5.62 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divmod_step_eq
% 5.44/5.62 thf(fact_1393_divmod__step__eq,axiom,
% 5.44/5.62 ! [L2: num,R: code_integer,Q2: code_integer] :
% 5.44/5.62 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 5.44/5.62 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 5.44/5.62 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 5.44/5.62 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 5.44/5.62 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 5.44/5.62 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divmod_step_eq
% 5.44/5.62 thf(fact_1394_succ__less__length__list,axiom,
% 5.44/5.62 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.44/5.62 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_option_nat
% 5.44/5.62 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 != none_nat )
% 5.44/5.62 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ none_nat
% 5.44/5.62 @ ( 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 @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % succ_less_length_list
% 5.44/5.62 thf(fact_1395_set__vebt_H__def,axiom,
% 5.44/5.62 ( vEBT_VEBT_set_vebt
% 5.44/5.62 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % set_vebt'_def
% 5.44/5.62 thf(fact_1396_zdiv__numeral__Bit0,axiom,
% 5.44/5.62 ! [V: num,W: num] :
% 5.44/5.62 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.44/5.62 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % zdiv_numeral_Bit0
% 5.44/5.62 thf(fact_1397_del__x__not__mi,axiom,
% 5.44/5.62 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ( ord_less_nat @ Mi @ X )
% 5.44/5.62 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.44/5.62 => ( ( Mi != Ma )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = H2 )
% 5.44/5.62 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = L2 )
% 5.44/5.62 => ( ( Newnode
% 5.44/5.62 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.62 => ( ( Newlist
% 5.44/5.62 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.44/5.62 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ Mi
% 5.44/5.62 @ ( if_nat @ ( X = Ma )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ Mi
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ Newlist
% 5.44/5.62 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.44/5.62 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % del_x_not_mi
% 5.44/5.62 thf(fact_1398_del__x__not__mi__new__node__nil,axiom,
% 5.44/5.62 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.44/5.62 ( ( ( ord_less_nat @ Mi @ X )
% 5.44/5.62 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.44/5.62 => ( ( Mi != Ma )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = H2 )
% 5.44/5.62 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = L2 )
% 5.44/5.62 => ( ( Newnode
% 5.44/5.62 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.62 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.44/5.62 => ( ( Sn
% 5.44/5.62 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.44/5.62 => ( ( Newlist
% 5.44/5.62 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.44/5.62 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ Mi
% 5.44/5.62 @ ( if_nat @ ( X = Ma )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ Mi
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ Newlist
% 5.44/5.62 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % del_x_not_mi_new_node_nil
% 5.44/5.62 thf(fact_1399_del__x__not__mia,axiom,
% 5.44/5.62 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ( ord_less_nat @ Mi @ X )
% 5.44/5.62 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.44/5.62 => ( ( Mi != Ma )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = H2 )
% 5.44/5.62 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = L2 )
% 5.44/5.62 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.62 @ ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ Mi
% 5.44/5.62 @ ( if_nat @ ( X = Ma )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ Mi
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.62 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.44/5.62 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % del_x_not_mia
% 5.44/5.62 thf(fact_1400_del__in__range,axiom,
% 5.44/5.62 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ( ord_less_eq_nat @ Mi @ X )
% 5.44/5.62 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.44/5.62 => ( ( Mi != Ma )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( ( X = Mi )
% 5.44/5.62 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 = Ma ) )
% 5.44/5.62 & ( ( X != Mi )
% 5.44/5.62 => ( X = Ma ) ) )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( ( X = Mi )
% 5.44/5.62 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 = Ma ) )
% 5.44/5.62 & ( ( X != Mi )
% 5.44/5.62 => ( X = Ma ) ) )
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ Summary ) )
% 5.44/5.62 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % del_in_range
% 5.44/5.62 thf(fact_1401_del__x__mi,axiom,
% 5.44/5.62 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat] :
% 5.44/5.62 ( ( ( X = Mi )
% 5.44/5.62 & ( ord_less_nat @ X @ Ma ) )
% 5.44/5.62 => ( ( Mi != Ma )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = H2 )
% 5.44/5.62 => ( ( Xn
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.44/5.62 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = L2 )
% 5.44/5.62 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.62 @ ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ Xn
% 5.44/5.62 @ ( if_nat @ ( Xn = Ma )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ Xn
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.62 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.44/5.62 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % del_x_mi
% 5.44/5.62 thf(fact_1402_del__x__mi__lets__in,axiom,
% 5.44/5.62 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.44/5.62 ( ( ( X = Mi )
% 5.44/5.62 & ( ord_less_nat @ X @ Ma ) )
% 5.44/5.62 => ( ( Mi != Ma )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = H2 )
% 5.44/5.62 => ( ( Xn
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.44/5.62 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = L2 )
% 5.44/5.62 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( ( Newnode
% 5.44/5.62 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.62 => ( ( Newlist
% 5.44/5.62 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.44/5.62 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ Xn
% 5.44/5.62 @ ( if_nat @ ( Xn = Ma )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ Xn
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ Newlist
% 5.44/5.62 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.44/5.62 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % del_x_mi_lets_in
% 5.44/5.62 thf(fact_1403_del__x__mi__lets__in__minNull,axiom,
% 5.44/5.62 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 5.44/5.62 ( ( ( X = Mi )
% 5.44/5.62 & ( ord_less_nat @ X @ Ma ) )
% 5.44/5.62 => ( ( Mi != Ma )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = H2 )
% 5.44/5.62 => ( ( Xn
% 5.44/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.44/5.62 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.62 = L2 )
% 5.44/5.62 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( ( Newnode
% 5.44/5.62 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.44/5.62 => ( ( Newlist
% 5.44/5.62 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.44/5.62 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.44/5.62 => ( ( Sn
% 5.44/5.62 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ Xn
% 5.44/5.62 @ ( if_nat @ ( Xn = Ma )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ Xn
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ Newlist
% 5.44/5.62 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % del_x_mi_lets_in_minNull
% 5.44/5.62 thf(fact_1404_del__x__mia,axiom,
% 5.44/5.62 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ( X = Mi )
% 5.44/5.62 & ( ord_less_nat @ X @ Ma ) )
% 5.44/5.62 => ( ( Mi != Ma )
% 5.44/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 = Ma )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 = Ma )
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ Deg
% 5.44/5.62 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ Summary ) )
% 5.44/5.62 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % del_x_mia
% 5.44/5.62 thf(fact_1405_pred__less__length__list,axiom,
% 5.44/5.62 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.44/5.62 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_option_nat
% 5.44/5.62 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 != none_nat )
% 5.44/5.62 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % pred_less_length_list
% 5.44/5.62 thf(fact_1406_pred__lesseq__max,axiom,
% 5.44/5.62 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.44/5.62 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 != none_nat )
% 5.44/5.62 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.62 @ none_nat ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % pred_lesseq_max
% 5.44/5.62 thf(fact_1407_succ__greatereq__min,axiom,
% 5.44/5.62 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.44/5.62 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.44/5.62 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 != none_nat )
% 5.44/5.62 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ none_nat
% 5.44/5.62 @ ( 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 @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.62 @ none_nat ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % succ_greatereq_min
% 5.44/5.62 thf(fact_1408_mult__commute__abs,axiom,
% 5.44/5.62 ! [C: complex] :
% 5.44/5.62 ( ( ^ [X2: complex] : ( times_times_complex @ X2 @ C ) )
% 5.44/5.62 = ( times_times_complex @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_commute_abs
% 5.44/5.62 thf(fact_1409_mult__commute__abs,axiom,
% 5.44/5.62 ! [C: real] :
% 5.44/5.62 ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 5.44/5.62 = ( times_times_real @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_commute_abs
% 5.44/5.62 thf(fact_1410_mult__commute__abs,axiom,
% 5.44/5.62 ! [C: nat] :
% 5.44/5.62 ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 5.44/5.62 = ( times_times_nat @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_commute_abs
% 5.44/5.62 thf(fact_1411_mult__commute__abs,axiom,
% 5.44/5.62 ! [C: int] :
% 5.44/5.62 ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 5.44/5.62 = ( times_times_int @ C ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_commute_abs
% 5.44/5.62 thf(fact_1412_lambda__one,axiom,
% 5.44/5.62 ( ( ^ [X2: extended_enat] : X2 )
% 5.44/5.62 = ( times_7803423173614009249d_enat @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.62
% 5.44/5.62 % lambda_one
% 5.44/5.62 thf(fact_1413_lambda__one,axiom,
% 5.44/5.62 ( ( ^ [X2: complex] : X2 )
% 5.44/5.62 = ( times_times_complex @ one_one_complex ) ) ).
% 5.44/5.62
% 5.44/5.62 % lambda_one
% 5.44/5.62 thf(fact_1414_lambda__one,axiom,
% 5.44/5.62 ( ( ^ [X2: real] : X2 )
% 5.44/5.62 = ( times_times_real @ one_one_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % lambda_one
% 5.44/5.62 thf(fact_1415_lambda__one,axiom,
% 5.44/5.62 ( ( ^ [X2: nat] : X2 )
% 5.44/5.62 = ( times_times_nat @ one_one_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % lambda_one
% 5.44/5.62 thf(fact_1416_lambda__one,axiom,
% 5.44/5.62 ( ( ^ [X2: int] : X2 )
% 5.44/5.62 = ( times_times_int @ one_one_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % lambda_one
% 5.44/5.62 thf(fact_1417_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.44/5.62 ! [X: produc5542196010084753463at_nat] :
% 5.44/5.62 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.44/5.62 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.44/5.62 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B3 ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.cases
% 5.44/5.62 thf(fact_1418_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.44/5.62 ! [X: produc8306885398267862888on_nat] :
% 5.44/5.62 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.44/5.62 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.44/5.62 => ~ ! [F2: nat > nat > nat,A3: nat,B3: nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B3 ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.cases
% 5.44/5.62 thf(fact_1419_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.44/5.62 ! [X: produc1193250871479095198on_num] :
% 5.44/5.62 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.44/5.62 => ( ! [Uw2: num > num > num,V2: num] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.44/5.62 => ~ ! [F2: num > num > num,A3: num,B3: num] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B3 ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_shift.cases
% 5.44/5.62 thf(fact_1420_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.44/5.62 ! [X: produc5491161045314408544at_nat] :
% 5.44/5.62 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.44/5.62 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.44/5.62 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X5: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X5 ) @ ( some_P7363390416028606310at_nat @ Y5 ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_comp_shift.cases
% 5.44/5.62 thf(fact_1421_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.44/5.62 ! [X: produc2233624965454879586on_nat] :
% 5.44/5.62 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.44/5.62 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.44/5.62 => ~ ! [F2: nat > nat > $o,X5: nat,Y5: nat] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X5 ) @ ( some_nat @ Y5 ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_comp_shift.cases
% 5.44/5.62 thf(fact_1422_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.44/5.62 ! [X: produc7036089656553540234on_num] :
% 5.44/5.62 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.44/5.62 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.44/5.62 => ~ ! [F2: num > num > $o,X5: num,Y5: num] :
% 5.44/5.62 ( X
% 5.44/5.62 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X5 ) @ ( some_num @ Y5 ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.option_comp_shift.cases
% 5.44/5.62 thf(fact_1423_set__vebt__def,axiom,
% 5.44/5.62 ( vEBT_set_vebt
% 5.44/5.62 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % set_vebt_def
% 5.44/5.62 thf(fact_1424_numeral__code_I2_J,axiom,
% 5.44/5.62 ! [N2: num] :
% 5.44/5.62 ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 5.44/5.62 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % numeral_code(2)
% 5.44/5.62 thf(fact_1425_numeral__code_I2_J,axiom,
% 5.44/5.62 ! [N2: num] :
% 5.44/5.62 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 5.44/5.62 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % numeral_code(2)
% 5.44/5.62 thf(fact_1426_numeral__code_I2_J,axiom,
% 5.44/5.62 ! [N2: num] :
% 5.44/5.62 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 5.44/5.62 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % numeral_code(2)
% 5.44/5.62 thf(fact_1427_numeral__code_I2_J,axiom,
% 5.44/5.62 ! [N2: num] :
% 5.44/5.62 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.44/5.62 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % numeral_code(2)
% 5.44/5.62 thf(fact_1428_numeral__code_I2_J,axiom,
% 5.44/5.62 ! [N2: num] :
% 5.44/5.62 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.44/5.62 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % numeral_code(2)
% 5.44/5.62 thf(fact_1429_power__numeral__even,axiom,
% 5.44/5.62 ! [Z: complex,W: num] :
% 5.44/5.62 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.44/5.62 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power_numeral_even
% 5.44/5.62 thf(fact_1430_power__numeral__even,axiom,
% 5.44/5.62 ! [Z: real,W: num] :
% 5.44/5.62 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.44/5.62 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power_numeral_even
% 5.44/5.62 thf(fact_1431_power__numeral__even,axiom,
% 5.44/5.62 ! [Z: nat,W: num] :
% 5.44/5.62 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.44/5.62 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power_numeral_even
% 5.44/5.62 thf(fact_1432_power__numeral__even,axiom,
% 5.44/5.62 ! [Z: int,W: num] :
% 5.44/5.62 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.44/5.62 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power_numeral_even
% 5.44/5.62 thf(fact_1433_linordered__field__no__lb,axiom,
% 5.44/5.62 ! [X3: real] :
% 5.44/5.62 ? [Y5: real] : ( ord_less_real @ Y5 @ X3 ) ).
% 5.44/5.62
% 5.44/5.62 % linordered_field_no_lb
% 5.44/5.62 thf(fact_1434_linordered__field__no__ub,axiom,
% 5.44/5.62 ! [X3: real] :
% 5.44/5.62 ? [X_1: real] : ( ord_less_real @ X3 @ X_1 ) ).
% 5.44/5.62
% 5.44/5.62 % linordered_field_no_ub
% 5.44/5.62 thf(fact_1435_times__divide__times__eq,axiom,
% 5.44/5.62 ! [X: real,Y: real,Z: real,W: real] :
% 5.44/5.62 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.44/5.62 = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % times_divide_times_eq
% 5.44/5.62 thf(fact_1436_times__divide__times__eq,axiom,
% 5.44/5.62 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 5.44/5.62 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % times_divide_times_eq
% 5.44/5.62 thf(fact_1437_divide__divide__times__eq,axiom,
% 5.44/5.62 ! [X: real,Y: real,Z: real,W: real] :
% 5.44/5.62 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.44/5.62 = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_divide_times_eq
% 5.44/5.62 thf(fact_1438_divide__divide__times__eq,axiom,
% 5.44/5.62 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_divide_times_eq
% 5.44/5.62 thf(fact_1439_divide__divide__eq__left_H,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.44/5.62 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_divide_eq_left'
% 5.44/5.62 thf(fact_1440_divide__divide__eq__left_H,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.44/5.62 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_divide_eq_left'
% 5.44/5.62 thf(fact_1441_add__divide__distrib,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_divide_distrib
% 5.44/5.62 thf(fact_1442_add__divide__distrib,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_divide_distrib
% 5.44/5.62 thf(fact_1443_diff__divide__distrib,axiom,
% 5.44/5.62 ! [A: real,B: real,C: real] :
% 5.44/5.62 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_divide_distrib
% 5.44/5.62 thf(fact_1444_diff__divide__distrib,axiom,
% 5.44/5.62 ! [A: complex,B: complex,C: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.44/5.62 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_divide_distrib
% 5.44/5.62 thf(fact_1445_vebt__insert_Osimps_I5_J,axiom,
% 5.44/5.62 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.44/5.62 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_VEBT_VEBT
% 5.44/5.62 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 & ~ ( ( X = Mi )
% 5.44/5.62 | ( X = Ma ) ) )
% 5.44/5.62 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.44/5.62 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_insert.simps(5)
% 5.44/5.62 thf(fact_1446_vebt__pred_Osimps_I7_J,axiom,
% 5.44/5.62 ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ( ord_less_nat @ Ma @ X )
% 5.44/5.62 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( some_nat @ Ma ) ) )
% 5.44/5.62 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.44/5.62 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 != none_nat )
% 5.44/5.62 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.62 @ none_nat ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_pred.simps(7)
% 5.44/5.62 thf(fact_1447_vebt__succ_Osimps_I6_J,axiom,
% 5.44/5.62 ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ( ord_less_nat @ X @ Mi )
% 5.44/5.62 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( some_nat @ Mi ) ) )
% 5.44/5.62 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.44/5.62 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 != none_nat )
% 5.44/5.62 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ none_nat
% 5.44/5.62 @ ( 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 @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.62 @ none_nat ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_succ.simps(6)
% 5.44/5.62 thf(fact_1448_is__pred__in__set__def,axiom,
% 5.44/5.62 ( vEBT_is_pred_in_set
% 5.44/5.62 = ( ^ [Xs: set_nat,X2: nat,Y3: nat] :
% 5.44/5.62 ( ( member_nat @ Y3 @ Xs )
% 5.44/5.62 & ( ord_less_nat @ Y3 @ X2 )
% 5.44/5.62 & ! [Z5: nat] :
% 5.44/5.62 ( ( member_nat @ Z5 @ Xs )
% 5.44/5.62 => ( ( ord_less_nat @ Z5 @ X2 )
% 5.44/5.62 => ( ord_less_eq_nat @ Z5 @ Y3 ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % is_pred_in_set_def
% 5.44/5.62 thf(fact_1449_is__succ__in__set__def,axiom,
% 5.44/5.62 ( vEBT_is_succ_in_set
% 5.44/5.62 = ( ^ [Xs: set_nat,X2: nat,Y3: nat] :
% 5.44/5.62 ( ( member_nat @ Y3 @ Xs )
% 5.44/5.62 & ( ord_less_nat @ X2 @ Y3 )
% 5.44/5.62 & ! [Z5: nat] :
% 5.44/5.62 ( ( member_nat @ Z5 @ Xs )
% 5.44/5.62 => ( ( ord_less_nat @ X2 @ Z5 )
% 5.44/5.62 => ( ord_less_eq_nat @ Y3 @ Z5 ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % is_succ_in_set_def
% 5.44/5.62 thf(fact_1450_discrete,axiom,
% 5.44/5.62 ( ord_less_nat
% 5.44/5.62 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % discrete
% 5.44/5.62 thf(fact_1451_discrete,axiom,
% 5.44/5.62 ( ord_less_int
% 5.44/5.62 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % discrete
% 5.44/5.62 thf(fact_1452_gt__half__sum,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % gt_half_sum
% 5.44/5.62 thf(fact_1453_less__half__sum,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ B )
% 5.44/5.62 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_half_sum
% 5.44/5.62 thf(fact_1454_vebt__delete_Osimps_I7_J,axiom,
% 5.44/5.62 ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.44/5.62 ( ( ( ( ord_less_nat @ X @ Mi )
% 5.44/5.62 | ( ord_less_nat @ Ma @ X ) )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 5.44/5.62 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 5.44/5.62 | ( ord_less_nat @ Ma @ X ) )
% 5.44/5.62 => ( ( ( ( X = Mi )
% 5.44/5.62 & ( X = Ma ) )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 5.44/5.62 & ( ~ ( ( X = Mi )
% 5.44/5.62 & ( X = Ma ) )
% 5.44/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( ( X = Mi )
% 5.44/5.62 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 = Ma ) )
% 5.44/5.62 & ( ( X != Mi )
% 5.44/5.62 => ( X = Ma ) ) )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ ( suc @ ( suc @ Va ) )
% 5.44/5.62 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ ( vEBT_Node
% 5.44/5.62 @ ( some_P7363390416028606310at_nat
% 5.44/5.62 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.44/5.62 @ ( if_nat
% 5.44/5.62 @ ( ( ( X = Mi )
% 5.44/5.62 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.44/5.62 = Ma ) )
% 5.44/5.62 & ( ( X != Mi )
% 5.44/5.62 => ( X = Ma ) ) )
% 5.44/5.62 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ Ma ) ) )
% 5.44/5.62 @ ( suc @ ( suc @ Va ) )
% 5.44/5.62 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 @ Summary ) )
% 5.44/5.62 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_delete.simps(7)
% 5.44/5.62 thf(fact_1455_vebt__member_Osimps_I5_J,axiom,
% 5.44/5.62 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.44/5.62 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.44/5.62 = ( ( X != Mi )
% 5.44/5.62 => ( ( X != Ma )
% 5.44/5.62 => ( ~ ( ord_less_nat @ X @ Mi )
% 5.44/5.62 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.44/5.62 => ( ~ ( ord_less_nat @ Ma @ X )
% 5.44/5.62 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.44/5.62 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_member.simps(5)
% 5.44/5.62 thf(fact_1456_succ__empty,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.62 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.44/5.62 = none_nat )
% 5.44/5.62 = ( ( collect_nat
% 5.44/5.62 @ ^ [Y3: nat] :
% 5.44/5.62 ( ( vEBT_vebt_member @ T @ Y3 )
% 5.44/5.62 & ( ord_less_nat @ X @ Y3 ) ) )
% 5.44/5.62 = bot_bot_set_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % succ_empty
% 5.44/5.62 thf(fact_1457_pred__empty,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.62 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.44/5.62 = none_nat )
% 5.44/5.62 = ( ( collect_nat
% 5.44/5.62 @ ^ [Y3: nat] :
% 5.44/5.62 ( ( vEBT_vebt_member @ T @ Y3 )
% 5.44/5.62 & ( ord_less_nat @ Y3 @ X ) ) )
% 5.44/5.62 = bot_bot_set_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % pred_empty
% 5.44/5.62 thf(fact_1458_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.44/5.62 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.44/5.62 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X )
% 5.44/5.62 = ( ( X = Mi )
% 5.44/5.62 | ( X = Ma )
% 5.44/5.62 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.membermima.simps(4)
% 5.44/5.62 thf(fact_1459_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.44/5.62 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 5.44/5.62 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S3 ) @ X )
% 5.44/5.62 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.naive_member.simps(3)
% 5.44/5.62 thf(fact_1460_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.44/5.62 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 5.44/5.62 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X )
% 5.44/5.62 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.44/5.62 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT_internal.membermima.simps(5)
% 5.44/5.62 thf(fact_1461_maxt__corr__help__empty,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT,N2: nat] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.62 => ( ( ( vEBT_vebt_maxt @ T )
% 5.44/5.62 = none_nat )
% 5.44/5.62 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.44/5.62 = bot_bot_set_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % maxt_corr_help_empty
% 5.44/5.62 thf(fact_1462_mint__corr__help__empty,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT,N2: nat] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.62 => ( ( ( vEBT_vebt_mint @ T )
% 5.44/5.62 = none_nat )
% 5.44/5.62 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.44/5.62 = bot_bot_set_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mint_corr_help_empty
% 5.44/5.62 thf(fact_1463_vebt__pred_Oelims,axiom,
% 5.44/5.62 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.44/5.62 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.44/5.62 = Y )
% 5.44/5.62 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.44/5.62 ( X
% 5.44/5.62 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.62 => ( ( Xa2 = zero_zero_nat )
% 5.44/5.62 => ( Y != none_nat ) ) )
% 5.44/5.62 => ( ! [A3: $o] :
% 5.44/5.62 ( ? [Uw2: $o] :
% 5.44/5.62 ( X
% 5.44/5.62 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.44/5.62 => ( ( Xa2
% 5.44/5.62 = ( suc @ zero_zero_nat ) )
% 5.44/5.62 => ~ ( ( A3
% 5.44/5.62 => ( Y
% 5.44/5.62 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.62 & ( ~ A3
% 5.44/5.62 => ( Y = none_nat ) ) ) ) )
% 5.44/5.62 => ( ! [A3: $o,B3: $o] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.62 => ( ? [Va2: nat] :
% 5.44/5.62 ( Xa2
% 5.44/5.62 = ( suc @ ( suc @ Va2 ) ) )
% 5.44/5.62 => ~ ( ( B3
% 5.44/5.62 => ( Y
% 5.44/5.62 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.62 & ( ~ B3
% 5.44/5.62 => ( ( A3
% 5.44/5.62 => ( Y
% 5.44/5.62 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.62 & ( ~ A3
% 5.44/5.62 => ( Y = none_nat ) ) ) ) ) ) )
% 5.44/5.62 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.44/5.62 ( X
% 5.44/5.62 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.44/5.62 => ( Y != none_nat ) )
% 5.44/5.62 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.44/5.62 ( X
% 5.44/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.44/5.62 => ( Y != none_nat ) )
% 5.44/5.62 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.44/5.62 ( X
% 5.44/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.44/5.62 => ( Y != none_nat ) )
% 5.44/5.62 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.62 ( ( X
% 5.44/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.62 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.62 => ( Y
% 5.44/5.62 = ( some_nat @ Ma2 ) ) )
% 5.44/5.62 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.62 => ( Y
% 5.44/5.62 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.62 != none_nat )
% 5.44/5.62 & ( 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 @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.62 @ ( 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 @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.62 @ ( if_option_nat
% 5.44/5.62 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.62 = none_nat )
% 5.44/5.62 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.44/5.62 @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.62 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % vebt_pred.elims
% 5.44/5.62 thf(fact_1464_valid__0__not,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT] :
% 5.44/5.62 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % valid_0_not
% 5.44/5.62 thf(fact_1465_valid__tree__deg__neq__0,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT] :
% 5.44/5.62 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % valid_tree_deg_neq_0
% 5.44/5.62 thf(fact_1466_deg__not__0,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT,N2: nat] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.62 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.62
% 5.44/5.62 % deg_not_0
% 5.44/5.62 thf(fact_1467_Leaf__0__not,axiom,
% 5.44/5.62 ! [A: $o,B: $o] :
% 5.44/5.62 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % Leaf_0_not
% 5.44/5.62 thf(fact_1468_deg1Leaf,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.44/5.62 = ( ? [A4: $o,B4: $o] :
% 5.44/5.62 ( T
% 5.44/5.62 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % deg1Leaf
% 5.44/5.62 thf(fact_1469_deg__1__Leaf,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.44/5.62 => ? [A3: $o,B3: $o] :
% 5.44/5.62 ( T
% 5.44/5.62 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % deg_1_Leaf
% 5.44/5.62 thf(fact_1470_deg__1__Leafy,axiom,
% 5.44/5.62 ! [T: vEBT_VEBT,N2: nat] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.62 => ( ( N2 = one_one_nat )
% 5.44/5.62 => ? [A3: $o,B3: $o] :
% 5.44/5.62 ( T
% 5.44/5.62 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % deg_1_Leafy
% 5.44/5.62 thf(fact_1471_both__member__options__def,axiom,
% 5.44/5.62 ( vEBT_V8194947554948674370ptions
% 5.44/5.62 = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 5.44/5.62 ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 5.44/5.62 | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % both_member_options_def
% 5.44/5.62 thf(fact_1472_member__valid__both__member__options,axiom,
% 5.44/5.62 ! [Tree: vEBT_VEBT,N2: nat,X: nat] :
% 5.44/5.62 ( ( vEBT_invar_vebt @ Tree @ N2 )
% 5.44/5.62 => ( ( vEBT_vebt_member @ Tree @ X )
% 5.44/5.62 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 5.44/5.62 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % member_valid_both_member_options
% 5.44/5.62 thf(fact_1473_VEBT_Oinject_I2_J,axiom,
% 5.44/5.62 ! [X21: $o,X222: $o,Y21: $o,Y222: $o] :
% 5.44/5.62 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 5.44/5.62 = ( vEBT_Leaf @ Y21 @ Y222 ) )
% 5.44/5.62 = ( ( X21 = Y21 )
% 5.44/5.62 & ( X222 = Y222 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % VEBT.inject(2)
% 5.44/5.62 thf(fact_1474_le__zero__eq,axiom,
% 5.44/5.62 ! [N2: extended_enat] :
% 5.44/5.62 ( ( ord_le2932123472753598470d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.44/5.62 = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_zero_eq
% 5.44/5.62 thf(fact_1475_le__zero__eq,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.44/5.62 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_zero_eq
% 5.44/5.62 thf(fact_1476_not__gr__zero,axiom,
% 5.44/5.62 ! [N2: extended_enat] :
% 5.44/5.62 ( ( ~ ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) )
% 5.44/5.62 = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.62
% 5.44/5.62 % not_gr_zero
% 5.44/5.62 thf(fact_1477_not__gr__zero,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.62 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % not_gr_zero
% 5.44/5.62 thf(fact_1478_mult__cancel__right,axiom,
% 5.44/5.62 ! [A: complex,C: complex,B: complex] :
% 5.44/5.62 ( ( ( times_times_complex @ A @ C )
% 5.44/5.62 = ( times_times_complex @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_complex )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right
% 5.44/5.62 thf(fact_1479_mult__cancel__right,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( ( times_times_real @ A @ C )
% 5.44/5.62 = ( times_times_real @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_real )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right
% 5.44/5.62 thf(fact_1480_mult__cancel__right,axiom,
% 5.44/5.62 ! [A: nat,C: nat,B: nat] :
% 5.44/5.62 ( ( ( times_times_nat @ A @ C )
% 5.44/5.62 = ( times_times_nat @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_nat )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right
% 5.44/5.62 thf(fact_1481_mult__cancel__right,axiom,
% 5.44/5.62 ! [A: int,C: int,B: int] :
% 5.44/5.62 ( ( ( times_times_int @ A @ C )
% 5.44/5.62 = ( times_times_int @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_int )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right
% 5.44/5.62 thf(fact_1482_mult__cancel__left,axiom,
% 5.44/5.62 ! [C: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( ( times_times_complex @ C @ A )
% 5.44/5.62 = ( times_times_complex @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_complex )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left
% 5.44/5.62 thf(fact_1483_mult__cancel__left,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( ( times_times_real @ C @ A )
% 5.44/5.62 = ( times_times_real @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_real )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left
% 5.44/5.62 thf(fact_1484_mult__cancel__left,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( ( times_times_nat @ C @ A )
% 5.44/5.62 = ( times_times_nat @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_nat )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left
% 5.44/5.62 thf(fact_1485_mult__cancel__left,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( ( times_times_int @ C @ A )
% 5.44/5.62 = ( times_times_int @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_int )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left
% 5.44/5.62 thf(fact_1486_mult__eq__0__iff,axiom,
% 5.44/5.62 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.62 ( ( ( times_7803423173614009249d_enat @ A @ B )
% 5.44/5.62 = zero_z5237406670263579293d_enat )
% 5.44/5.62 = ( ( A = zero_z5237406670263579293d_enat )
% 5.44/5.62 | ( B = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_eq_0_iff
% 5.44/5.62 thf(fact_1487_mult__eq__0__iff,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( ( times_times_complex @ A @ B )
% 5.44/5.62 = zero_zero_complex )
% 5.44/5.62 = ( ( A = zero_zero_complex )
% 5.44/5.62 | ( B = zero_zero_complex ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_eq_0_iff
% 5.44/5.62 thf(fact_1488_mult__eq__0__iff,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ( times_times_real @ A @ B )
% 5.44/5.62 = zero_zero_real )
% 5.44/5.62 = ( ( A = zero_zero_real )
% 5.44/5.62 | ( B = zero_zero_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_eq_0_iff
% 5.44/5.62 thf(fact_1489_mult__eq__0__iff,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ( times_times_nat @ A @ B )
% 5.44/5.62 = zero_zero_nat )
% 5.44/5.62 = ( ( A = zero_zero_nat )
% 5.44/5.62 | ( B = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_eq_0_iff
% 5.44/5.62 thf(fact_1490_mult__eq__0__iff,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ( times_times_int @ A @ B )
% 5.44/5.62 = zero_zero_int )
% 5.44/5.62 = ( ( A = zero_zero_int )
% 5.44/5.62 | ( B = zero_zero_int ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_eq_0_iff
% 5.44/5.62 thf(fact_1491_mult__zero__right,axiom,
% 5.44/5.62 ! [A: extended_enat] :
% 5.44/5.62 ( ( times_7803423173614009249d_enat @ A @ zero_z5237406670263579293d_enat )
% 5.44/5.62 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_right
% 5.44/5.62 thf(fact_1492_mult__zero__right,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.44/5.62 = zero_zero_complex ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_right
% 5.44/5.62 thf(fact_1493_mult__zero__right,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( times_times_real @ A @ zero_zero_real )
% 5.44/5.62 = zero_zero_real ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_right
% 5.44/5.62 thf(fact_1494_mult__zero__right,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_right
% 5.44/5.62 thf(fact_1495_mult__zero__right,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( times_times_int @ A @ zero_zero_int )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_right
% 5.44/5.62 thf(fact_1496_mult__zero__left,axiom,
% 5.44/5.62 ! [A: extended_enat] :
% 5.44/5.62 ( ( times_7803423173614009249d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.62 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_left
% 5.44/5.62 thf(fact_1497_mult__zero__left,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.44/5.62 = zero_zero_complex ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_left
% 5.44/5.62 thf(fact_1498_mult__zero__left,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( times_times_real @ zero_zero_real @ A )
% 5.44/5.62 = zero_zero_real ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_left
% 5.44/5.62 thf(fact_1499_mult__zero__left,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_left
% 5.44/5.62 thf(fact_1500_mult__zero__left,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( times_times_int @ zero_zero_int @ A )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % mult_zero_left
% 5.44/5.62 thf(fact_1501_add__0,axiom,
% 5.44/5.62 ! [A: extended_enat] :
% 5.44/5.62 ( ( plus_p3455044024723400733d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_0
% 5.44/5.62 thf(fact_1502_add__0,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_0
% 5.44/5.62 thf(fact_1503_add__0,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_0
% 5.44/5.62 thf(fact_1504_add__0,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_0
% 5.44/5.62 thf(fact_1505_add__0,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add_0
% 5.44/5.62 thf(fact_1506_zero__eq__add__iff__both__eq__0,axiom,
% 5.44/5.62 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.62 ( ( zero_z5237406670263579293d_enat
% 5.44/5.62 = ( plus_p3455044024723400733d_enat @ X @ Y ) )
% 5.44/5.62 = ( ( X = zero_z5237406670263579293d_enat )
% 5.44/5.62 & ( Y = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_eq_add_iff_both_eq_0
% 5.44/5.62 thf(fact_1507_zero__eq__add__iff__both__eq__0,axiom,
% 5.44/5.62 ! [X: nat,Y: nat] :
% 5.44/5.62 ( ( zero_zero_nat
% 5.44/5.62 = ( plus_plus_nat @ X @ Y ) )
% 5.44/5.62 = ( ( X = zero_zero_nat )
% 5.44/5.62 & ( Y = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_eq_add_iff_both_eq_0
% 5.44/5.62 thf(fact_1508_add__eq__0__iff__both__eq__0,axiom,
% 5.44/5.62 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.62 ( ( ( plus_p3455044024723400733d_enat @ X @ Y )
% 5.44/5.62 = zero_z5237406670263579293d_enat )
% 5.44/5.62 = ( ( X = zero_z5237406670263579293d_enat )
% 5.44/5.62 & ( Y = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_eq_0_iff_both_eq_0
% 5.44/5.62 thf(fact_1509_add__eq__0__iff__both__eq__0,axiom,
% 5.44/5.62 ! [X: nat,Y: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ X @ Y )
% 5.44/5.62 = zero_zero_nat )
% 5.44/5.62 = ( ( X = zero_zero_nat )
% 5.44/5.62 & ( Y = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_eq_0_iff_both_eq_0
% 5.44/5.62 thf(fact_1510_add__cancel__right__right,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( plus_plus_complex @ A @ B ) )
% 5.44/5.62 = ( B = zero_zero_complex ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_right_right
% 5.44/5.62 thf(fact_1511_add__cancel__right__right,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( plus_plus_real @ A @ B ) )
% 5.44/5.62 = ( B = zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_right_right
% 5.44/5.62 thf(fact_1512_add__cancel__right__right,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( plus_plus_nat @ A @ B ) )
% 5.44/5.62 = ( B = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_right_right
% 5.44/5.62 thf(fact_1513_add__cancel__right__right,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( plus_plus_int @ A @ B ) )
% 5.44/5.62 = ( B = zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_right_right
% 5.44/5.62 thf(fact_1514_add__cancel__right__left,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( plus_plus_complex @ B @ A ) )
% 5.44/5.62 = ( B = zero_zero_complex ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_right_left
% 5.44/5.62 thf(fact_1515_add__cancel__right__left,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( plus_plus_real @ B @ A ) )
% 5.44/5.62 = ( B = zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_right_left
% 5.44/5.62 thf(fact_1516_add__cancel__right__left,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( plus_plus_nat @ B @ A ) )
% 5.44/5.62 = ( B = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_right_left
% 5.44/5.62 thf(fact_1517_add__cancel__right__left,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( plus_plus_int @ B @ A ) )
% 5.44/5.62 = ( B = zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_right_left
% 5.44/5.62 thf(fact_1518_add__cancel__left__right,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ A @ B )
% 5.44/5.62 = A )
% 5.44/5.62 = ( B = zero_zero_complex ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_left_right
% 5.44/5.62 thf(fact_1519_add__cancel__left__right,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ A @ B )
% 5.44/5.62 = A )
% 5.44/5.62 = ( B = zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_left_right
% 5.44/5.62 thf(fact_1520_add__cancel__left__right,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ A @ B )
% 5.44/5.62 = A )
% 5.44/5.62 = ( B = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_left_right
% 5.44/5.62 thf(fact_1521_add__cancel__left__right,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ A @ B )
% 5.44/5.62 = A )
% 5.44/5.62 = ( B = zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_left_right
% 5.44/5.62 thf(fact_1522_add__cancel__left__left,axiom,
% 5.44/5.62 ! [B: complex,A: complex] :
% 5.44/5.62 ( ( ( plus_plus_complex @ B @ A )
% 5.44/5.62 = A )
% 5.44/5.62 = ( B = zero_zero_complex ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_left_left
% 5.44/5.62 thf(fact_1523_add__cancel__left__left,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ B @ A )
% 5.44/5.62 = A )
% 5.44/5.62 = ( B = zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_left_left
% 5.44/5.62 thf(fact_1524_add__cancel__left__left,axiom,
% 5.44/5.62 ! [B: nat,A: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ B @ A )
% 5.44/5.62 = A )
% 5.44/5.62 = ( B = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_left_left
% 5.44/5.62 thf(fact_1525_add__cancel__left__left,axiom,
% 5.44/5.62 ! [B: int,A: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ B @ A )
% 5.44/5.62 = A )
% 5.44/5.62 = ( B = zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_cancel_left_left
% 5.44/5.62 thf(fact_1526_double__zero__sym,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( zero_zero_real
% 5.44/5.62 = ( plus_plus_real @ A @ A ) )
% 5.44/5.62 = ( A = zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % double_zero_sym
% 5.44/5.62 thf(fact_1527_double__zero__sym,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( zero_zero_int
% 5.44/5.62 = ( plus_plus_int @ A @ A ) )
% 5.44/5.62 = ( A = zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % double_zero_sym
% 5.44/5.62 thf(fact_1528_add_Oright__neutral,axiom,
% 5.44/5.62 ! [A: extended_enat] :
% 5.44/5.62 ( ( plus_p3455044024723400733d_enat @ A @ zero_z5237406670263579293d_enat )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add.right_neutral
% 5.44/5.62 thf(fact_1529_add_Oright__neutral,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add.right_neutral
% 5.44/5.62 thf(fact_1530_add_Oright__neutral,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add.right_neutral
% 5.44/5.62 thf(fact_1531_add_Oright__neutral,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add.right_neutral
% 5.44/5.62 thf(fact_1532_add_Oright__neutral,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % add.right_neutral
% 5.44/5.62 thf(fact_1533_div__by__0,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_0
% 5.44/5.62 thf(fact_1534_div__by__0,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.44/5.62 = zero_zero_real ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_0
% 5.44/5.62 thf(fact_1535_div__by__0,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_0
% 5.44/5.62 thf(fact_1536_div__by__0,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.44/5.62 = zero_zero_complex ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_0
% 5.44/5.62 thf(fact_1537_div__by__0,axiom,
% 5.44/5.62 ! [A: code_integer] :
% 5.44/5.62 ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 5.44/5.62 = zero_z3403309356797280102nteger ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_0
% 5.44/5.62 thf(fact_1538_div__0,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % div_0
% 5.44/5.62 thf(fact_1539_div__0,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.44/5.62 = zero_zero_real ) ).
% 5.44/5.62
% 5.44/5.62 % div_0
% 5.44/5.62 thf(fact_1540_div__0,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % div_0
% 5.44/5.62 thf(fact_1541_div__0,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.44/5.62 = zero_zero_complex ) ).
% 5.44/5.62
% 5.44/5.62 % div_0
% 5.44/5.62 thf(fact_1542_div__0,axiom,
% 5.44/5.62 ! [A: code_integer] :
% 5.44/5.62 ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 5.44/5.62 = zero_z3403309356797280102nteger ) ).
% 5.44/5.62
% 5.44/5.62 % div_0
% 5.44/5.62 thf(fact_1543_bits__div__by__0,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % bits_div_by_0
% 5.44/5.62 thf(fact_1544_bits__div__by__0,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % bits_div_by_0
% 5.44/5.62 thf(fact_1545_bits__div__by__0,axiom,
% 5.44/5.62 ! [A: code_integer] :
% 5.44/5.62 ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 5.44/5.62 = zero_z3403309356797280102nteger ) ).
% 5.44/5.62
% 5.44/5.62 % bits_div_by_0
% 5.44/5.62 thf(fact_1546_bits__div__0,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % bits_div_0
% 5.44/5.62 thf(fact_1547_bits__div__0,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % bits_div_0
% 5.44/5.62 thf(fact_1548_bits__div__0,axiom,
% 5.44/5.62 ! [A: code_integer] :
% 5.44/5.62 ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 5.44/5.62 = zero_z3403309356797280102nteger ) ).
% 5.44/5.62
% 5.44/5.62 % bits_div_0
% 5.44/5.62 thf(fact_1549_division__ring__divide__zero,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.44/5.62 = zero_zero_real ) ).
% 5.44/5.62
% 5.44/5.62 % division_ring_divide_zero
% 5.44/5.62 thf(fact_1550_division__ring__divide__zero,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.44/5.62 = zero_zero_complex ) ).
% 5.44/5.62
% 5.44/5.62 % division_ring_divide_zero
% 5.44/5.62 thf(fact_1551_divide__cancel__right,axiom,
% 5.44/5.62 ! [A: real,C: real,B: real] :
% 5.44/5.62 ( ( ( divide_divide_real @ A @ C )
% 5.44/5.62 = ( divide_divide_real @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_real )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_cancel_right
% 5.44/5.62 thf(fact_1552_divide__cancel__right,axiom,
% 5.44/5.62 ! [A: complex,C: complex,B: complex] :
% 5.44/5.62 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.44/5.62 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_complex )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_cancel_right
% 5.44/5.62 thf(fact_1553_divide__cancel__left,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( ( divide_divide_real @ C @ A )
% 5.44/5.62 = ( divide_divide_real @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_real )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_cancel_left
% 5.44/5.62 thf(fact_1554_divide__cancel__left,axiom,
% 5.44/5.62 ! [C: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.44/5.62 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_complex )
% 5.44/5.62 | ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_cancel_left
% 5.44/5.62 thf(fact_1555_divide__eq__0__iff,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ( divide_divide_real @ A @ B )
% 5.44/5.62 = zero_zero_real )
% 5.44/5.62 = ( ( A = zero_zero_real )
% 5.44/5.62 | ( B = zero_zero_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_eq_0_iff
% 5.44/5.62 thf(fact_1556_divide__eq__0__iff,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.44/5.62 = zero_zero_complex )
% 5.44/5.62 = ( ( A = zero_zero_complex )
% 5.44/5.62 | ( B = zero_zero_complex ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_eq_0_iff
% 5.44/5.62 thf(fact_1557_less__nat__zero__code,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % less_nat_zero_code
% 5.44/5.62 thf(fact_1558_neq0__conv,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( N2 != zero_zero_nat )
% 5.44/5.62 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.62
% 5.44/5.62 % neq0_conv
% 5.44/5.62 thf(fact_1559_bot__nat__0_Onot__eq__extremum,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( A != zero_zero_nat )
% 5.44/5.62 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % bot_nat_0.not_eq_extremum
% 5.44/5.62 thf(fact_1560_bot__nat__0_Oextremum,axiom,
% 5.44/5.62 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.44/5.62
% 5.44/5.62 % bot_nat_0.extremum
% 5.44/5.62 thf(fact_1561_le0,axiom,
% 5.44/5.62 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.44/5.62
% 5.44/5.62 % le0
% 5.44/5.62 thf(fact_1562_Nat_Oadd__0__right,axiom,
% 5.44/5.62 ! [M: nat] :
% 5.44/5.62 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.44/5.62 = M ) ).
% 5.44/5.62
% 5.44/5.62 % Nat.add_0_right
% 5.44/5.62 thf(fact_1563_add__is__0,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ( plus_plus_nat @ M @ N2 )
% 5.44/5.62 = zero_zero_nat )
% 5.44/5.62 = ( ( M = zero_zero_nat )
% 5.44/5.62 & ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_is_0
% 5.44/5.62 thf(fact_1564_mult__cancel2,axiom,
% 5.44/5.62 ! [M: nat,K: nat,N2: nat] :
% 5.44/5.62 ( ( ( times_times_nat @ M @ K )
% 5.44/5.62 = ( times_times_nat @ N2 @ K ) )
% 5.44/5.62 = ( ( M = N2 )
% 5.44/5.62 | ( K = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel2
% 5.44/5.62 thf(fact_1565_mult__cancel1,axiom,
% 5.44/5.62 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ( times_times_nat @ K @ M )
% 5.44/5.62 = ( times_times_nat @ K @ N2 ) )
% 5.44/5.62 = ( ( M = N2 )
% 5.44/5.62 | ( K = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel1
% 5.44/5.62 thf(fact_1566_mult__0__right,axiom,
% 5.44/5.62 ! [M: nat] :
% 5.44/5.62 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % mult_0_right
% 5.44/5.62 thf(fact_1567_mult__is__0,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ( times_times_nat @ M @ N2 )
% 5.44/5.62 = zero_zero_nat )
% 5.44/5.62 = ( ( M = zero_zero_nat )
% 5.44/5.62 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_is_0
% 5.44/5.62 thf(fact_1568_diff__self__eq__0,axiom,
% 5.44/5.62 ! [M: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ M @ M )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % diff_self_eq_0
% 5.44/5.62 thf(fact_1569_diff__0__eq__0,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % diff_0_eq_0
% 5.44/5.62 thf(fact_1570_max__nat_Oeq__neutr__iff,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ( ord_max_nat @ A @ B )
% 5.44/5.62 = zero_zero_nat )
% 5.44/5.62 = ( ( A = zero_zero_nat )
% 5.44/5.62 & ( B = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_nat.eq_neutr_iff
% 5.44/5.62 thf(fact_1571_max__nat_Oleft__neutral,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % max_nat.left_neutral
% 5.44/5.62 thf(fact_1572_max__nat_Oneutr__eq__iff,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( zero_zero_nat
% 5.44/5.62 = ( ord_max_nat @ A @ B ) )
% 5.44/5.62 = ( ( A = zero_zero_nat )
% 5.44/5.62 & ( B = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_nat.neutr_eq_iff
% 5.44/5.62 thf(fact_1573_max__nat_Oright__neutral,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % max_nat.right_neutral
% 5.44/5.62 thf(fact_1574_max__0L,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 5.44/5.62 = N2 ) ).
% 5.44/5.62
% 5.44/5.62 % max_0L
% 5.44/5.62 thf(fact_1575_max__0R,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 5.44/5.62 = N2 ) ).
% 5.44/5.62
% 5.44/5.62 % max_0R
% 5.44/5.62 thf(fact_1576_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.44/5.62 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_le_double_add_iff_zero_le_single_add
% 5.44/5.62 thf(fact_1577_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.44/5.62 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_le_double_add_iff_zero_le_single_add
% 5.44/5.62 thf(fact_1578_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.44/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % double_add_le_zero_iff_single_add_le_zero
% 5.44/5.62 thf(fact_1579_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.44/5.62 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % double_add_le_zero_iff_single_add_le_zero
% 5.44/5.62 thf(fact_1580_le__add__same__cancel2,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.44/5.62 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_same_cancel2
% 5.44/5.62 thf(fact_1581_le__add__same__cancel2,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.44/5.62 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_same_cancel2
% 5.44/5.62 thf(fact_1582_le__add__same__cancel2,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.44/5.62 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_same_cancel2
% 5.44/5.62 thf(fact_1583_le__add__same__cancel1,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.44/5.62 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_same_cancel1
% 5.44/5.62 thf(fact_1584_le__add__same__cancel1,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.44/5.62 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_same_cancel1
% 5.44/5.62 thf(fact_1585_le__add__same__cancel1,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.44/5.62 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % le_add_same_cancel1
% 5.44/5.62 thf(fact_1586_add__le__same__cancel2,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.44/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_same_cancel2
% 5.44/5.62 thf(fact_1587_add__le__same__cancel2,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.44/5.62 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_same_cancel2
% 5.44/5.62 thf(fact_1588_add__le__same__cancel2,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.44/5.62 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_same_cancel2
% 5.44/5.62 thf(fact_1589_add__le__same__cancel1,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.44/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_same_cancel1
% 5.44/5.62 thf(fact_1590_add__le__same__cancel1,axiom,
% 5.44/5.62 ! [B: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.44/5.62 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_same_cancel1
% 5.44/5.62 thf(fact_1591_add__le__same__cancel1,axiom,
% 5.44/5.62 ! [B: int,A: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.44/5.62 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_le_same_cancel1
% 5.44/5.62 thf(fact_1592_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.44/5.62 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_less_double_add_iff_zero_less_single_add
% 5.44/5.62 thf(fact_1593_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.44/5.62 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_less_double_add_iff_zero_less_single_add
% 5.44/5.62 thf(fact_1594_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.44/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % double_add_less_zero_iff_single_add_less_zero
% 5.44/5.62 thf(fact_1595_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.44/5.62 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % double_add_less_zero_iff_single_add_less_zero
% 5.44/5.62 thf(fact_1596_less__add__same__cancel2,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.44/5.62 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_same_cancel2
% 5.44/5.62 thf(fact_1597_less__add__same__cancel2,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.44/5.62 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_same_cancel2
% 5.44/5.62 thf(fact_1598_less__add__same__cancel2,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.44/5.62 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_same_cancel2
% 5.44/5.62 thf(fact_1599_less__add__same__cancel1,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.44/5.62 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_same_cancel1
% 5.44/5.62 thf(fact_1600_less__add__same__cancel1,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.44/5.62 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_same_cancel1
% 5.44/5.62 thf(fact_1601_less__add__same__cancel1,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.44/5.62 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_add_same_cancel1
% 5.44/5.62 thf(fact_1602_add__less__same__cancel2,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.44/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_same_cancel2
% 5.44/5.62 thf(fact_1603_add__less__same__cancel2,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.44/5.62 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_same_cancel2
% 5.44/5.62 thf(fact_1604_add__less__same__cancel2,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.44/5.62 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_same_cancel2
% 5.44/5.62 thf(fact_1605_add__less__same__cancel1,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.44/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_same_cancel1
% 5.44/5.62 thf(fact_1606_add__less__same__cancel1,axiom,
% 5.44/5.62 ! [B: nat,A: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.44/5.62 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_same_cancel1
% 5.44/5.62 thf(fact_1607_add__less__same__cancel1,axiom,
% 5.44/5.62 ! [B: int,A: int] :
% 5.44/5.62 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.44/5.62 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_less_same_cancel1
% 5.44/5.62 thf(fact_1608_diff__ge__0__iff__ge,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.44/5.62 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_ge_0_iff_ge
% 5.44/5.62 thf(fact_1609_diff__ge__0__iff__ge,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.44/5.62 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_ge_0_iff_ge
% 5.44/5.62 thf(fact_1610_diff__gt__0__iff__gt,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.44/5.62 = ( ord_less_real @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_gt_0_iff_gt
% 5.44/5.62 thf(fact_1611_diff__gt__0__iff__gt,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.44/5.62 = ( ord_less_int @ B @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_gt_0_iff_gt
% 5.44/5.62 thf(fact_1612_sum__squares__eq__zero__iff,axiom,
% 5.44/5.62 ! [X: real,Y: real] :
% 5.44/5.62 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.44/5.62 = zero_zero_real )
% 5.44/5.62 = ( ( X = zero_zero_real )
% 5.44/5.62 & ( Y = zero_zero_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % sum_squares_eq_zero_iff
% 5.44/5.62 thf(fact_1613_sum__squares__eq__zero__iff,axiom,
% 5.44/5.62 ! [X: int,Y: int] :
% 5.44/5.62 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.44/5.62 = zero_zero_int )
% 5.44/5.62 = ( ( X = zero_zero_int )
% 5.44/5.62 & ( Y = zero_zero_int ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % sum_squares_eq_zero_iff
% 5.44/5.62 thf(fact_1614_mult__cancel__right2,axiom,
% 5.44/5.62 ! [A: complex,C: complex] :
% 5.44/5.62 ( ( ( times_times_complex @ A @ C )
% 5.44/5.62 = C )
% 5.44/5.62 = ( ( C = zero_zero_complex )
% 5.44/5.62 | ( A = one_one_complex ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right2
% 5.44/5.62 thf(fact_1615_mult__cancel__right2,axiom,
% 5.44/5.62 ! [A: real,C: real] :
% 5.44/5.62 ( ( ( times_times_real @ A @ C )
% 5.44/5.62 = C )
% 5.44/5.62 = ( ( C = zero_zero_real )
% 5.44/5.62 | ( A = one_one_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right2
% 5.44/5.62 thf(fact_1616_mult__cancel__right2,axiom,
% 5.44/5.62 ! [A: int,C: int] :
% 5.44/5.62 ( ( ( times_times_int @ A @ C )
% 5.44/5.62 = C )
% 5.44/5.62 = ( ( C = zero_zero_int )
% 5.44/5.62 | ( A = one_one_int ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right2
% 5.44/5.62 thf(fact_1617_mult__cancel__right1,axiom,
% 5.44/5.62 ! [C: complex,B: complex] :
% 5.44/5.62 ( ( C
% 5.44/5.62 = ( times_times_complex @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_complex )
% 5.44/5.62 | ( B = one_one_complex ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right1
% 5.44/5.62 thf(fact_1618_mult__cancel__right1,axiom,
% 5.44/5.62 ! [C: real,B: real] :
% 5.44/5.62 ( ( C
% 5.44/5.62 = ( times_times_real @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_real )
% 5.44/5.62 | ( B = one_one_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right1
% 5.44/5.62 thf(fact_1619_mult__cancel__right1,axiom,
% 5.44/5.62 ! [C: int,B: int] :
% 5.44/5.62 ( ( C
% 5.44/5.62 = ( times_times_int @ B @ C ) )
% 5.44/5.62 = ( ( C = zero_zero_int )
% 5.44/5.62 | ( B = one_one_int ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_right1
% 5.44/5.62 thf(fact_1620_mult__cancel__left2,axiom,
% 5.44/5.62 ! [C: complex,A: complex] :
% 5.44/5.62 ( ( ( times_times_complex @ C @ A )
% 5.44/5.62 = C )
% 5.44/5.62 = ( ( C = zero_zero_complex )
% 5.44/5.62 | ( A = one_one_complex ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left2
% 5.44/5.62 thf(fact_1621_mult__cancel__left2,axiom,
% 5.44/5.62 ! [C: real,A: real] :
% 5.44/5.62 ( ( ( times_times_real @ C @ A )
% 5.44/5.62 = C )
% 5.44/5.62 = ( ( C = zero_zero_real )
% 5.44/5.62 | ( A = one_one_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left2
% 5.44/5.62 thf(fact_1622_mult__cancel__left2,axiom,
% 5.44/5.62 ! [C: int,A: int] :
% 5.44/5.62 ( ( ( times_times_int @ C @ A )
% 5.44/5.62 = C )
% 5.44/5.62 = ( ( C = zero_zero_int )
% 5.44/5.62 | ( A = one_one_int ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left2
% 5.44/5.62 thf(fact_1623_mult__cancel__left1,axiom,
% 5.44/5.62 ! [C: complex,B: complex] :
% 5.44/5.62 ( ( C
% 5.44/5.62 = ( times_times_complex @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_complex )
% 5.44/5.62 | ( B = one_one_complex ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left1
% 5.44/5.62 thf(fact_1624_mult__cancel__left1,axiom,
% 5.44/5.62 ! [C: real,B: real] :
% 5.44/5.62 ( ( C
% 5.44/5.62 = ( times_times_real @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_real )
% 5.44/5.62 | ( B = one_one_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left1
% 5.44/5.62 thf(fact_1625_mult__cancel__left1,axiom,
% 5.44/5.62 ! [C: int,B: int] :
% 5.44/5.62 ( ( C
% 5.44/5.62 = ( times_times_int @ C @ B ) )
% 5.44/5.62 = ( ( C = zero_zero_int )
% 5.44/5.62 | ( B = one_one_int ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_cancel_left1
% 5.44/5.62 thf(fact_1626_nonzero__mult__div__cancel__right,axiom,
% 5.44/5.62 ! [B: nat,A: nat] :
% 5.44/5.62 ( ( B != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_right
% 5.44/5.62 thf(fact_1627_nonzero__mult__div__cancel__right,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( B != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_right
% 5.44/5.62 thf(fact_1628_nonzero__mult__div__cancel__right,axiom,
% 5.44/5.62 ! [B: int,A: int] :
% 5.44/5.62 ( ( B != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_right
% 5.44/5.62 thf(fact_1629_nonzero__mult__div__cancel__right,axiom,
% 5.44/5.62 ! [B: complex,A: complex] :
% 5.44/5.62 ( ( B != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_right
% 5.44/5.62 thf(fact_1630_nonzero__mult__div__cancel__right,axiom,
% 5.44/5.62 ! [B: code_integer,A: code_integer] :
% 5.44/5.62 ( ( B != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.44/5.62 = A ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_right
% 5.44/5.62 thf(fact_1631_nonzero__mult__div__cancel__left,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( A != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.44/5.62 = B ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_left
% 5.44/5.62 thf(fact_1632_nonzero__mult__div__cancel__left,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( A != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.44/5.62 = B ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_left
% 5.44/5.62 thf(fact_1633_nonzero__mult__div__cancel__left,axiom,
% 5.44/5.62 ! [A: int,B: int] :
% 5.44/5.62 ( ( A != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.44/5.62 = B ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_left
% 5.44/5.62 thf(fact_1634_nonzero__mult__div__cancel__left,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( A != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.44/5.62 = B ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_left
% 5.44/5.62 thf(fact_1635_nonzero__mult__div__cancel__left,axiom,
% 5.44/5.62 ! [A: code_integer,B: code_integer] :
% 5.44/5.62 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 5.44/5.62 = B ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_div_cancel_left
% 5.44/5.62 thf(fact_1636_div__mult__mult1__if,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( ( C = zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.44/5.62 = zero_zero_nat ) )
% 5.44/5.62 & ( ( C != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.44/5.62 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult1_if
% 5.44/5.62 thf(fact_1637_div__mult__mult1__if,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( ( C = zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.62 = zero_zero_int ) )
% 5.44/5.62 & ( ( C != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.62 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult1_if
% 5.44/5.62 thf(fact_1638_div__mult__mult1__if,axiom,
% 5.44/5.62 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.62 ( ( ( C = zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.44/5.62 = zero_z3403309356797280102nteger ) )
% 5.44/5.62 & ( ( C != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.44/5.62 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult1_if
% 5.44/5.62 thf(fact_1639_div__mult__mult2,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( C != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.44/5.62 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult2
% 5.44/5.62 thf(fact_1640_div__mult__mult2,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( C != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.44/5.62 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult2
% 5.44/5.62 thf(fact_1641_div__mult__mult2,axiom,
% 5.44/5.62 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.62 ( ( C != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.44/5.62 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult2
% 5.44/5.62 thf(fact_1642_div__mult__mult1,axiom,
% 5.44/5.62 ! [C: nat,A: nat,B: nat] :
% 5.44/5.62 ( ( C != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.44/5.62 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult1
% 5.44/5.62 thf(fact_1643_div__mult__mult1,axiom,
% 5.44/5.62 ! [C: int,A: int,B: int] :
% 5.44/5.62 ( ( C != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.62 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult1
% 5.44/5.62 thf(fact_1644_div__mult__mult1,axiom,
% 5.44/5.62 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.62 ( ( C != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.44/5.62 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_mult1
% 5.44/5.62 thf(fact_1645_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( C != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.44/5.62 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_divide_mult_cancel_right2
% 5.44/5.62 thf(fact_1646_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.44/5.62 ! [C: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( C != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_divide_mult_cancel_right2
% 5.44/5.62 thf(fact_1647_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( C != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.44/5.62 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_divide_mult_cancel_right
% 5.44/5.62 thf(fact_1648_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.44/5.62 ! [C: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( C != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_divide_mult_cancel_right
% 5.44/5.62 thf(fact_1649_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( C != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.44/5.62 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_divide_mult_cancel_left2
% 5.44/5.62 thf(fact_1650_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.44/5.62 ! [C: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( C != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_divide_mult_cancel_left2
% 5.44/5.62 thf(fact_1651_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( C != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.62 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_divide_mult_cancel_left
% 5.44/5.62 thf(fact_1652_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.44/5.62 ! [C: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( C != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_mult_divide_mult_cancel_left
% 5.44/5.62 thf(fact_1653_mult__divide__mult__cancel__left__if,axiom,
% 5.44/5.62 ! [C: real,A: real,B: real] :
% 5.44/5.62 ( ( ( C = zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.62 = zero_zero_real ) )
% 5.44/5.62 & ( ( C != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.62 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_divide_mult_cancel_left_if
% 5.44/5.62 thf(fact_1654_mult__divide__mult__cancel__left__if,axiom,
% 5.44/5.62 ! [C: complex,A: complex,B: complex] :
% 5.44/5.62 ( ( ( C = zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.44/5.62 = zero_zero_complex ) )
% 5.44/5.62 & ( ( C != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_divide_mult_cancel_left_if
% 5.44/5.62 thf(fact_1655_diff__add__zero,axiom,
% 5.44/5.62 ! [A: nat,B: nat] :
% 5.44/5.62 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % diff_add_zero
% 5.44/5.62 thf(fact_1656_diff__numeral__special_I9_J,axiom,
% 5.44/5.62 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.44/5.62 = zero_zero_complex ) ).
% 5.44/5.62
% 5.44/5.62 % diff_numeral_special(9)
% 5.44/5.62 thf(fact_1657_diff__numeral__special_I9_J,axiom,
% 5.44/5.62 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.44/5.62 = zero_zero_real ) ).
% 5.44/5.62
% 5.44/5.62 % diff_numeral_special(9)
% 5.44/5.62 thf(fact_1658_diff__numeral__special_I9_J,axiom,
% 5.44/5.62 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % diff_numeral_special(9)
% 5.44/5.62 thf(fact_1659_div__self,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( A != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ A @ A )
% 5.44/5.62 = one_one_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_self
% 5.44/5.62 thf(fact_1660_div__self,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( A != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ A @ A )
% 5.44/5.62 = one_one_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_self
% 5.44/5.62 thf(fact_1661_div__self,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( A != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ A @ A )
% 5.44/5.62 = one_one_int ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_self
% 5.44/5.62 thf(fact_1662_div__self,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( A != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.44/5.62 = one_one_complex ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_self
% 5.44/5.62 thf(fact_1663_div__self,axiom,
% 5.44/5.62 ! [A: code_integer] :
% 5.44/5.62 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ A @ A )
% 5.44/5.62 = one_one_Code_integer ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_self
% 5.44/5.62 thf(fact_1664_zero__eq__1__divide__iff,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( zero_zero_real
% 5.44/5.62 = ( divide_divide_real @ one_one_real @ A ) )
% 5.44/5.62 = ( A = zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_eq_1_divide_iff
% 5.44/5.62 thf(fact_1665_one__divide__eq__0__iff,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.44/5.62 = zero_zero_real )
% 5.44/5.62 = ( A = zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_divide_eq_0_iff
% 5.44/5.62 thf(fact_1666_eq__divide__eq__1,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( one_one_real
% 5.44/5.62 = ( divide_divide_real @ B @ A ) )
% 5.44/5.62 = ( ( A != zero_zero_real )
% 5.44/5.62 & ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_divide_eq_1
% 5.44/5.62 thf(fact_1667_divide__eq__eq__1,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( ( divide_divide_real @ B @ A )
% 5.44/5.62 = one_one_real )
% 5.44/5.62 = ( ( A != zero_zero_real )
% 5.44/5.62 & ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_eq_eq_1
% 5.44/5.62 thf(fact_1668_divide__self__if,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ( A = zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ A @ A )
% 5.44/5.62 = zero_zero_real ) )
% 5.44/5.62 & ( ( A != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ A @ A )
% 5.44/5.62 = one_one_real ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_self_if
% 5.44/5.62 thf(fact_1669_divide__self__if,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( ( A = zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.44/5.62 = zero_zero_complex ) )
% 5.44/5.62 & ( ( A != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.44/5.62 = one_one_complex ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_self_if
% 5.44/5.62 thf(fact_1670_divide__self,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( A != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ A @ A )
% 5.44/5.62 = one_one_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_self
% 5.44/5.62 thf(fact_1671_divide__self,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( A != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.44/5.62 = one_one_complex ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_self
% 5.44/5.62 thf(fact_1672_one__eq__divide__iff,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( one_one_real
% 5.44/5.62 = ( divide_divide_real @ A @ B ) )
% 5.44/5.62 = ( ( B != zero_zero_real )
% 5.44/5.62 & ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_eq_divide_iff
% 5.44/5.62 thf(fact_1673_one__eq__divide__iff,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( one_one_complex
% 5.44/5.62 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.62 = ( ( B != zero_zero_complex )
% 5.44/5.62 & ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_eq_divide_iff
% 5.44/5.62 thf(fact_1674_divide__eq__1__iff,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ( divide_divide_real @ A @ B )
% 5.44/5.62 = one_one_real )
% 5.44/5.62 = ( ( B != zero_zero_real )
% 5.44/5.62 & ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_eq_1_iff
% 5.44/5.62 thf(fact_1675_divide__eq__1__iff,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.44/5.62 = one_one_complex )
% 5.44/5.62 = ( ( B != zero_zero_complex )
% 5.44/5.62 & ( A = B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_eq_1_iff
% 5.44/5.62 thf(fact_1676_power__0__Suc,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ ( suc @ N2 ) )
% 5.44/5.62 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.62
% 5.44/5.62 % power_0_Suc
% 5.44/5.62 thf(fact_1677_power__0__Suc,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % power_0_Suc
% 5.44/5.62 thf(fact_1678_power__0__Suc,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 5.44/5.62 = zero_zero_real ) ).
% 5.44/5.62
% 5.44/5.62 % power_0_Suc
% 5.44/5.62 thf(fact_1679_power__0__Suc,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % power_0_Suc
% 5.44/5.62 thf(fact_1680_power__0__Suc,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 5.44/5.62 = zero_zero_complex ) ).
% 5.44/5.62
% 5.44/5.62 % power_0_Suc
% 5.44/5.62 thf(fact_1681_power__zero__numeral,axiom,
% 5.44/5.62 ! [K: num] :
% 5.44/5.62 ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ ( numeral_numeral_nat @ K ) )
% 5.44/5.62 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.62
% 5.44/5.62 % power_zero_numeral
% 5.44/5.62 thf(fact_1682_power__zero__numeral,axiom,
% 5.44/5.62 ! [K: num] :
% 5.44/5.62 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.44/5.62 = zero_zero_nat ) ).
% 5.44/5.62
% 5.44/5.62 % power_zero_numeral
% 5.44/5.62 thf(fact_1683_power__zero__numeral,axiom,
% 5.44/5.62 ! [K: num] :
% 5.44/5.62 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.44/5.62 = zero_zero_real ) ).
% 5.44/5.62
% 5.44/5.62 % power_zero_numeral
% 5.44/5.62 thf(fact_1684_power__zero__numeral,axiom,
% 5.44/5.62 ! [K: num] :
% 5.44/5.62 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.44/5.62 = zero_zero_int ) ).
% 5.44/5.62
% 5.44/5.62 % power_zero_numeral
% 5.44/5.62 thf(fact_1685_power__zero__numeral,axiom,
% 5.44/5.62 ! [K: num] :
% 5.44/5.62 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.44/5.62 = zero_zero_complex ) ).
% 5.44/5.62
% 5.44/5.62 % power_zero_numeral
% 5.44/5.62 thf(fact_1686_power__Suc0__right,axiom,
% 5.44/5.62 ! [A: nat] :
% 5.44/5.62 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % power_Suc0_right
% 5.44/5.62 thf(fact_1687_power__Suc0__right,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % power_Suc0_right
% 5.44/5.62 thf(fact_1688_power__Suc0__right,axiom,
% 5.44/5.62 ! [A: int] :
% 5.44/5.62 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % power_Suc0_right
% 5.44/5.62 thf(fact_1689_power__Suc0__right,axiom,
% 5.44/5.62 ! [A: complex] :
% 5.44/5.62 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.44/5.62 = A ) ).
% 5.44/5.62
% 5.44/5.62 % power_Suc0_right
% 5.44/5.62 thf(fact_1690_less__Suc0,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.44/5.62 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_Suc0
% 5.44/5.62 thf(fact_1691_zero__less__Suc,axiom,
% 5.44/5.62 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_less_Suc
% 5.44/5.62 thf(fact_1692_max__0__1_I4_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ zero_z3403309356797280102nteger )
% 5.44/5.62 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(4)
% 5.44/5.62 thf(fact_1693_max__0__1_I4_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 5.44/5.62 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(4)
% 5.44/5.62 thf(fact_1694_max__0__1_I4_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 5.44/5.62 = ( numeral_numeral_real @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(4)
% 5.44/5.62 thf(fact_1695_max__0__1_I4_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 5.44/5.62 = ( numeral_numeral_nat @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(4)
% 5.44/5.62 thf(fact_1696_max__0__1_I4_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 5.44/5.62 = ( numeral_numeral_int @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(4)
% 5.44/5.62 thf(fact_1697_max__0__1_I3_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X ) )
% 5.44/5.62 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(3)
% 5.44/5.62 thf(fact_1698_max__0__1_I3_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.44/5.62 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(3)
% 5.44/5.62 thf(fact_1699_max__0__1_I3_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 5.44/5.62 = ( numeral_numeral_real @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(3)
% 5.44/5.62 thf(fact_1700_max__0__1_I3_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 5.44/5.62 = ( numeral_numeral_nat @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(3)
% 5.44/5.62 thf(fact_1701_max__0__1_I3_J,axiom,
% 5.44/5.62 ! [X: num] :
% 5.44/5.62 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 5.44/5.62 = ( numeral_numeral_int @ X ) ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(3)
% 5.44/5.62 thf(fact_1702_one__eq__mult__iff,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ( suc @ zero_zero_nat )
% 5.44/5.62 = ( times_times_nat @ M @ N2 ) )
% 5.44/5.62 = ( ( M
% 5.44/5.62 = ( suc @ zero_zero_nat ) )
% 5.44/5.62 & ( N2
% 5.44/5.62 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % one_eq_mult_iff
% 5.44/5.62 thf(fact_1703_mult__eq__1__iff,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ( times_times_nat @ M @ N2 )
% 5.44/5.62 = ( suc @ zero_zero_nat ) )
% 5.44/5.62 = ( ( M
% 5.44/5.62 = ( suc @ zero_zero_nat ) )
% 5.44/5.62 & ( N2
% 5.44/5.62 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_eq_1_iff
% 5.44/5.62 thf(fact_1704_add__gr__0,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.62 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.62 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % add_gr_0
% 5.44/5.62 thf(fact_1705_max__0__1_I1_J,axiom,
% 5.44/5.62 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.44/5.62 = one_one_real ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(1)
% 5.44/5.62 thf(fact_1706_max__0__1_I1_J,axiom,
% 5.44/5.62 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.44/5.62 = one_one_nat ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(1)
% 5.44/5.62 thf(fact_1707_max__0__1_I1_J,axiom,
% 5.44/5.62 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.44/5.62 = one_on7984719198319812577d_enat ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(1)
% 5.44/5.62 thf(fact_1708_max__0__1_I1_J,axiom,
% 5.44/5.62 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.44/5.62 = one_one_int ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(1)
% 5.44/5.62 thf(fact_1709_max__0__1_I1_J,axiom,
% 5.44/5.62 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 5.44/5.62 = one_one_Code_integer ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(1)
% 5.44/5.62 thf(fact_1710_max__0__1_I2_J,axiom,
% 5.44/5.62 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.44/5.62 = one_one_real ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(2)
% 5.44/5.62 thf(fact_1711_max__0__1_I2_J,axiom,
% 5.44/5.62 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.44/5.62 = one_one_nat ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(2)
% 5.44/5.62 thf(fact_1712_max__0__1_I2_J,axiom,
% 5.44/5.62 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.44/5.62 = one_on7984719198319812577d_enat ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(2)
% 5.44/5.62 thf(fact_1713_max__0__1_I2_J,axiom,
% 5.44/5.62 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.44/5.62 = one_one_int ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(2)
% 5.44/5.62 thf(fact_1714_max__0__1_I2_J,axiom,
% 5.44/5.62 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 5.44/5.62 = one_one_Code_integer ) ).
% 5.44/5.62
% 5.44/5.62 % max_0_1(2)
% 5.44/5.62 thf(fact_1715_div__by__Suc__0,axiom,
% 5.44/5.62 ! [M: nat] :
% 5.44/5.62 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.44/5.62 = M ) ).
% 5.44/5.62
% 5.44/5.62 % div_by_Suc_0
% 5.44/5.62 thf(fact_1716_nat__mult__less__cancel__disj,axiom,
% 5.44/5.62 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.62 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.62 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_mult_less_cancel_disj
% 5.44/5.62 thf(fact_1717_nat__0__less__mult__iff,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.62 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.62 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_0_less_mult_iff
% 5.44/5.62 thf(fact_1718_mult__less__cancel2,axiom,
% 5.44/5.62 ! [M: nat,K: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.44/5.62 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.62 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % mult_less_cancel2
% 5.44/5.62 thf(fact_1719_power__Suc__0,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.62 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % power_Suc_0
% 5.44/5.62 thf(fact_1720_nat__power__eq__Suc__0__iff,axiom,
% 5.44/5.62 ! [X: nat,M: nat] :
% 5.44/5.62 ( ( ( power_power_nat @ X @ M )
% 5.44/5.62 = ( suc @ zero_zero_nat ) )
% 5.44/5.62 = ( ( M = zero_zero_nat )
% 5.44/5.62 | ( X
% 5.44/5.62 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_power_eq_Suc_0_iff
% 5.44/5.62 thf(fact_1721_zero__less__diff,axiom,
% 5.44/5.62 ! [N2: nat,M: nat] :
% 5.44/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 5.44/5.62 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_less_diff
% 5.44/5.62 thf(fact_1722_div__less,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.62 => ( ( divide_divide_nat @ M @ N2 )
% 5.44/5.62 = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_less
% 5.44/5.62 thf(fact_1723_nat__zero__less__power__iff,axiom,
% 5.44/5.62 ! [X: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N2 ) )
% 5.44/5.62 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.44/5.62 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_zero_less_power_iff
% 5.44/5.62 thf(fact_1724_diff__is__0__eq_H,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.62 => ( ( minus_minus_nat @ M @ N2 )
% 5.44/5.62 = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_is_0_eq'
% 5.44/5.62 thf(fact_1725_diff__is__0__eq,axiom,
% 5.44/5.62 ! [M: nat,N2: nat] :
% 5.44/5.62 ( ( ( minus_minus_nat @ M @ N2 )
% 5.44/5.62 = zero_zero_nat )
% 5.44/5.62 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.62
% 5.44/5.62 % diff_is_0_eq
% 5.44/5.62 thf(fact_1726_less__one,axiom,
% 5.44/5.62 ! [N2: nat] :
% 5.44/5.62 ( ( ord_less_nat @ N2 @ one_one_nat )
% 5.44/5.62 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_one
% 5.44/5.62 thf(fact_1727_nat__mult__div__cancel__disj,axiom,
% 5.44/5.62 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.62 ( ( ( K = zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.62 = zero_zero_nat ) )
% 5.44/5.62 & ( ( K != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.62 = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nat_mult_div_cancel_disj
% 5.44/5.62 thf(fact_1728_divide__le__0__1__iff,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.44/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_le_0_1_iff
% 5.44/5.62 thf(fact_1729_zero__le__divide__1__iff,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.44/5.62 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_le_divide_1_iff
% 5.44/5.62 thf(fact_1730_eq__divide__eq__numeral1_I1_J,axiom,
% 5.44/5.62 ! [A: real,B: real,W: num] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.62 = ( ( ( ( numeral_numeral_real @ W )
% 5.44/5.62 != zero_zero_real )
% 5.44/5.62 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.44/5.62 = B ) )
% 5.44/5.62 & ( ( ( numeral_numeral_real @ W )
% 5.44/5.62 = zero_zero_real )
% 5.44/5.62 => ( A = zero_zero_real ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_divide_eq_numeral1(1)
% 5.44/5.62 thf(fact_1731_eq__divide__eq__numeral1_I1_J,axiom,
% 5.44/5.62 ! [A: complex,B: complex,W: num] :
% 5.44/5.62 ( ( A
% 5.44/5.62 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.62 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.44/5.62 != zero_zero_complex )
% 5.44/5.62 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.62 = B ) )
% 5.44/5.62 & ( ( ( numera6690914467698888265omplex @ W )
% 5.44/5.62 = zero_zero_complex )
% 5.44/5.62 => ( A = zero_zero_complex ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % eq_divide_eq_numeral1(1)
% 5.44/5.62 thf(fact_1732_divide__eq__eq__numeral1_I1_J,axiom,
% 5.44/5.62 ! [B: real,W: num,A: real] :
% 5.44/5.62 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.44/5.62 = A )
% 5.44/5.62 = ( ( ( ( numeral_numeral_real @ W )
% 5.44/5.62 != zero_zero_real )
% 5.44/5.62 => ( B
% 5.44/5.62 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.44/5.62 & ( ( ( numeral_numeral_real @ W )
% 5.44/5.62 = zero_zero_real )
% 5.44/5.62 => ( A = zero_zero_real ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_eq_eq_numeral1(1)
% 5.44/5.62 thf(fact_1733_divide__eq__eq__numeral1_I1_J,axiom,
% 5.44/5.62 ! [B: complex,W: num,A: complex] :
% 5.44/5.62 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.62 = A )
% 5.44/5.62 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.44/5.62 != zero_zero_complex )
% 5.44/5.62 => ( B
% 5.44/5.62 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.44/5.62 & ( ( ( numera6690914467698888265omplex @ W )
% 5.44/5.62 = zero_zero_complex )
% 5.44/5.62 => ( A = zero_zero_complex ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_eq_eq_numeral1(1)
% 5.44/5.62 thf(fact_1734_zero__less__divide__1__iff,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.44/5.62 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.44/5.62
% 5.44/5.62 % zero_less_divide_1_iff
% 5.44/5.62 thf(fact_1735_less__divide__eq__1__pos,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.62 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.44/5.62 = ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_divide_eq_1_pos
% 5.44/5.62 thf(fact_1736_less__divide__eq__1__neg,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.62 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.44/5.62 = ( ord_less_real @ B @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % less_divide_eq_1_neg
% 5.44/5.62 thf(fact_1737_divide__less__eq__1__pos,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.62 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.44/5.62 = ( ord_less_real @ B @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_less_eq_1_pos
% 5.44/5.62 thf(fact_1738_divide__less__eq__1__neg,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.62 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.44/5.62 = ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_less_eq_1_neg
% 5.44/5.62 thf(fact_1739_divide__less__0__1__iff,axiom,
% 5.44/5.62 ! [A: real] :
% 5.44/5.62 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.44/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.44/5.62
% 5.44/5.62 % divide_less_0_1_iff
% 5.44/5.62 thf(fact_1740_div__mult__self4,axiom,
% 5.44/5.62 ! [B: nat,C: nat,A: nat] :
% 5.44/5.62 ( ( B != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.44/5.62 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self4
% 5.44/5.62 thf(fact_1741_div__mult__self4,axiom,
% 5.44/5.62 ! [B: int,C: int,A: int] :
% 5.44/5.62 ( ( B != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.44/5.62 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self4
% 5.44/5.62 thf(fact_1742_div__mult__self4,axiom,
% 5.44/5.62 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.44/5.62 ( ( B != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.44/5.62 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self4
% 5.44/5.62 thf(fact_1743_div__mult__self3,axiom,
% 5.44/5.62 ! [B: nat,C: nat,A: nat] :
% 5.44/5.62 ( ( B != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.44/5.62 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self3
% 5.44/5.62 thf(fact_1744_div__mult__self3,axiom,
% 5.44/5.62 ! [B: int,C: int,A: int] :
% 5.44/5.62 ( ( B != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.44/5.62 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self3
% 5.44/5.62 thf(fact_1745_div__mult__self3,axiom,
% 5.44/5.62 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.44/5.62 ( ( B != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.44/5.62 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self3
% 5.44/5.62 thf(fact_1746_div__mult__self2,axiom,
% 5.44/5.62 ! [B: nat,A: nat,C: nat] :
% 5.44/5.62 ( ( B != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.44/5.62 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self2
% 5.44/5.62 thf(fact_1747_div__mult__self2,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( B != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.44/5.62 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self2
% 5.44/5.62 thf(fact_1748_div__mult__self2,axiom,
% 5.44/5.62 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.62 ( ( B != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.44/5.62 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self2
% 5.44/5.62 thf(fact_1749_div__mult__self1,axiom,
% 5.44/5.62 ! [B: nat,A: nat,C: nat] :
% 5.44/5.62 ( ( B != zero_zero_nat )
% 5.44/5.62 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.44/5.62 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self1
% 5.44/5.62 thf(fact_1750_div__mult__self1,axiom,
% 5.44/5.62 ! [B: int,A: int,C: int] :
% 5.44/5.62 ( ( B != zero_zero_int )
% 5.44/5.62 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.44/5.62 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self1
% 5.44/5.62 thf(fact_1751_div__mult__self1,axiom,
% 5.44/5.62 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.62 ( ( B != zero_z3403309356797280102nteger )
% 5.44/5.62 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.44/5.62 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % div_mult_self1
% 5.44/5.62 thf(fact_1752_nonzero__divide__mult__cancel__right,axiom,
% 5.44/5.62 ! [B: real,A: real] :
% 5.44/5.62 ( ( B != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.44/5.62 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_divide_mult_cancel_right
% 5.44/5.62 thf(fact_1753_nonzero__divide__mult__cancel__right,axiom,
% 5.44/5.62 ! [B: complex,A: complex] :
% 5.44/5.62 ( ( B != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_divide_mult_cancel_right
% 5.44/5.62 thf(fact_1754_nonzero__divide__mult__cancel__left,axiom,
% 5.44/5.62 ! [A: real,B: real] :
% 5.44/5.62 ( ( A != zero_zero_real )
% 5.44/5.62 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.44/5.62 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_divide_mult_cancel_left
% 5.44/5.62 thf(fact_1755_nonzero__divide__mult__cancel__left,axiom,
% 5.44/5.62 ! [A: complex,B: complex] :
% 5.44/5.62 ( ( A != zero_zero_complex )
% 5.44/5.62 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.44/5.62 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % nonzero_divide_mult_cancel_left
% 5.44/5.62 thf(fact_1756_power__eq__0__iff,axiom,
% 5.44/5.62 ! [A: nat,N2: nat] :
% 5.44/5.62 ( ( ( power_power_nat @ A @ N2 )
% 5.44/5.62 = zero_zero_nat )
% 5.44/5.62 = ( ( A = zero_zero_nat )
% 5.44/5.62 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power_eq_0_iff
% 5.44/5.62 thf(fact_1757_power__eq__0__iff,axiom,
% 5.44/5.62 ! [A: real,N2: nat] :
% 5.44/5.62 ( ( ( power_power_real @ A @ N2 )
% 5.44/5.62 = zero_zero_real )
% 5.44/5.62 = ( ( A = zero_zero_real )
% 5.44/5.62 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power_eq_0_iff
% 5.44/5.62 thf(fact_1758_power__eq__0__iff,axiom,
% 5.44/5.62 ! [A: int,N2: nat] :
% 5.44/5.62 ( ( ( power_power_int @ A @ N2 )
% 5.44/5.62 = zero_zero_int )
% 5.44/5.62 = ( ( A = zero_zero_int )
% 5.44/5.62 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.62
% 5.44/5.62 % power_eq_0_iff
% 5.44/5.62 thf(fact_1759_power__eq__0__iff,axiom,
% 5.44/5.62 ! [A: complex,N2: nat] :
% 5.44/5.62 ( ( ( power_power_complex @ A @ N2 )
% 5.44/5.62 = zero_zero_complex )
% 5.44/5.62 = ( ( A = zero_zero_complex )
% 5.44/5.63 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_0_iff
% 5.44/5.63 thf(fact_1760_Suc__pred,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.44/5.63 = N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % Suc_pred
% 5.44/5.63 thf(fact_1761_one__le__mult__iff,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.63 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.44/5.63 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % one_le_mult_iff
% 5.44/5.63 thf(fact_1762_nat__mult__le__cancel__disj,axiom,
% 5.44/5.63 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.63 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.63 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_mult_le_cancel_disj
% 5.44/5.63 thf(fact_1763_mult__le__cancel2,axiom,
% 5.44/5.63 ! [M: nat,K: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.44/5.63 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.63 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel2
% 5.44/5.63 thf(fact_1764_div__mult__self1__is__m,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 5.44/5.63 = M ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_mult_self1_is_m
% 5.44/5.63 thf(fact_1765_div__mult__self__is__m,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 5.44/5.63 = M ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_mult_self_is_m
% 5.44/5.63 thf(fact_1766_le__divide__eq__1__pos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.44/5.63 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_divide_eq_1_pos
% 5.44/5.63 thf(fact_1767_le__divide__eq__1__neg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.44/5.63 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_divide_eq_1_neg
% 5.44/5.63 thf(fact_1768_divide__le__eq__1__pos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.44/5.63 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_le_eq_1_pos
% 5.44/5.63 thf(fact_1769_divide__le__eq__1__neg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.44/5.63 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_le_eq_1_neg
% 5.44/5.63 thf(fact_1770_power__strict__decreasing__iff,axiom,
% 5.44/5.63 ! [B: real,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ( ord_less_real @ B @ one_one_real )
% 5.44/5.63 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_decreasing_iff
% 5.44/5.63 thf(fact_1771_power__strict__decreasing__iff,axiom,
% 5.44/5.63 ! [B: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.44/5.63 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_decreasing_iff
% 5.44/5.63 thf(fact_1772_power__strict__decreasing__iff,axiom,
% 5.44/5.63 ! [B: int,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ord_less_int @ B @ one_one_int )
% 5.44/5.63 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_decreasing_iff
% 5.44/5.63 thf(fact_1773_zero__eq__power2,axiom,
% 5.44/5.63 ! [A: nat] :
% 5.44/5.63 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_nat )
% 5.44/5.63 = ( A = zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_eq_power2
% 5.44/5.63 thf(fact_1774_zero__eq__power2,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_real )
% 5.44/5.63 = ( A = zero_zero_real ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_eq_power2
% 5.44/5.63 thf(fact_1775_zero__eq__power2,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_int )
% 5.44/5.63 = ( A = zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_eq_power2
% 5.44/5.63 thf(fact_1776_zero__eq__power2,axiom,
% 5.44/5.63 ! [A: complex] :
% 5.44/5.63 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_complex )
% 5.44/5.63 = ( A = zero_zero_complex ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_eq_power2
% 5.44/5.63 thf(fact_1777_power__mono__iff,axiom,
% 5.44/5.63 ! [A: real,B: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_mono_iff
% 5.44/5.63 thf(fact_1778_power__mono__iff,axiom,
% 5.44/5.63 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_mono_iff
% 5.44/5.63 thf(fact_1779_power__mono__iff,axiom,
% 5.44/5.63 ! [A: int,B: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_mono_iff
% 5.44/5.63 thf(fact_1780_Suc__diff__1,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.44/5.63 = N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % Suc_diff_1
% 5.44/5.63 thf(fact_1781_bits__1__div__2,axiom,
% 5.44/5.63 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % bits_1_div_2
% 5.44/5.63 thf(fact_1782_bits__1__div__2,axiom,
% 5.44/5.63 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % bits_1_div_2
% 5.44/5.63 thf(fact_1783_bits__1__div__2,axiom,
% 5.44/5.63 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_z3403309356797280102nteger ) ).
% 5.44/5.63
% 5.44/5.63 % bits_1_div_2
% 5.44/5.63 thf(fact_1784_one__div__two__eq__zero,axiom,
% 5.44/5.63 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % one_div_two_eq_zero
% 5.44/5.63 thf(fact_1785_one__div__two__eq__zero,axiom,
% 5.44/5.63 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % one_div_two_eq_zero
% 5.44/5.63 thf(fact_1786_one__div__two__eq__zero,axiom,
% 5.44/5.63 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_z3403309356797280102nteger ) ).
% 5.44/5.63
% 5.44/5.63 % one_div_two_eq_zero
% 5.44/5.63 thf(fact_1787_power2__eq__iff__nonneg,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 = ( X = Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_eq_iff_nonneg
% 5.44/5.63 thf(fact_1788_power2__eq__iff__nonneg,axiom,
% 5.44/5.63 ! [X: nat,Y: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.44/5.63 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 = ( X = Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_eq_iff_nonneg
% 5.44/5.63 thf(fact_1789_power2__eq__iff__nonneg,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.63 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 = ( X = Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_eq_iff_nonneg
% 5.44/5.63 thf(fact_1790_power2__less__eq__zero__iff,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.44/5.63 = ( A = zero_zero_real ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_less_eq_zero_iff
% 5.44/5.63 thf(fact_1791_power2__less__eq__zero__iff,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.44/5.63 = ( A = zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_less_eq_zero_iff
% 5.44/5.63 thf(fact_1792_zero__less__power2,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 = ( A != zero_zero_real ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_power2
% 5.44/5.63 thf(fact_1793_zero__less__power2,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 = ( A != zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_power2
% 5.44/5.63 thf(fact_1794_power__decreasing__iff,axiom,
% 5.44/5.63 ! [B: real,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ( ord_less_real @ B @ one_one_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_decreasing_iff
% 5.44/5.63 thf(fact_1795_power__decreasing__iff,axiom,
% 5.44/5.63 ! [B: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_decreasing_iff
% 5.44/5.63 thf(fact_1796_power__decreasing__iff,axiom,
% 5.44/5.63 ! [B: int,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ord_less_int @ B @ one_one_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.44/5.63 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_decreasing_iff
% 5.44/5.63 thf(fact_1797_sum__power2__eq__zero__iff,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 = zero_zero_real )
% 5.44/5.63 = ( ( X = zero_zero_real )
% 5.44/5.63 & ( Y = zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_power2_eq_zero_iff
% 5.44/5.63 thf(fact_1798_sum__power2__eq__zero__iff,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 = zero_zero_int )
% 5.44/5.63 = ( ( X = zero_zero_int )
% 5.44/5.63 & ( Y = zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_power2_eq_zero_iff
% 5.44/5.63 thf(fact_1799_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.44/5.63 ! [A: $o,B: $o,X: nat] :
% 5.44/5.63 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.44/5.63 = ( ( ( X = zero_zero_nat )
% 5.44/5.63 => A )
% 5.44/5.63 & ( ( X != zero_zero_nat )
% 5.44/5.63 => ( ( ( X = one_one_nat )
% 5.44/5.63 => B )
% 5.44/5.63 & ( X = one_one_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.naive_member.simps(1)
% 5.44/5.63 thf(fact_1800_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.44/5.63 ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.44/5.63 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.membermima.simps(1)
% 5.44/5.63 thf(fact_1801_vebt__delete_Osimps_I1_J,axiom,
% 5.44/5.63 ! [A: $o,B: $o] :
% 5.44/5.63 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 5.44/5.63 = ( vEBT_Leaf @ $false @ B ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_delete.simps(1)
% 5.44/5.63 thf(fact_1802_VEBT_Osize_I4_J,axiom,
% 5.44/5.63 ! [X21: $o,X222: $o] :
% 5.44/5.63 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.44/5.63 = zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT.size(4)
% 5.44/5.63 thf(fact_1803_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.44/5.63 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.44/5.63 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.naive_member.simps(2)
% 5.44/5.63 thf(fact_1804_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.44/5.63 ! [Uu: $o] :
% 5.44/5.63 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.minNull.simps(3)
% 5.44/5.63 thf(fact_1805_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.44/5.63 ! [Uv: $o] :
% 5.44/5.63 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.minNull.simps(2)
% 5.44/5.63 thf(fact_1806_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.44/5.63 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.minNull.simps(1)
% 5.44/5.63 thf(fact_1807_vebt__delete_Osimps_I2_J,axiom,
% 5.44/5.63 ! [A: $o,B: $o] :
% 5.44/5.63 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.63 = ( vEBT_Leaf @ A @ $false ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_delete.simps(2)
% 5.44/5.63 thf(fact_1808_vebt__member_Osimps_I1_J,axiom,
% 5.44/5.63 ! [A: $o,B: $o,X: nat] :
% 5.44/5.63 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.44/5.63 = ( ( ( X = zero_zero_nat )
% 5.44/5.63 => A )
% 5.44/5.63 & ( ( X != zero_zero_nat )
% 5.44/5.63 => ( ( ( X = one_one_nat )
% 5.44/5.63 => B )
% 5.44/5.63 & ( X = one_one_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_member.simps(1)
% 5.44/5.63 thf(fact_1809_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.44/5.63 ! [X: produc9072475918466114483BT_nat] :
% 5.44/5.63 ( ! [A3: $o,B3: $o,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X5 ) )
% 5.44/5.63 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.44/5.63 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ X5 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.naive_member.cases
% 5.44/5.63 thf(fact_1810_invar__vebt_Ointros_I1_J,axiom,
% 5.44/5.63 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % invar_vebt.intros(1)
% 5.44/5.63 thf(fact_1811_power__0__left,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ( N2 = zero_zero_nat )
% 5.44/5.63 => ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.44/5.63 = one_on7984719198319812577d_enat ) )
% 5.44/5.63 & ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.44/5.63 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_0_left
% 5.44/5.63 thf(fact_1812_power__0__left,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ( N2 = zero_zero_nat )
% 5.44/5.63 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 = one_one_nat ) )
% 5.44/5.63 & ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 = zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_0_left
% 5.44/5.63 thf(fact_1813_power__0__left,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ( N2 = zero_zero_nat )
% 5.44/5.63 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.44/5.63 = one_one_real ) )
% 5.44/5.63 & ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.44/5.63 = zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_0_left
% 5.44/5.63 thf(fact_1814_power__0__left,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ( N2 = zero_zero_nat )
% 5.44/5.63 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.44/5.63 = one_one_int ) )
% 5.44/5.63 & ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.44/5.63 = zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_0_left
% 5.44/5.63 thf(fact_1815_power__0__left,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ( N2 = zero_zero_nat )
% 5.44/5.63 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.44/5.63 = one_one_complex ) )
% 5.44/5.63 & ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.44/5.63 = zero_zero_complex ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_0_left
% 5.44/5.63 thf(fact_1816_zero__power,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.44/5.63 = zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power
% 5.44/5.63 thf(fact_1817_zero__power,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 = zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power
% 5.44/5.63 thf(fact_1818_zero__power,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.44/5.63 = zero_zero_real ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power
% 5.44/5.63 thf(fact_1819_zero__power,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.44/5.63 = zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power
% 5.44/5.63 thf(fact_1820_zero__power,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.44/5.63 = zero_zero_complex ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power
% 5.44/5.63 thf(fact_1821_VEBT_Odistinct_I1_J,axiom,
% 5.44/5.63 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.44/5.63 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.44/5.63 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT.distinct(1)
% 5.44/5.63 thf(fact_1822_VEBT_Oexhaust,axiom,
% 5.44/5.63 ! [Y: vEBT_VEBT] :
% 5.44/5.63 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.44/5.63 ( Y
% 5.44/5.63 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.44/5.63 => ~ ! [X212: $o,X223: $o] :
% 5.44/5.63 ( Y
% 5.44/5.63 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT.exhaust
% 5.44/5.63 thf(fact_1823_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.44/5.63 ! [X: produc9072475918466114483BT_nat] :
% 5.44/5.63 ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 5.44/5.63 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.valid'.cases
% 5.44/5.63 thf(fact_1824_vebt__insert_Osimps_I1_J,axiom,
% 5.44/5.63 ! [X: nat,A: $o,B: $o] :
% 5.44/5.63 ( ( ( X = zero_zero_nat )
% 5.44/5.63 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.44/5.63 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.44/5.63 & ( ( X != zero_zero_nat )
% 5.44/5.63 => ( ( ( X = one_one_nat )
% 5.44/5.63 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.44/5.63 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.44/5.63 & ( ( X != one_one_nat )
% 5.44/5.63 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.44/5.63 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_insert.simps(1)
% 5.44/5.63 thf(fact_1825_vebt__pred_Osimps_I1_J,axiom,
% 5.44/5.63 ! [Uu: $o,Uv: $o] :
% 5.44/5.63 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.44/5.63 = none_nat ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_pred.simps(1)
% 5.44/5.63 thf(fact_1826_zero__le,axiom,
% 5.44/5.63 ! [X: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ X ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le
% 5.44/5.63 thf(fact_1827_zero__le,axiom,
% 5.44/5.63 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le
% 5.44/5.63 thf(fact_1828_le__numeral__extra_I3_J,axiom,
% 5.44/5.63 ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat ).
% 5.44/5.63
% 5.44/5.63 % le_numeral_extra(3)
% 5.44/5.63 thf(fact_1829_le__numeral__extra_I3_J,axiom,
% 5.44/5.63 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.44/5.63
% 5.44/5.63 % le_numeral_extra(3)
% 5.44/5.63 thf(fact_1830_le__numeral__extra_I3_J,axiom,
% 5.44/5.63 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.44/5.63
% 5.44/5.63 % le_numeral_extra(3)
% 5.44/5.63 thf(fact_1831_le__numeral__extra_I3_J,axiom,
% 5.44/5.63 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.44/5.63
% 5.44/5.63 % le_numeral_extra(3)
% 5.44/5.63 thf(fact_1832_zero__less__iff__neq__zero,axiom,
% 5.44/5.63 ! [N2: extended_enat] :
% 5.44/5.63 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.44/5.63 = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_iff_neq_zero
% 5.44/5.63 thf(fact_1833_zero__less__iff__neq__zero,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 = ( N2 != zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_iff_neq_zero
% 5.44/5.63 thf(fact_1834_gr__implies__not__zero,axiom,
% 5.44/5.63 ! [M: extended_enat,N2: extended_enat] :
% 5.44/5.63 ( ( ord_le72135733267957522d_enat @ M @ N2 )
% 5.44/5.63 => ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.63
% 5.44/5.63 % gr_implies_not_zero
% 5.44/5.63 thf(fact_1835_gr__implies__not__zero,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.63 => ( N2 != zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % gr_implies_not_zero
% 5.44/5.63 thf(fact_1836_not__less__zero,axiom,
% 5.44/5.63 ! [N2: extended_enat] :
% 5.44/5.63 ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % not_less_zero
% 5.44/5.63 thf(fact_1837_not__less__zero,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % not_less_zero
% 5.44/5.63 thf(fact_1838_gr__zeroI,axiom,
% 5.44/5.63 ! [N2: extended_enat] :
% 5.44/5.63 ( ( N2 != zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % gr_zeroI
% 5.44/5.63 thf(fact_1839_gr__zeroI,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % gr_zeroI
% 5.44/5.63 thf(fact_1840_field__lbound__gt__zero,axiom,
% 5.44/5.63 ! [D1: real,D22: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.44/5.63 => ? [E2: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.44/5.63 & ( ord_less_real @ E2 @ D1 )
% 5.44/5.63 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % field_lbound_gt_zero
% 5.44/5.63 thf(fact_1841_less__numeral__extra_I3_J,axiom,
% 5.44/5.63 ~ ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % less_numeral_extra(3)
% 5.44/5.63 thf(fact_1842_less__numeral__extra_I3_J,axiom,
% 5.44/5.63 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % less_numeral_extra(3)
% 5.44/5.63 thf(fact_1843_less__numeral__extra_I3_J,axiom,
% 5.44/5.63 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % less_numeral_extra(3)
% 5.44/5.63 thf(fact_1844_less__numeral__extra_I3_J,axiom,
% 5.44/5.63 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % less_numeral_extra(3)
% 5.44/5.63 thf(fact_1845_zero__neq__numeral,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ( zero_z5237406670263579293d_enat
% 5.44/5.63 != ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_numeral
% 5.44/5.63 thf(fact_1846_zero__neq__numeral,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ( zero_zero_complex
% 5.44/5.63 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_numeral
% 5.44/5.63 thf(fact_1847_zero__neq__numeral,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ( zero_zero_real
% 5.44/5.63 != ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_numeral
% 5.44/5.63 thf(fact_1848_zero__neq__numeral,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ( zero_zero_nat
% 5.44/5.63 != ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_numeral
% 5.44/5.63 thf(fact_1849_zero__neq__numeral,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ( zero_zero_int
% 5.44/5.63 != ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_numeral
% 5.44/5.63 thf(fact_1850_mult__right__cancel,axiom,
% 5.44/5.63 ! [C: complex,A: complex,B: complex] :
% 5.44/5.63 ( ( C != zero_zero_complex )
% 5.44/5.63 => ( ( ( times_times_complex @ A @ C )
% 5.44/5.63 = ( times_times_complex @ B @ C ) )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_cancel
% 5.44/5.63 thf(fact_1851_mult__right__cancel,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( C != zero_zero_real )
% 5.44/5.63 => ( ( ( times_times_real @ A @ C )
% 5.44/5.63 = ( times_times_real @ B @ C ) )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_cancel
% 5.44/5.63 thf(fact_1852_mult__right__cancel,axiom,
% 5.44/5.63 ! [C: nat,A: nat,B: nat] :
% 5.44/5.63 ( ( C != zero_zero_nat )
% 5.44/5.63 => ( ( ( times_times_nat @ A @ C )
% 5.44/5.63 = ( times_times_nat @ B @ C ) )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_cancel
% 5.44/5.63 thf(fact_1853_mult__right__cancel,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( C != zero_zero_int )
% 5.44/5.63 => ( ( ( times_times_int @ A @ C )
% 5.44/5.63 = ( times_times_int @ B @ C ) )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_cancel
% 5.44/5.63 thf(fact_1854_mult__left__cancel,axiom,
% 5.44/5.63 ! [C: complex,A: complex,B: complex] :
% 5.44/5.63 ( ( C != zero_zero_complex )
% 5.44/5.63 => ( ( ( times_times_complex @ C @ A )
% 5.44/5.63 = ( times_times_complex @ C @ B ) )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_cancel
% 5.44/5.63 thf(fact_1855_mult__left__cancel,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( C != zero_zero_real )
% 5.44/5.63 => ( ( ( times_times_real @ C @ A )
% 5.44/5.63 = ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_cancel
% 5.44/5.63 thf(fact_1856_mult__left__cancel,axiom,
% 5.44/5.63 ! [C: nat,A: nat,B: nat] :
% 5.44/5.63 ( ( C != zero_zero_nat )
% 5.44/5.63 => ( ( ( times_times_nat @ C @ A )
% 5.44/5.63 = ( times_times_nat @ C @ B ) )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_cancel
% 5.44/5.63 thf(fact_1857_mult__left__cancel,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( C != zero_zero_int )
% 5.44/5.63 => ( ( ( times_times_int @ C @ A )
% 5.44/5.63 = ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_cancel
% 5.44/5.63 thf(fact_1858_no__zero__divisors,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( A != zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( B != zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( times_7803423173614009249d_enat @ A @ B )
% 5.44/5.63 != zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % no_zero_divisors
% 5.44/5.63 thf(fact_1859_no__zero__divisors,axiom,
% 5.44/5.63 ! [A: complex,B: complex] :
% 5.44/5.63 ( ( A != zero_zero_complex )
% 5.44/5.63 => ( ( B != zero_zero_complex )
% 5.44/5.63 => ( ( times_times_complex @ A @ B )
% 5.44/5.63 != zero_zero_complex ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % no_zero_divisors
% 5.44/5.63 thf(fact_1860_no__zero__divisors,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( A != zero_zero_real )
% 5.44/5.63 => ( ( B != zero_zero_real )
% 5.44/5.63 => ( ( times_times_real @ A @ B )
% 5.44/5.63 != zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % no_zero_divisors
% 5.44/5.63 thf(fact_1861_no__zero__divisors,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( A != zero_zero_nat )
% 5.44/5.63 => ( ( B != zero_zero_nat )
% 5.44/5.63 => ( ( times_times_nat @ A @ B )
% 5.44/5.63 != zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % no_zero_divisors
% 5.44/5.63 thf(fact_1862_no__zero__divisors,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( A != zero_zero_int )
% 5.44/5.63 => ( ( B != zero_zero_int )
% 5.44/5.63 => ( ( times_times_int @ A @ B )
% 5.44/5.63 != zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % no_zero_divisors
% 5.44/5.63 thf(fact_1863_divisors__zero,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ( times_7803423173614009249d_enat @ A @ B )
% 5.44/5.63 = zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( A = zero_z5237406670263579293d_enat )
% 5.44/5.63 | ( B = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divisors_zero
% 5.44/5.63 thf(fact_1864_divisors__zero,axiom,
% 5.44/5.63 ! [A: complex,B: complex] :
% 5.44/5.63 ( ( ( times_times_complex @ A @ B )
% 5.44/5.63 = zero_zero_complex )
% 5.44/5.63 => ( ( A = zero_zero_complex )
% 5.44/5.63 | ( B = zero_zero_complex ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divisors_zero
% 5.44/5.63 thf(fact_1865_divisors__zero,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ( times_times_real @ A @ B )
% 5.44/5.63 = zero_zero_real )
% 5.44/5.63 => ( ( A = zero_zero_real )
% 5.44/5.63 | ( B = zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divisors_zero
% 5.44/5.63 thf(fact_1866_divisors__zero,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ( times_times_nat @ A @ B )
% 5.44/5.63 = zero_zero_nat )
% 5.44/5.63 => ( ( A = zero_zero_nat )
% 5.44/5.63 | ( B = zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divisors_zero
% 5.44/5.63 thf(fact_1867_divisors__zero,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ( times_times_int @ A @ B )
% 5.44/5.63 = zero_zero_int )
% 5.44/5.63 => ( ( A = zero_zero_int )
% 5.44/5.63 | ( B = zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divisors_zero
% 5.44/5.63 thf(fact_1868_mult__not__zero,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ( times_7803423173614009249d_enat @ A @ B )
% 5.44/5.63 != zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( A != zero_z5237406670263579293d_enat )
% 5.44/5.63 & ( B != zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_not_zero
% 5.44/5.63 thf(fact_1869_mult__not__zero,axiom,
% 5.44/5.63 ! [A: complex,B: complex] :
% 5.44/5.63 ( ( ( times_times_complex @ A @ B )
% 5.44/5.63 != zero_zero_complex )
% 5.44/5.63 => ( ( A != zero_zero_complex )
% 5.44/5.63 & ( B != zero_zero_complex ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_not_zero
% 5.44/5.63 thf(fact_1870_mult__not__zero,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ( times_times_real @ A @ B )
% 5.44/5.63 != zero_zero_real )
% 5.44/5.63 => ( ( A != zero_zero_real )
% 5.44/5.63 & ( B != zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_not_zero
% 5.44/5.63 thf(fact_1871_mult__not__zero,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ( times_times_nat @ A @ B )
% 5.44/5.63 != zero_zero_nat )
% 5.44/5.63 => ( ( A != zero_zero_nat )
% 5.44/5.63 & ( B != zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_not_zero
% 5.44/5.63 thf(fact_1872_mult__not__zero,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ( times_times_int @ A @ B )
% 5.44/5.63 != zero_zero_int )
% 5.44/5.63 => ( ( A != zero_zero_int )
% 5.44/5.63 & ( B != zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_not_zero
% 5.44/5.63 thf(fact_1873_add_Ogroup__left__neutral,axiom,
% 5.44/5.63 ! [A: complex] :
% 5.44/5.63 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % add.group_left_neutral
% 5.44/5.63 thf(fact_1874_add_Ogroup__left__neutral,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % add.group_left_neutral
% 5.44/5.63 thf(fact_1875_add_Ogroup__left__neutral,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % add.group_left_neutral
% 5.44/5.63 thf(fact_1876_add_Ocomm__neutral,axiom,
% 5.44/5.63 ! [A: extended_enat] :
% 5.44/5.63 ( ( plus_p3455044024723400733d_enat @ A @ zero_z5237406670263579293d_enat )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % add.comm_neutral
% 5.44/5.63 thf(fact_1877_add_Ocomm__neutral,axiom,
% 5.44/5.63 ! [A: complex] :
% 5.44/5.63 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % add.comm_neutral
% 5.44/5.63 thf(fact_1878_add_Ocomm__neutral,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % add.comm_neutral
% 5.44/5.63 thf(fact_1879_add_Ocomm__neutral,axiom,
% 5.44/5.63 ! [A: nat] :
% 5.44/5.63 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % add.comm_neutral
% 5.44/5.63 thf(fact_1880_add_Ocomm__neutral,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % add.comm_neutral
% 5.44/5.63 thf(fact_1881_comm__monoid__add__class_Oadd__0,axiom,
% 5.44/5.63 ! [A: extended_enat] :
% 5.44/5.63 ( ( plus_p3455044024723400733d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % comm_monoid_add_class.add_0
% 5.44/5.63 thf(fact_1882_comm__monoid__add__class_Oadd__0,axiom,
% 5.44/5.63 ! [A: complex] :
% 5.44/5.63 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % comm_monoid_add_class.add_0
% 5.44/5.63 thf(fact_1883_comm__monoid__add__class_Oadd__0,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % comm_monoid_add_class.add_0
% 5.44/5.63 thf(fact_1884_comm__monoid__add__class_Oadd__0,axiom,
% 5.44/5.63 ! [A: nat] :
% 5.44/5.63 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % comm_monoid_add_class.add_0
% 5.44/5.63 thf(fact_1885_comm__monoid__add__class_Oadd__0,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.44/5.63 = A ) ).
% 5.44/5.63
% 5.44/5.63 % comm_monoid_add_class.add_0
% 5.44/5.63 thf(fact_1886_zero__neq__one,axiom,
% 5.44/5.63 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_one
% 5.44/5.63 thf(fact_1887_zero__neq__one,axiom,
% 5.44/5.63 zero_zero_complex != one_one_complex ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_one
% 5.44/5.63 thf(fact_1888_zero__neq__one,axiom,
% 5.44/5.63 zero_zero_real != one_one_real ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_one
% 5.44/5.63 thf(fact_1889_zero__neq__one,axiom,
% 5.44/5.63 zero_zero_nat != one_one_nat ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_one
% 5.44/5.63 thf(fact_1890_zero__neq__one,axiom,
% 5.44/5.63 zero_zero_int != one_one_int ).
% 5.44/5.63
% 5.44/5.63 % zero_neq_one
% 5.44/5.63 thf(fact_1891_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.44/5.63 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.44/5.63 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.membermima.simps(2)
% 5.44/5.63 thf(fact_1892_power__not__zero,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( A != zero_zero_nat )
% 5.44/5.63 => ( ( power_power_nat @ A @ N2 )
% 5.44/5.63 != zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_not_zero
% 5.44/5.63 thf(fact_1893_power__not__zero,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( A != zero_zero_real )
% 5.44/5.63 => ( ( power_power_real @ A @ N2 )
% 5.44/5.63 != zero_zero_real ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_not_zero
% 5.44/5.63 thf(fact_1894_power__not__zero,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( A != zero_zero_int )
% 5.44/5.63 => ( ( power_power_int @ A @ N2 )
% 5.44/5.63 != zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_not_zero
% 5.44/5.63 thf(fact_1895_power__not__zero,axiom,
% 5.44/5.63 ! [A: complex,N2: nat] :
% 5.44/5.63 ( ( A != zero_zero_complex )
% 5.44/5.63 => ( ( power_power_complex @ A @ N2 )
% 5.44/5.63 != zero_zero_complex ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_not_zero
% 5.44/5.63 thf(fact_1896_num_Osize_I4_J,axiom,
% 5.44/5.63 ( ( size_size_num @ one )
% 5.44/5.63 = zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % num.size(4)
% 5.44/5.63 thf(fact_1897_nat_Odistinct_I1_J,axiom,
% 5.44/5.63 ! [X22: nat] :
% 5.44/5.63 ( zero_zero_nat
% 5.44/5.63 != ( suc @ X22 ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat.distinct(1)
% 5.44/5.63 thf(fact_1898_old_Onat_Odistinct_I2_J,axiom,
% 5.44/5.63 ! [Nat2: nat] :
% 5.44/5.63 ( ( suc @ Nat2 )
% 5.44/5.63 != zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % old.nat.distinct(2)
% 5.44/5.63 thf(fact_1899_old_Onat_Odistinct_I1_J,axiom,
% 5.44/5.63 ! [Nat2: nat] :
% 5.44/5.63 ( zero_zero_nat
% 5.44/5.63 != ( suc @ Nat2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % old.nat.distinct(1)
% 5.44/5.63 thf(fact_1900_nat_OdiscI,axiom,
% 5.44/5.63 ! [Nat: nat,X22: nat] :
% 5.44/5.63 ( ( Nat
% 5.44/5.63 = ( suc @ X22 ) )
% 5.44/5.63 => ( Nat != zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat.discI
% 5.44/5.63 thf(fact_1901_old_Onat_Oexhaust,axiom,
% 5.44/5.63 ! [Y: nat] :
% 5.44/5.63 ( ( Y != zero_zero_nat )
% 5.44/5.63 => ~ ! [Nat3: nat] :
% 5.44/5.63 ( Y
% 5.44/5.63 != ( suc @ Nat3 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % old.nat.exhaust
% 5.44/5.63 thf(fact_1902_vebt__buildup_Ocases,axiom,
% 5.44/5.63 ! [X: nat] :
% 5.44/5.63 ( ( X != zero_zero_nat )
% 5.44/5.63 => ( ( X
% 5.44/5.63 != ( suc @ zero_zero_nat ) )
% 5.44/5.63 => ~ ! [Va2: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_buildup.cases
% 5.44/5.63 thf(fact_1903_nat__induct,axiom,
% 5.44/5.63 ! [P: nat > $o,N2: nat] :
% 5.44/5.63 ( ( P @ zero_zero_nat )
% 5.44/5.63 => ( ! [N4: nat] :
% 5.44/5.63 ( ( P @ N4 )
% 5.44/5.63 => ( P @ ( suc @ N4 ) ) )
% 5.44/5.63 => ( P @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_induct
% 5.44/5.63 thf(fact_1904_diff__induct,axiom,
% 5.44/5.63 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.44/5.63 ( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
% 5.44/5.63 => ( ! [Y5: nat] : ( P @ zero_zero_nat @ ( suc @ Y5 ) )
% 5.44/5.63 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.63 ( ( P @ X5 @ Y5 )
% 5.44/5.63 => ( P @ ( suc @ X5 ) @ ( suc @ Y5 ) ) )
% 5.44/5.63 => ( P @ M @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % diff_induct
% 5.44/5.63 thf(fact_1905_zero__induct,axiom,
% 5.44/5.63 ! [P: nat > $o,K: nat] :
% 5.44/5.63 ( ( P @ K )
% 5.44/5.63 => ( ! [N4: nat] :
% 5.44/5.63 ( ( P @ ( suc @ N4 ) )
% 5.44/5.63 => ( P @ N4 ) )
% 5.44/5.63 => ( P @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_induct
% 5.44/5.63 thf(fact_1906_Suc__neq__Zero,axiom,
% 5.44/5.63 ! [M: nat] :
% 5.44/5.63 ( ( suc @ M )
% 5.44/5.63 != zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % Suc_neq_Zero
% 5.44/5.63 thf(fact_1907_Zero__neq__Suc,axiom,
% 5.44/5.63 ! [M: nat] :
% 5.44/5.63 ( zero_zero_nat
% 5.44/5.63 != ( suc @ M ) ) ).
% 5.44/5.63
% 5.44/5.63 % Zero_neq_Suc
% 5.44/5.63 thf(fact_1908_Zero__not__Suc,axiom,
% 5.44/5.63 ! [M: nat] :
% 5.44/5.63 ( zero_zero_nat
% 5.44/5.63 != ( suc @ M ) ) ).
% 5.44/5.63
% 5.44/5.63 % Zero_not_Suc
% 5.44/5.63 thf(fact_1909_not0__implies__Suc,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ? [M5: nat] :
% 5.44/5.63 ( N2
% 5.44/5.63 = ( suc @ M5 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % not0_implies_Suc
% 5.44/5.63 thf(fact_1910_infinite__descent0,axiom,
% 5.44/5.63 ! [P: nat > $o,N2: nat] :
% 5.44/5.63 ( ( P @ zero_zero_nat )
% 5.44/5.63 => ( ! [N4: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.44/5.63 => ( ~ ( P @ N4 )
% 5.44/5.63 => ? [M2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ M2 @ N4 )
% 5.44/5.63 & ~ ( P @ M2 ) ) ) )
% 5.44/5.63 => ( P @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % infinite_descent0
% 5.44/5.63 thf(fact_1911_gr__implies__not0,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.63 => ( N2 != zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % gr_implies_not0
% 5.44/5.63 thf(fact_1912_less__zeroE,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % less_zeroE
% 5.44/5.63 thf(fact_1913_not__less0,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % not_less0
% 5.44/5.63 thf(fact_1914_not__gr0,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.63 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % not_gr0
% 5.44/5.63 thf(fact_1915_gr0I,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % gr0I
% 5.44/5.63 thf(fact_1916_bot__nat__0_Oextremum__strict,axiom,
% 5.44/5.63 ! [A: nat] :
% 5.44/5.63 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % bot_nat_0.extremum_strict
% 5.44/5.63 thf(fact_1917_less__eq__nat_Osimps_I1_J,axiom,
% 5.44/5.63 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.44/5.63
% 5.44/5.63 % less_eq_nat.simps(1)
% 5.44/5.63 thf(fact_1918_bot__nat__0_Oextremum__unique,axiom,
% 5.44/5.63 ! [A: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.44/5.63 = ( A = zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % bot_nat_0.extremum_unique
% 5.44/5.63 thf(fact_1919_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.44/5.63 ! [A: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.44/5.63 => ( A = zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % bot_nat_0.extremum_uniqueI
% 5.44/5.63 thf(fact_1920_le__0__eq,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.44/5.63 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_0_eq
% 5.44/5.63 thf(fact_1921_add__eq__self__zero,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( plus_plus_nat @ M @ N2 )
% 5.44/5.63 = M )
% 5.44/5.63 => ( N2 = zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_eq_self_zero
% 5.44/5.63 thf(fact_1922_plus__nat_Oadd__0,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 = N2 ) ).
% 5.44/5.63
% 5.44/5.63 % plus_nat.add_0
% 5.44/5.63 thf(fact_1923_nat__mult__eq__cancel__disj,axiom,
% 5.44/5.63 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ( times_times_nat @ K @ M )
% 5.44/5.63 = ( times_times_nat @ K @ N2 ) )
% 5.44/5.63 = ( ( K = zero_zero_nat )
% 5.44/5.63 | ( M = N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_mult_eq_cancel_disj
% 5.44/5.63 thf(fact_1924_mult__0,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 = zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % mult_0
% 5.44/5.63 thf(fact_1925_diffs0__imp__equal,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( minus_minus_nat @ M @ N2 )
% 5.44/5.63 = zero_zero_nat )
% 5.44/5.63 => ( ( ( minus_minus_nat @ N2 @ M )
% 5.44/5.63 = zero_zero_nat )
% 5.44/5.63 => ( M = N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % diffs0_imp_equal
% 5.44/5.63 thf(fact_1926_minus__nat_Odiff__0,axiom,
% 5.44/5.63 ! [M: nat] :
% 5.44/5.63 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.44/5.63 = M ) ).
% 5.44/5.63
% 5.44/5.63 % minus_nat.diff_0
% 5.44/5.63 thf(fact_1927_vebt__delete_Osimps_I3_J,axiom,
% 5.44/5.63 ! [A: $o,B: $o,N2: nat] :
% 5.44/5.63 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N2 ) ) )
% 5.44/5.63 = ( vEBT_Leaf @ A @ B ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_delete.simps(3)
% 5.44/5.63 thf(fact_1928_power__eq__imp__eq__base,axiom,
% 5.44/5.63 ! [A: real,N2: nat,B: real] :
% 5.44/5.63 ( ( ( power_power_real @ A @ N2 )
% 5.44/5.63 = ( power_power_real @ B @ N2 ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( A = B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_imp_eq_base
% 5.44/5.63 thf(fact_1929_power__eq__imp__eq__base,axiom,
% 5.44/5.63 ! [A: nat,N2: nat,B: nat] :
% 5.44/5.63 ( ( ( power_power_nat @ A @ N2 )
% 5.44/5.63 = ( power_power_nat @ B @ N2 ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( A = B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_imp_eq_base
% 5.44/5.63 thf(fact_1930_power__eq__imp__eq__base,axiom,
% 5.44/5.63 ! [A: int,N2: nat,B: int] :
% 5.44/5.63 ( ( ( power_power_int @ A @ N2 )
% 5.44/5.63 = ( power_power_int @ B @ N2 ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( A = B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_imp_eq_base
% 5.44/5.63 thf(fact_1931_power__eq__iff__eq__base,axiom,
% 5.44/5.63 ! [N2: nat,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ( ( power_power_real @ A @ N2 )
% 5.44/5.63 = ( power_power_real @ B @ N2 ) )
% 5.44/5.63 = ( A = B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_iff_eq_base
% 5.44/5.63 thf(fact_1932_power__eq__iff__eq__base,axiom,
% 5.44/5.63 ! [N2: nat,A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ( power_power_nat @ A @ N2 )
% 5.44/5.63 = ( power_power_nat @ B @ N2 ) )
% 5.44/5.63 = ( A = B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_iff_eq_base
% 5.44/5.63 thf(fact_1933_power__eq__iff__eq__base,axiom,
% 5.44/5.63 ! [N2: nat,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ( power_power_int @ A @ N2 )
% 5.44/5.63 = ( power_power_int @ B @ N2 ) )
% 5.44/5.63 = ( A = B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_iff_eq_base
% 5.44/5.63 thf(fact_1934_lambda__zero,axiom,
% 5.44/5.63 ( ( ^ [H: extended_enat] : zero_z5237406670263579293d_enat )
% 5.44/5.63 = ( times_7803423173614009249d_enat @ zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.63
% 5.44/5.63 % lambda_zero
% 5.44/5.63 thf(fact_1935_lambda__zero,axiom,
% 5.44/5.63 ( ( ^ [H: complex] : zero_zero_complex )
% 5.44/5.63 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.44/5.63
% 5.44/5.63 % lambda_zero
% 5.44/5.63 thf(fact_1936_lambda__zero,axiom,
% 5.44/5.63 ( ( ^ [H: real] : zero_zero_real )
% 5.44/5.63 = ( times_times_real @ zero_zero_real ) ) ).
% 5.44/5.63
% 5.44/5.63 % lambda_zero
% 5.44/5.63 thf(fact_1937_lambda__zero,axiom,
% 5.44/5.63 ( ( ^ [H: nat] : zero_zero_nat )
% 5.44/5.63 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % lambda_zero
% 5.44/5.63 thf(fact_1938_lambda__zero,axiom,
% 5.44/5.63 ( ( ^ [H: int] : zero_zero_int )
% 5.44/5.63 = ( times_times_int @ zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % lambda_zero
% 5.44/5.63 thf(fact_1939_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.44/5.63 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.44/5.63 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 5.44/5.63 = ( ( X = Mi )
% 5.44/5.63 | ( X = Ma ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.membermima.simps(3)
% 5.44/5.63 thf(fact_1940_power__strict__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_mono
% 5.44/5.63 thf(fact_1941_power__strict__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_mono
% 5.44/5.63 thf(fact_1942_power__strict__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_mono
% 5.44/5.63 thf(fact_1943_vebt__delete_Ocases,axiom,
% 5.44/5.63 ! [X: produc9072475918466114483BT_nat] :
% 5.44/5.63 ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 5.44/5.63 => ( ! [A3: $o,B3: $o,N4: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N4 ) ) ) )
% 5.44/5.63 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Uu2 ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X5 ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X5 ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_delete.cases
% 5.44/5.63 thf(fact_1944_vebt__member_Ocases,axiom,
% 5.44/5.63 ! [X: produc9072475918466114483BT_nat] :
% 5.44/5.63 ( ! [A3: $o,B3: $o,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X5 ) )
% 5.44/5.63 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X5 ) )
% 5.44/5.63 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X5 ) )
% 5.44/5.63 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X5 ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_member.cases
% 5.44/5.63 thf(fact_1945_VEBT__internal_OminNull_Ocases,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 != ( vEBT_Leaf @ $false @ $false ) )
% 5.44/5.63 => ( ! [Uv2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.44/5.63 => ( ! [Uu2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.44/5.63 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.44/5.63 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.minNull.cases
% 5.44/5.63 thf(fact_1946_vebt__mint_Osimps_I1_J,axiom,
% 5.44/5.63 ! [A: $o,B: $o] :
% 5.44/5.63 ( ( A
% 5.44/5.63 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.44/5.63 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.63 & ( ~ A
% 5.44/5.63 => ( ( B
% 5.44/5.63 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.44/5.63 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.63 & ( ~ B
% 5.44/5.63 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.44/5.63 = none_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_mint.simps(1)
% 5.44/5.63 thf(fact_1947_vebt__maxt_Osimps_I1_J,axiom,
% 5.44/5.63 ! [B: $o,A: $o] :
% 5.44/5.63 ( ( B
% 5.44/5.63 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.44/5.63 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.63 & ( ~ B
% 5.44/5.63 => ( ( A
% 5.44/5.63 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.44/5.63 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.63 & ( ~ A
% 5.44/5.63 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.44/5.63 = none_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_maxt.simps(1)
% 5.44/5.63 thf(fact_1948_vebt__pred_Osimps_I2_J,axiom,
% 5.44/5.63 ! [A: $o,Uw: $o] :
% 5.44/5.63 ( ( A
% 5.44/5.63 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.63 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.63 & ( ~ A
% 5.44/5.63 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.63 = none_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_pred.simps(2)
% 5.44/5.63 thf(fact_1949_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT] :
% 5.44/5.63 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.44/5.63 => ( ! [Uv2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.44/5.63 => ( ! [Uu2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.44/5.63 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.minNull.elims(3)
% 5.44/5.63 thf(fact_1950_vebt__succ_Osimps_I1_J,axiom,
% 5.44/5.63 ! [B: $o,Uu: $o] :
% 5.44/5.63 ( ( B
% 5.44/5.63 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.44/5.63 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.63 & ( ~ B
% 5.44/5.63 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.44/5.63 = none_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_succ.simps(1)
% 5.44/5.63 thf(fact_1951_not__numeral__le__zero,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % not_numeral_le_zero
% 5.44/5.63 thf(fact_1952_not__numeral__le__zero,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % not_numeral_le_zero
% 5.44/5.63 thf(fact_1953_not__numeral__le__zero,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % not_numeral_le_zero
% 5.44/5.63 thf(fact_1954_not__numeral__le__zero,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % not_numeral_le_zero
% 5.44/5.63 thf(fact_1955_zero__le__numeral,axiom,
% 5.44/5.63 ! [N2: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_numeral
% 5.44/5.63 thf(fact_1956_zero__le__numeral,axiom,
% 5.44/5.63 ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_numeral
% 5.44/5.63 thf(fact_1957_zero__le__numeral,axiom,
% 5.44/5.63 ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_numeral
% 5.44/5.63 thf(fact_1958_zero__le__numeral,axiom,
% 5.44/5.63 ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_numeral
% 5.44/5.63 thf(fact_1959_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ C @ A ) @ ( times_7803423173614009249d_enat @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.44/5.63 thf(fact_1960_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.44/5.63 thf(fact_1961_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.44/5.63 thf(fact_1962_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.44/5.63 thf(fact_1963_zero__le__mult__iff,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.44/5.63 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_mult_iff
% 5.44/5.63 thf(fact_1964_zero__le__mult__iff,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.44/5.63 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.44/5.63 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_mult_iff
% 5.44/5.63 thf(fact_1965_mult__nonneg__nonpos2,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonpos2
% 5.44/5.63 thf(fact_1966_mult__nonneg__nonpos2,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonpos2
% 5.44/5.63 thf(fact_1967_mult__nonneg__nonpos2,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonpos2
% 5.44/5.63 thf(fact_1968_mult__nonpos__nonneg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonpos_nonneg
% 5.44/5.63 thf(fact_1969_mult__nonpos__nonneg,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonpos_nonneg
% 5.44/5.63 thf(fact_1970_mult__nonpos__nonneg,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonpos_nonneg
% 5.44/5.63 thf(fact_1971_mult__nonneg__nonpos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonpos
% 5.44/5.63 thf(fact_1972_mult__nonneg__nonpos,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonpos
% 5.44/5.63 thf(fact_1973_mult__nonneg__nonpos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonpos
% 5.44/5.63 thf(fact_1974_mult__nonneg__nonneg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonneg
% 5.44/5.63 thf(fact_1975_mult__nonneg__nonneg,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonneg
% 5.44/5.63 thf(fact_1976_mult__nonneg__nonneg,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonneg_nonneg
% 5.44/5.63 thf(fact_1977_split__mult__neg__le,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.44/5.63 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.44/5.63
% 5.44/5.63 % split_mult_neg_le
% 5.44/5.63 thf(fact_1978_split__mult__neg__le,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.44/5.63 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.44/5.63 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % split_mult_neg_le
% 5.44/5.63 thf(fact_1979_split__mult__neg__le,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.44/5.63 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % split_mult_neg_le
% 5.44/5.63 thf(fact_1980_mult__le__0__iff,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.44/5.63 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_0_iff
% 5.44/5.63 thf(fact_1981_mult__le__0__iff,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.44/5.63 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.44/5.63 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_0_iff
% 5.44/5.63 thf(fact_1982_mult__right__mono,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_mono
% 5.44/5.63 thf(fact_1983_mult__right__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_mono
% 5.44/5.63 thf(fact_1984_mult__right__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_mono
% 5.44/5.63 thf(fact_1985_mult__right__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_mono
% 5.44/5.63 thf(fact_1986_mult__right__mono__neg,axiom,
% 5.44/5.63 ! [B: real,A: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_mono_neg
% 5.44/5.63 thf(fact_1987_mult__right__mono__neg,axiom,
% 5.44/5.63 ! [B: int,A: int,C: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_mono_neg
% 5.44/5.63 thf(fact_1988_mult__left__mono,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ C @ A ) @ ( times_7803423173614009249d_enat @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_mono
% 5.44/5.63 thf(fact_1989_mult__left__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_mono
% 5.44/5.63 thf(fact_1990_mult__left__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_mono
% 5.44/5.63 thf(fact_1991_mult__left__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_mono
% 5.44/5.63 thf(fact_1992_mult__nonpos__nonpos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonpos_nonpos
% 5.44/5.63 thf(fact_1993_mult__nonpos__nonpos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_nonpos_nonpos
% 5.44/5.63 thf(fact_1994_mult__left__mono__neg,axiom,
% 5.44/5.63 ! [B: real,A: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_mono_neg
% 5.44/5.63 thf(fact_1995_mult__left__mono__neg,axiom,
% 5.44/5.63 ! [B: int,A: int,C: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_mono_neg
% 5.44/5.63 thf(fact_1996_split__mult__pos__le,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.44/5.63 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % split_mult_pos_le
% 5.44/5.63 thf(fact_1997_split__mult__pos__le,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.44/5.63 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.44/5.63 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % split_mult_pos_le
% 5.44/5.63 thf(fact_1998_zero__le__square,axiom,
% 5.44/5.63 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_square
% 5.44/5.63 thf(fact_1999_zero__le__square,axiom,
% 5.44/5.63 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_square
% 5.44/5.63 thf(fact_2000_mult__mono_H,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat,C: extended_enat,D: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ C @ D )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_mono'
% 5.44/5.63 thf(fact_2001_mult__mono_H,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_mono'
% 5.44/5.63 thf(fact_2002_mult__mono_H,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_mono'
% 5.44/5.63 thf(fact_2003_mult__mono_H,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_mono'
% 5.44/5.63 thf(fact_2004_mult__mono,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat,C: extended_enat,D: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ C @ D )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ ( times_7803423173614009249d_enat @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_mono
% 5.44/5.63 thf(fact_2005_mult__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_mono
% 5.44/5.63 thf(fact_2006_mult__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_mono
% 5.44/5.63 thf(fact_2007_mult__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_mono
% 5.44/5.63 thf(fact_2008_not__numeral__less__zero,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % not_numeral_less_zero
% 5.44/5.63 thf(fact_2009_not__numeral__less__zero,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % not_numeral_less_zero
% 5.44/5.63 thf(fact_2010_not__numeral__less__zero,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % not_numeral_less_zero
% 5.44/5.63 thf(fact_2011_not__numeral__less__zero,axiom,
% 5.44/5.63 ! [N2: num] :
% 5.44/5.63 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % not_numeral_less_zero
% 5.44/5.63 thf(fact_2012_zero__less__numeral,axiom,
% 5.44/5.63 ! [N2: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_numeral
% 5.44/5.63 thf(fact_2013_zero__less__numeral,axiom,
% 5.44/5.63 ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_numeral
% 5.44/5.63 thf(fact_2014_zero__less__numeral,axiom,
% 5.44/5.63 ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_numeral
% 5.44/5.63 thf(fact_2015_zero__less__numeral,axiom,
% 5.44/5.63 ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_numeral
% 5.44/5.63 thf(fact_2016_add__nonpos__eq__0__iff,axiom,
% 5.44/5.63 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ X @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ Y @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( ( plus_p3455044024723400733d_enat @ X @ Y )
% 5.44/5.63 = zero_z5237406670263579293d_enat )
% 5.44/5.63 = ( ( X = zero_z5237406670263579293d_enat )
% 5.44/5.63 & ( Y = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_eq_0_iff
% 5.44/5.63 thf(fact_2017_add__nonpos__eq__0__iff,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.44/5.63 => ( ( ( plus_plus_real @ X @ Y )
% 5.44/5.63 = zero_zero_real )
% 5.44/5.63 = ( ( X = zero_zero_real )
% 5.44/5.63 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_eq_0_iff
% 5.44/5.63 thf(fact_2018_add__nonpos__eq__0__iff,axiom,
% 5.44/5.63 ! [X: nat,Y: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.44/5.63 => ( ( ( plus_plus_nat @ X @ Y )
% 5.44/5.63 = zero_zero_nat )
% 5.44/5.63 = ( ( X = zero_zero_nat )
% 5.44/5.63 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_eq_0_iff
% 5.44/5.63 thf(fact_2019_add__nonpos__eq__0__iff,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.44/5.63 => ( ( ( plus_plus_int @ X @ Y )
% 5.44/5.63 = zero_zero_int )
% 5.44/5.63 = ( ( X = zero_zero_int )
% 5.44/5.63 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_eq_0_iff
% 5.44/5.63 thf(fact_2020_add__nonneg__eq__0__iff,axiom,
% 5.44/5.63 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ X )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ Y )
% 5.44/5.63 => ( ( ( plus_p3455044024723400733d_enat @ X @ Y )
% 5.44/5.63 = zero_z5237406670263579293d_enat )
% 5.44/5.63 = ( ( X = zero_z5237406670263579293d_enat )
% 5.44/5.63 & ( Y = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_eq_0_iff
% 5.44/5.63 thf(fact_2021_add__nonneg__eq__0__iff,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ( plus_plus_real @ X @ Y )
% 5.44/5.63 = zero_zero_real )
% 5.44/5.63 = ( ( X = zero_zero_real )
% 5.44/5.63 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_eq_0_iff
% 5.44/5.63 thf(fact_2022_add__nonneg__eq__0__iff,axiom,
% 5.44/5.63 ! [X: nat,Y: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.44/5.63 => ( ( ( plus_plus_nat @ X @ Y )
% 5.44/5.63 = zero_zero_nat )
% 5.44/5.63 = ( ( X = zero_zero_nat )
% 5.44/5.63 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_eq_0_iff
% 5.44/5.63 thf(fact_2023_add__nonneg__eq__0__iff,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.63 => ( ( ( plus_plus_int @ X @ Y )
% 5.44/5.63 = zero_zero_int )
% 5.44/5.63 = ( ( X = zero_zero_int )
% 5.44/5.63 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_eq_0_iff
% 5.44/5.63 thf(fact_2024_add__nonpos__nonpos,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ B @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_nonpos
% 5.44/5.63 thf(fact_2025_add__nonpos__nonpos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_nonpos
% 5.44/5.63 thf(fact_2026_add__nonpos__nonpos,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.44/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_nonpos
% 5.44/5.63 thf(fact_2027_add__nonpos__nonpos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_nonpos
% 5.44/5.63 thf(fact_2028_add__nonneg__nonneg,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_nonneg
% 5.44/5.63 thf(fact_2029_add__nonneg__nonneg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_nonneg
% 5.44/5.63 thf(fact_2030_add__nonneg__nonneg,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_nonneg
% 5.44/5.63 thf(fact_2031_add__nonneg__nonneg,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_nonneg
% 5.44/5.63 thf(fact_2032_add__increasing2,axiom,
% 5.44/5.63 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ B @ ( plus_p3455044024723400733d_enat @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_increasing2
% 5.44/5.63 thf(fact_2033_add__increasing2,axiom,
% 5.44/5.63 ! [C: real,B: real,A: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ A )
% 5.44/5.63 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_increasing2
% 5.44/5.63 thf(fact_2034_add__increasing2,axiom,
% 5.44/5.63 ! [C: nat,B: nat,A: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.63 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_increasing2
% 5.44/5.63 thf(fact_2035_add__increasing2,axiom,
% 5.44/5.63 ! [C: int,B: int,A: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ A )
% 5.44/5.63 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_increasing2
% 5.44/5.63 thf(fact_2036_add__decreasing2,axiom,
% 5.44/5.63 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ C @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_decreasing2
% 5.44/5.63 thf(fact_2037_add__decreasing2,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_decreasing2
% 5.44/5.63 thf(fact_2038_add__decreasing2,axiom,
% 5.44/5.63 ! [C: nat,A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_decreasing2
% 5.44/5.63 thf(fact_2039_add__decreasing2,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ A @ B )
% 5.44/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_decreasing2
% 5.44/5.63 thf(fact_2040_add__increasing,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ B @ C )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ B @ ( plus_p3455044024723400733d_enat @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_increasing
% 5.44/5.63 thf(fact_2041_add__increasing,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ C )
% 5.44/5.63 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_increasing
% 5.44/5.63 thf(fact_2042_add__increasing,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.63 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_increasing
% 5.44/5.63 thf(fact_2043_add__increasing,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.63 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_increasing
% 5.44/5.63 thf(fact_2044_add__decreasing,axiom,
% 5.44/5.63 ! [A: extended_enat,C: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_decreasing
% 5.44/5.63 thf(fact_2045_add__decreasing,axiom,
% 5.44/5.63 ! [A: real,C: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ C @ B )
% 5.44/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_decreasing
% 5.44/5.63 thf(fact_2046_add__decreasing,axiom,
% 5.44/5.63 ! [A: nat,C: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ C @ B )
% 5.44/5.63 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_decreasing
% 5.44/5.63 thf(fact_2047_add__decreasing,axiom,
% 5.44/5.63 ! [A: int,C: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ C @ B )
% 5.44/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_decreasing
% 5.44/5.63 thf(fact_2048_not__one__le__zero,axiom,
% 5.44/5.63 ~ ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % not_one_le_zero
% 5.44/5.63 thf(fact_2049_not__one__le__zero,axiom,
% 5.44/5.63 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % not_one_le_zero
% 5.44/5.63 thf(fact_2050_not__one__le__zero,axiom,
% 5.44/5.63 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % not_one_le_zero
% 5.44/5.63 thf(fact_2051_not__one__le__zero,axiom,
% 5.44/5.63 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % not_one_le_zero
% 5.44/5.63 thf(fact_2052_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.44/5.63 ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat ).
% 5.44/5.63
% 5.44/5.63 % linordered_nonzero_semiring_class.zero_le_one
% 5.44/5.63 thf(fact_2053_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.44/5.63 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.44/5.63
% 5.44/5.63 % linordered_nonzero_semiring_class.zero_le_one
% 5.44/5.63 thf(fact_2054_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.44/5.63 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.44/5.63
% 5.44/5.63 % linordered_nonzero_semiring_class.zero_le_one
% 5.44/5.63 thf(fact_2055_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.44/5.63 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.44/5.63
% 5.44/5.63 % linordered_nonzero_semiring_class.zero_le_one
% 5.44/5.63 thf(fact_2056_zero__less__one__class_Ozero__le__one,axiom,
% 5.44/5.63 ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat ).
% 5.44/5.63
% 5.44/5.63 % zero_less_one_class.zero_le_one
% 5.44/5.63 thf(fact_2057_zero__less__one__class_Ozero__le__one,axiom,
% 5.44/5.63 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.44/5.63
% 5.44/5.63 % zero_less_one_class.zero_le_one
% 5.44/5.63 thf(fact_2058_zero__less__one__class_Ozero__le__one,axiom,
% 5.44/5.63 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.44/5.63
% 5.44/5.63 % zero_less_one_class.zero_le_one
% 5.44/5.63 thf(fact_2059_zero__less__one__class_Ozero__le__one,axiom,
% 5.44/5.63 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.44/5.63
% 5.44/5.63 % zero_less_one_class.zero_le_one
% 5.44/5.63 thf(fact_2060_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.44/5.63 thf(fact_2061_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.44/5.63 thf(fact_2062_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.44/5.63 thf(fact_2063_mult__less__cancel__right__disj,axiom,
% 5.44/5.63 ! [A: real,C: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 & ( ord_less_real @ A @ B ) )
% 5.44/5.63 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_right_disj
% 5.44/5.63 thf(fact_2064_mult__less__cancel__right__disj,axiom,
% 5.44/5.63 ! [A: int,C: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 & ( ord_less_int @ A @ B ) )
% 5.44/5.63 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_right_disj
% 5.44/5.63 thf(fact_2065_mult__strict__right__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_right_mono
% 5.44/5.63 thf(fact_2066_mult__strict__right__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_right_mono
% 5.44/5.63 thf(fact_2067_mult__strict__right__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_right_mono
% 5.44/5.63 thf(fact_2068_mult__strict__right__mono__neg,axiom,
% 5.44/5.63 ! [B: real,A: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ B @ A )
% 5.44/5.63 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_right_mono_neg
% 5.44/5.63 thf(fact_2069_mult__strict__right__mono__neg,axiom,
% 5.44/5.63 ! [B: int,A: int,C: int] :
% 5.44/5.63 ( ( ord_less_int @ B @ A )
% 5.44/5.63 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_right_mono_neg
% 5.44/5.63 thf(fact_2070_mult__less__cancel__left__disj,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 & ( ord_less_real @ A @ B ) )
% 5.44/5.63 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left_disj
% 5.44/5.63 thf(fact_2071_mult__less__cancel__left__disj,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 & ( ord_less_int @ A @ B ) )
% 5.44/5.63 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left_disj
% 5.44/5.63 thf(fact_2072_mult__strict__left__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_left_mono
% 5.44/5.63 thf(fact_2073_mult__strict__left__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_left_mono
% 5.44/5.63 thf(fact_2074_mult__strict__left__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_left_mono
% 5.44/5.63 thf(fact_2075_mult__strict__left__mono__neg,axiom,
% 5.44/5.63 ! [B: real,A: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ B @ A )
% 5.44/5.63 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_left_mono_neg
% 5.44/5.63 thf(fact_2076_mult__strict__left__mono__neg,axiom,
% 5.44/5.63 ! [B: int,A: int,C: int] :
% 5.44/5.63 ( ( ord_less_int @ B @ A )
% 5.44/5.63 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_left_mono_neg
% 5.44/5.63 thf(fact_2077_mult__less__cancel__left__pos,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left_pos
% 5.44/5.63 thf(fact_2078_mult__less__cancel__left__pos,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ord_less_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left_pos
% 5.44/5.63 thf(fact_2079_mult__less__cancel__left__neg,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ord_less_real @ B @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left_neg
% 5.44/5.63 thf(fact_2080_mult__less__cancel__left__neg,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ord_less_int @ B @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left_neg
% 5.44/5.63 thf(fact_2081_zero__less__mult__pos2,axiom,
% 5.44/5.63 ! [B: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_mult_pos2
% 5.44/5.63 thf(fact_2082_zero__less__mult__pos2,axiom,
% 5.44/5.63 ! [B: nat,A: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_mult_pos2
% 5.44/5.63 thf(fact_2083_zero__less__mult__pos2,axiom,
% 5.44/5.63 ! [B: int,A: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_mult_pos2
% 5.44/5.63 thf(fact_2084_zero__less__mult__pos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_mult_pos
% 5.44/5.63 thf(fact_2085_zero__less__mult__pos,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_mult_pos
% 5.44/5.63 thf(fact_2086_zero__less__mult__pos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_mult_pos
% 5.44/5.63 thf(fact_2087_zero__less__mult__iff,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.44/5.63 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_mult_iff
% 5.44/5.63 thf(fact_2088_zero__less__mult__iff,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.44/5.63 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.44/5.63 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_mult_iff
% 5.44/5.63 thf(fact_2089_mult__pos__neg2,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_neg2
% 5.44/5.63 thf(fact_2090_mult__pos__neg2,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_neg2
% 5.44/5.63 thf(fact_2091_mult__pos__neg2,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_neg2
% 5.44/5.63 thf(fact_2092_mult__pos__pos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_pos
% 5.44/5.63 thf(fact_2093_mult__pos__pos,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_pos
% 5.44/5.63 thf(fact_2094_mult__pos__pos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_pos
% 5.44/5.63 thf(fact_2095_mult__pos__neg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_neg
% 5.44/5.63 thf(fact_2096_mult__pos__neg,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_neg
% 5.44/5.63 thf(fact_2097_mult__pos__neg,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_pos_neg
% 5.44/5.63 thf(fact_2098_mult__neg__pos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_neg_pos
% 5.44/5.63 thf(fact_2099_mult__neg__pos,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_neg_pos
% 5.44/5.63 thf(fact_2100_mult__neg__pos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_neg_pos
% 5.44/5.63 thf(fact_2101_mult__less__0__iff,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.44/5.63 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_0_iff
% 5.44/5.63 thf(fact_2102_mult__less__0__iff,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.44/5.63 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.44/5.63 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_0_iff
% 5.44/5.63 thf(fact_2103_not__square__less__zero,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % not_square_less_zero
% 5.44/5.63 thf(fact_2104_not__square__less__zero,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % not_square_less_zero
% 5.44/5.63 thf(fact_2105_mult__neg__neg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_neg_neg
% 5.44/5.63 thf(fact_2106_mult__neg__neg,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_neg_neg
% 5.44/5.63 thf(fact_2107_pos__add__strict,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.63 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.63 => ( ord_le72135733267957522d_enat @ B @ ( plus_p3455044024723400733d_enat @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos_add_strict
% 5.44/5.63 thf(fact_2108_pos__add__strict,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ B @ C )
% 5.44/5.63 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos_add_strict
% 5.44/5.63 thf(fact_2109_pos__add__strict,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ B @ C )
% 5.44/5.63 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos_add_strict
% 5.44/5.63 thf(fact_2110_pos__add__strict,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ B @ C )
% 5.44/5.63 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos_add_strict
% 5.44/5.63 thf(fact_2111_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.63 => ~ ! [C3: extended_enat] :
% 5.44/5.63 ( ( B
% 5.44/5.63 = ( plus_p3455044024723400733d_enat @ A @ C3 ) )
% 5.44/5.63 => ( C3 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % canonically_ordered_monoid_add_class.lessE
% 5.44/5.63 thf(fact_2112_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ~ ! [C3: nat] :
% 5.44/5.63 ( ( B
% 5.44/5.63 = ( plus_plus_nat @ A @ C3 ) )
% 5.44/5.63 => ( C3 = zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % canonically_ordered_monoid_add_class.lessE
% 5.44/5.63 thf(fact_2113_add__pos__pos,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B )
% 5.44/5.63 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_pos_pos
% 5.44/5.63 thf(fact_2114_add__pos__pos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_pos_pos
% 5.44/5.63 thf(fact_2115_add__pos__pos,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_pos_pos
% 5.44/5.63 thf(fact_2116_add__pos__pos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_pos_pos
% 5.44/5.63 thf(fact_2117_add__neg__neg,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( ord_le72135733267957522d_enat @ B @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_neg_neg
% 5.44/5.63 thf(fact_2118_add__neg__neg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_neg_neg
% 5.44/5.63 thf(fact_2119_add__neg__neg,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.44/5.63 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_neg_neg
% 5.44/5.63 thf(fact_2120_add__neg__neg,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_neg_neg
% 5.44/5.63 thf(fact_2121_add__less__zeroD,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.63 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_less_zeroD
% 5.44/5.63 thf(fact_2122_add__less__zeroD,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.44/5.63 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_less_zeroD
% 5.44/5.63 thf(fact_2123_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT] :
% 5.44/5.63 ( ( vEBT_VEBT_minNull @ X )
% 5.44/5.63 => ( ( X
% 5.44/5.63 != ( vEBT_Leaf @ $false @ $false ) )
% 5.44/5.63 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.minNull.elims(2)
% 5.44/5.63 thf(fact_2124_not__one__less__zero,axiom,
% 5.44/5.63 ~ ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % not_one_less_zero
% 5.44/5.63 thf(fact_2125_not__one__less__zero,axiom,
% 5.44/5.63 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % not_one_less_zero
% 5.44/5.63 thf(fact_2126_not__one__less__zero,axiom,
% 5.44/5.63 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % not_one_less_zero
% 5.44/5.63 thf(fact_2127_not__one__less__zero,axiom,
% 5.44/5.63 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % not_one_less_zero
% 5.44/5.63 thf(fact_2128_zero__less__one,axiom,
% 5.44/5.63 ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat ).
% 5.44/5.63
% 5.44/5.63 % zero_less_one
% 5.44/5.63 thf(fact_2129_zero__less__one,axiom,
% 5.44/5.63 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.44/5.63
% 5.44/5.63 % zero_less_one
% 5.44/5.63 thf(fact_2130_zero__less__one,axiom,
% 5.44/5.63 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.44/5.63
% 5.44/5.63 % zero_less_one
% 5.44/5.63 thf(fact_2131_zero__less__one,axiom,
% 5.44/5.63 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.44/5.63
% 5.44/5.63 % zero_less_one
% 5.44/5.63 thf(fact_2132_less__numeral__extra_I1_J,axiom,
% 5.44/5.63 ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat ).
% 5.44/5.63
% 5.44/5.63 % less_numeral_extra(1)
% 5.44/5.63 thf(fact_2133_less__numeral__extra_I1_J,axiom,
% 5.44/5.63 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.44/5.63
% 5.44/5.63 % less_numeral_extra(1)
% 5.44/5.63 thf(fact_2134_less__numeral__extra_I1_J,axiom,
% 5.44/5.63 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.44/5.63
% 5.44/5.63 % less_numeral_extra(1)
% 5.44/5.63 thf(fact_2135_less__numeral__extra_I1_J,axiom,
% 5.44/5.63 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.44/5.63
% 5.44/5.63 % less_numeral_extra(1)
% 5.44/5.63 thf(fact_2136_le__iff__diff__le__0,axiom,
% 5.44/5.63 ( ord_less_eq_real
% 5.44/5.63 = ( ^ [A4: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B4 ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_iff_diff_le_0
% 5.44/5.63 thf(fact_2137_le__iff__diff__le__0,axiom,
% 5.44/5.63 ( ord_less_eq_int
% 5.44/5.63 = ( ^ [A4: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_iff_diff_le_0
% 5.44/5.63 thf(fact_2138_divide__right__mono__neg,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_right_mono_neg
% 5.44/5.63 thf(fact_2139_divide__nonpos__nonpos,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_nonpos_nonpos
% 5.44/5.63 thf(fact_2140_divide__nonpos__nonneg,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_nonpos_nonneg
% 5.44/5.63 thf(fact_2141_divide__nonneg__nonpos,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_nonneg_nonpos
% 5.44/5.63 thf(fact_2142_divide__nonneg__nonneg,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_nonneg_nonneg
% 5.44/5.63 thf(fact_2143_zero__le__divide__iff,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.44/5.63 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_divide_iff
% 5.44/5.63 thf(fact_2144_divide__right__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_right_mono
% 5.44/5.63 thf(fact_2145_divide__le__0__iff,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.44/5.63 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_le_0_iff
% 5.44/5.63 thf(fact_2146_less__iff__diff__less__0,axiom,
% 5.44/5.63 ( ord_less_real
% 5.44/5.63 = ( ^ [A4: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B4 ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_iff_diff_less_0
% 5.44/5.63 thf(fact_2147_less__iff__diff__less__0,axiom,
% 5.44/5.63 ( ord_less_int
% 5.44/5.63 = ( ^ [A4: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_iff_diff_less_0
% 5.44/5.63 thf(fact_2148_zero__le__power,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_power
% 5.44/5.63 thf(fact_2149_zero__le__power,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_power
% 5.44/5.63 thf(fact_2150_zero__le__power,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_power
% 5.44/5.63 thf(fact_2151_power__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_mono
% 5.44/5.63 thf(fact_2152_power__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_mono
% 5.44/5.63 thf(fact_2153_power__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_mono
% 5.44/5.63 thf(fact_2154_divide__strict__right__mono__neg,axiom,
% 5.44/5.63 ! [B: real,A: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ B @ A )
% 5.44/5.63 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_strict_right_mono_neg
% 5.44/5.63 thf(fact_2155_divide__strict__right__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_strict_right_mono
% 5.44/5.63 thf(fact_2156_zero__less__divide__iff,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.44/5.63 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_divide_iff
% 5.44/5.63 thf(fact_2157_divide__less__cancel,axiom,
% 5.44/5.63 ! [A: real,C: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ B @ A ) )
% 5.44/5.63 & ( C != zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_less_cancel
% 5.44/5.63 thf(fact_2158_divide__less__0__iff,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.44/5.63 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_less_0_iff
% 5.44/5.63 thf(fact_2159_divide__pos__pos,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_pos_pos
% 5.44/5.63 thf(fact_2160_divide__pos__neg,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_pos_neg
% 5.44/5.63 thf(fact_2161_divide__neg__pos,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_neg_pos
% 5.44/5.63 thf(fact_2162_divide__neg__neg,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_neg_neg
% 5.44/5.63 thf(fact_2163_zero__less__power,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_power
% 5.44/5.63 thf(fact_2164_zero__less__power,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_power
% 5.44/5.63 thf(fact_2165_zero__less__power,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_power
% 5.44/5.63 thf(fact_2166_nonzero__eq__divide__eq,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( C != zero_zero_real )
% 5.44/5.63 => ( ( A
% 5.44/5.63 = ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( times_times_real @ A @ C )
% 5.44/5.63 = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nonzero_eq_divide_eq
% 5.44/5.63 thf(fact_2167_nonzero__eq__divide__eq,axiom,
% 5.44/5.63 ! [C: complex,A: complex,B: complex] :
% 5.44/5.63 ( ( C != zero_zero_complex )
% 5.44/5.63 => ( ( A
% 5.44/5.63 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.63 = ( ( times_times_complex @ A @ C )
% 5.44/5.63 = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nonzero_eq_divide_eq
% 5.44/5.63 thf(fact_2168_nonzero__divide__eq__eq,axiom,
% 5.44/5.63 ! [C: real,B: real,A: real] :
% 5.44/5.63 ( ( C != zero_zero_real )
% 5.44/5.63 => ( ( ( divide_divide_real @ B @ C )
% 5.44/5.63 = A )
% 5.44/5.63 = ( B
% 5.44/5.63 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nonzero_divide_eq_eq
% 5.44/5.63 thf(fact_2169_nonzero__divide__eq__eq,axiom,
% 5.44/5.63 ! [C: complex,B: complex,A: complex] :
% 5.44/5.63 ( ( C != zero_zero_complex )
% 5.44/5.63 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.44/5.63 = A )
% 5.44/5.63 = ( B
% 5.44/5.63 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nonzero_divide_eq_eq
% 5.44/5.63 thf(fact_2170_eq__divide__imp,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( C != zero_zero_real )
% 5.44/5.63 => ( ( ( times_times_real @ A @ C )
% 5.44/5.63 = B )
% 5.44/5.63 => ( A
% 5.44/5.63 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % eq_divide_imp
% 5.44/5.63 thf(fact_2171_eq__divide__imp,axiom,
% 5.44/5.63 ! [C: complex,A: complex,B: complex] :
% 5.44/5.63 ( ( C != zero_zero_complex )
% 5.44/5.63 => ( ( ( times_times_complex @ A @ C )
% 5.44/5.63 = B )
% 5.44/5.63 => ( A
% 5.44/5.63 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % eq_divide_imp
% 5.44/5.63 thf(fact_2172_divide__eq__imp,axiom,
% 5.44/5.63 ! [C: real,B: real,A: real] :
% 5.44/5.63 ( ( C != zero_zero_real )
% 5.44/5.63 => ( ( B
% 5.44/5.63 = ( times_times_real @ A @ C ) )
% 5.44/5.63 => ( ( divide_divide_real @ B @ C )
% 5.44/5.63 = A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_eq_imp
% 5.44/5.63 thf(fact_2173_divide__eq__imp,axiom,
% 5.44/5.63 ! [C: complex,B: complex,A: complex] :
% 5.44/5.63 ( ( C != zero_zero_complex )
% 5.44/5.63 => ( ( B
% 5.44/5.63 = ( times_times_complex @ A @ C ) )
% 5.44/5.63 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.44/5.63 = A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_eq_imp
% 5.44/5.63 thf(fact_2174_eq__divide__eq,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( A
% 5.44/5.63 = ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( ( C != zero_zero_real )
% 5.44/5.63 => ( ( times_times_real @ A @ C )
% 5.44/5.63 = B ) )
% 5.44/5.63 & ( ( C = zero_zero_real )
% 5.44/5.63 => ( A = zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % eq_divide_eq
% 5.44/5.63 thf(fact_2175_eq__divide__eq,axiom,
% 5.44/5.63 ! [A: complex,B: complex,C: complex] :
% 5.44/5.63 ( ( A
% 5.44/5.63 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.63 = ( ( ( C != zero_zero_complex )
% 5.44/5.63 => ( ( times_times_complex @ A @ C )
% 5.44/5.63 = B ) )
% 5.44/5.63 & ( ( C = zero_zero_complex )
% 5.44/5.63 => ( A = zero_zero_complex ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % eq_divide_eq
% 5.44/5.63 thf(fact_2176_divide__eq__eq,axiom,
% 5.44/5.63 ! [B: real,C: real,A: real] :
% 5.44/5.63 ( ( ( divide_divide_real @ B @ C )
% 5.44/5.63 = A )
% 5.44/5.63 = ( ( ( C != zero_zero_real )
% 5.44/5.63 => ( B
% 5.44/5.63 = ( times_times_real @ A @ C ) ) )
% 5.44/5.63 & ( ( C = zero_zero_real )
% 5.44/5.63 => ( A = zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_eq_eq
% 5.44/5.63 thf(fact_2177_divide__eq__eq,axiom,
% 5.44/5.63 ! [B: complex,C: complex,A: complex] :
% 5.44/5.63 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.44/5.63 = A )
% 5.44/5.63 = ( ( ( C != zero_zero_complex )
% 5.44/5.63 => ( B
% 5.44/5.63 = ( times_times_complex @ A @ C ) ) )
% 5.44/5.63 & ( ( C = zero_zero_complex )
% 5.44/5.63 => ( A = zero_zero_complex ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_eq_eq
% 5.44/5.63 thf(fact_2178_frac__eq__eq,axiom,
% 5.44/5.63 ! [Y: real,Z: real,X: real,W: real] :
% 5.44/5.63 ( ( Y != zero_zero_real )
% 5.44/5.63 => ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( ( divide_divide_real @ X @ Y )
% 5.44/5.63 = ( divide_divide_real @ W @ Z ) )
% 5.44/5.63 = ( ( times_times_real @ X @ Z )
% 5.44/5.63 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % frac_eq_eq
% 5.44/5.63 thf(fact_2179_frac__eq__eq,axiom,
% 5.44/5.63 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.44/5.63 ( ( Y != zero_zero_complex )
% 5.44/5.63 => ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 5.44/5.63 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.44/5.63 = ( ( times_times_complex @ X @ Z )
% 5.44/5.63 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % frac_eq_eq
% 5.44/5.63 thf(fact_2180_right__inverse__eq,axiom,
% 5.44/5.63 ! [B: real,A: real] :
% 5.44/5.63 ( ( B != zero_zero_real )
% 5.44/5.63 => ( ( ( divide_divide_real @ A @ B )
% 5.44/5.63 = one_one_real )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % right_inverse_eq
% 5.44/5.63 thf(fact_2181_right__inverse__eq,axiom,
% 5.44/5.63 ! [B: complex,A: complex] :
% 5.44/5.63 ( ( B != zero_zero_complex )
% 5.44/5.63 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.44/5.63 = one_one_complex )
% 5.44/5.63 = ( A = B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % right_inverse_eq
% 5.44/5.63 thf(fact_2182_power__0,axiom,
% 5.44/5.63 ! [A: extended_enat] :
% 5.44/5.63 ( ( power_8040749407984259932d_enat @ A @ zero_zero_nat )
% 5.44/5.63 = one_on7984719198319812577d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % power_0
% 5.44/5.63 thf(fact_2183_power__0,axiom,
% 5.44/5.63 ! [A: nat] :
% 5.44/5.63 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.44/5.63 = one_one_nat ) ).
% 5.44/5.63
% 5.44/5.63 % power_0
% 5.44/5.63 thf(fact_2184_power__0,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( power_power_real @ A @ zero_zero_nat )
% 5.44/5.63 = one_one_real ) ).
% 5.44/5.63
% 5.44/5.63 % power_0
% 5.44/5.63 thf(fact_2185_power__0,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ( ( power_power_int @ A @ zero_zero_nat )
% 5.44/5.63 = one_one_int ) ).
% 5.44/5.63
% 5.44/5.63 % power_0
% 5.44/5.63 thf(fact_2186_power__0,axiom,
% 5.44/5.63 ! [A: complex] :
% 5.44/5.63 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.44/5.63 = one_one_complex ) ).
% 5.44/5.63
% 5.44/5.63 % power_0
% 5.44/5.63 thf(fact_2187_Ex__less__Suc2,axiom,
% 5.44/5.63 ! [N2: nat,P: nat > $o] :
% 5.44/5.63 ( ( ? [I5: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 5.44/5.63 & ( P @ I5 ) ) )
% 5.44/5.63 = ( ( P @ zero_zero_nat )
% 5.44/5.63 | ? [I5: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I5 @ N2 )
% 5.44/5.63 & ( P @ ( suc @ I5 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % Ex_less_Suc2
% 5.44/5.63 thf(fact_2188_gr0__conv__Suc,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 = ( ? [M6: nat] :
% 5.44/5.63 ( N2
% 5.44/5.63 = ( suc @ M6 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % gr0_conv_Suc
% 5.44/5.63 thf(fact_2189_All__less__Suc2,axiom,
% 5.44/5.63 ! [N2: nat,P: nat > $o] :
% 5.44/5.63 ( ( ! [I5: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 5.44/5.63 => ( P @ I5 ) ) )
% 5.44/5.63 = ( ( P @ zero_zero_nat )
% 5.44/5.63 & ! [I5: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I5 @ N2 )
% 5.44/5.63 => ( P @ ( suc @ I5 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % All_less_Suc2
% 5.44/5.63 thf(fact_2190_gr0__implies__Suc,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ? [M5: nat] :
% 5.44/5.63 ( N2
% 5.44/5.63 = ( suc @ M5 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % gr0_implies_Suc
% 5.44/5.63 thf(fact_2191_less__Suc__eq__0__disj,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.44/5.63 = ( ( M = zero_zero_nat )
% 5.44/5.63 | ? [J3: nat] :
% 5.44/5.63 ( ( M
% 5.44/5.63 = ( suc @ J3 ) )
% 5.44/5.63 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_Suc_eq_0_disj
% 5.44/5.63 thf(fact_2192_add__is__1,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( plus_plus_nat @ M @ N2 )
% 5.44/5.63 = ( suc @ zero_zero_nat ) )
% 5.44/5.63 = ( ( ( M
% 5.44/5.63 = ( suc @ zero_zero_nat ) )
% 5.44/5.63 & ( N2 = zero_zero_nat ) )
% 5.44/5.63 | ( ( M = zero_zero_nat )
% 5.44/5.63 & ( N2
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_is_1
% 5.44/5.63 thf(fact_2193_one__is__add,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( suc @ zero_zero_nat )
% 5.44/5.63 = ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.63 = ( ( ( M
% 5.44/5.63 = ( suc @ zero_zero_nat ) )
% 5.44/5.63 & ( N2 = zero_zero_nat ) )
% 5.44/5.63 | ( ( M = zero_zero_nat )
% 5.44/5.63 & ( N2
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % one_is_add
% 5.44/5.63 thf(fact_2194_option_Osize_I4_J,axiom,
% 5.44/5.63 ! [X22: product_prod_nat_nat] :
% 5.44/5.63 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % option.size(4)
% 5.44/5.63 thf(fact_2195_option_Osize_I4_J,axiom,
% 5.44/5.63 ! [X22: nat] :
% 5.44/5.63 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % option.size(4)
% 5.44/5.63 thf(fact_2196_option_Osize_I4_J,axiom,
% 5.44/5.63 ! [X22: num] :
% 5.44/5.63 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % option.size(4)
% 5.44/5.63 thf(fact_2197_ex__least__nat__le,axiom,
% 5.44/5.63 ! [P: nat > $o,N2: nat] :
% 5.44/5.63 ( ( P @ N2 )
% 5.44/5.63 => ( ~ ( P @ zero_zero_nat )
% 5.44/5.63 => ? [K2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.44/5.63 & ! [I: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I @ K2 )
% 5.44/5.63 => ~ ( P @ I ) )
% 5.44/5.63 & ( P @ K2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % ex_least_nat_le
% 5.44/5.63 thf(fact_2198_less__imp__add__positive,axiom,
% 5.44/5.63 ! [I2: nat,J: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.63 => ? [K2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.44/5.63 & ( ( plus_plus_nat @ I2 @ K2 )
% 5.44/5.63 = J ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_imp_add_positive
% 5.44/5.63 thf(fact_2199_option_Osize_I3_J,axiom,
% 5.44/5.63 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % option.size(3)
% 5.44/5.63 thf(fact_2200_option_Osize_I3_J,axiom,
% 5.44/5.63 ( ( size_size_option_nat @ none_nat )
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % option.size(3)
% 5.44/5.63 thf(fact_2201_option_Osize_I3_J,axiom,
% 5.44/5.63 ( ( size_size_option_num @ none_num )
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % option.size(3)
% 5.44/5.63 thf(fact_2202_nat__mult__less__cancel1,axiom,
% 5.44/5.63 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.63 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.63 = ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_mult_less_cancel1
% 5.44/5.63 thf(fact_2203_nat__mult__eq__cancel1,axiom,
% 5.44/5.63 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.63 => ( ( ( times_times_nat @ K @ M )
% 5.44/5.63 = ( times_times_nat @ K @ N2 ) )
% 5.44/5.63 = ( M = N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_mult_eq_cancel1
% 5.44/5.63 thf(fact_2204_mult__less__mono2,axiom,
% 5.44/5.63 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_mono2
% 5.44/5.63 thf(fact_2205_mult__less__mono1,axiom,
% 5.44/5.63 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_mono1
% 5.44/5.63 thf(fact_2206_diff__less,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.63 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % diff_less
% 5.44/5.63 thf(fact_2207_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( divide_divide_nat @ M @ N2 )
% 5.44/5.63 = zero_zero_nat )
% 5.44/5.63 = ( ( ord_less_nat @ M @ N2 )
% 5.44/5.63 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % Euclidean_Division.div_eq_0_iff
% 5.44/5.63 thf(fact_2208_One__nat__def,axiom,
% 5.44/5.63 ( one_one_nat
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % One_nat_def
% 5.44/5.63 thf(fact_2209_nat__power__less__imp__less,axiom,
% 5.44/5.63 ! [I2: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 5.44/5.63 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 5.44/5.63 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_power_less_imp_less
% 5.44/5.63 thf(fact_2210_diff__add__0,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.63 = zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % diff_add_0
% 5.44/5.63 thf(fact_2211_mult__eq__self__implies__10,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( M
% 5.44/5.63 = ( times_times_nat @ M @ N2 ) )
% 5.44/5.63 => ( ( N2 = one_one_nat )
% 5.44/5.63 | ( M = zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_eq_self_implies_10
% 5.44/5.63 thf(fact_2212_vebt__member_Osimps_I3_J,axiom,
% 5.44/5.63 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.44/5.63 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_member.simps(3)
% 5.44/5.63 thf(fact_2213_VEBT__internal_Omembermima_Ocases,axiom,
% 5.44/5.63 ! [X: produc9072475918466114483BT_nat] :
% 5.44/5.63 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.44/5.63 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X5 ) )
% 5.44/5.63 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ X5 ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.membermima.cases
% 5.44/5.63 thf(fact_2214_vebt__insert_Ocases,axiom,
% 5.44/5.63 ! [X: produc9072475918466114483BT_nat] :
% 5.44/5.63 ( ! [A3: $o,B3: $o,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X5 ) )
% 5.44/5.63 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S2 ) @ X5 ) )
% 5.44/5.63 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) @ X5 ) )
% 5.44/5.63 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_insert.cases
% 5.44/5.63 thf(fact_2215_vebt__pred_Ocases,axiom,
% 5.44/5.63 ! [X: produc9072475918466114483BT_nat] :
% 5.44/5.63 ( ! [Uu2: $o,Uv2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.44/5.63 => ( ! [A3: $o,Uw2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.44/5.63 => ( ! [A3: $o,B3: $o,Va2: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 5.44/5.63 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 5.44/5.63 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Vf ) )
% 5.44/5.63 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_pred.cases
% 5.44/5.63 thf(fact_2216_vebt__succ_Ocases,axiom,
% 5.44/5.63 ! [X: produc9072475918466114483BT_nat] :
% 5.44/5.63 ( ! [Uu2: $o,B3: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) )
% 5.44/5.63 => ( ! [Uv2: $o,Uw2: $o,N4: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N4 ) ) )
% 5.44/5.63 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 5.44/5.63 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve ) )
% 5.44/5.63 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_succ.cases
% 5.44/5.63 thf(fact_2217_vebt__insert_Osimps_I2_J,axiom,
% 5.44/5.63 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 5.44/5.63 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S3 ) @ X )
% 5.44/5.63 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S3 ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_insert.simps(2)
% 5.44/5.63 thf(fact_2218_vebt__pred_Osimps_I3_J,axiom,
% 5.44/5.63 ! [B: $o,A: $o,Va: nat] :
% 5.44/5.63 ( ( B
% 5.44/5.63 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.44/5.63 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.63 & ( ~ B
% 5.44/5.63 => ( ( A
% 5.44/5.63 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.44/5.63 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.63 & ( ~ A
% 5.44/5.63 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.44/5.63 = none_nat ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_pred.simps(3)
% 5.44/5.63 thf(fact_2219_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Y: $o] :
% 5.44/5.63 ( ( ( vEBT_VEBT_minNull @ X )
% 5.44/5.63 = Y )
% 5.44/5.63 => ( ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ $false @ $false ) )
% 5.44/5.63 => ~ Y )
% 5.44/5.63 => ( ( ? [Uv2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.44/5.63 => Y )
% 5.44/5.63 => ( ( ? [Uu2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.44/5.63 => Y )
% 5.44/5.63 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.44/5.63 => ~ Y )
% 5.44/5.63 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.44/5.63 => Y ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.minNull.elims(1)
% 5.44/5.63 thf(fact_2220_vebt__succ_Osimps_I2_J,axiom,
% 5.44/5.63 ! [Uv: $o,Uw: $o,N2: nat] :
% 5.44/5.63 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) )
% 5.44/5.63 = none_nat ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_succ.simps(2)
% 5.44/5.63 thf(fact_2221_mult__less__le__imp__less,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_le_imp_less
% 5.44/5.63 thf(fact_2222_mult__less__le__imp__less,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_le_imp_less
% 5.44/5.63 thf(fact_2223_mult__less__le__imp__less,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_le_imp_less
% 5.44/5.63 thf(fact_2224_mult__le__less__imp__less,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_real @ C @ D )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_less_imp_less
% 5.44/5.63 thf(fact_2225_mult__le__less__imp__less,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_nat @ C @ D )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_less_imp_less
% 5.44/5.63 thf(fact_2226_mult__le__less__imp__less,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_int @ C @ D )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_less_imp_less
% 5.44/5.63 thf(fact_2227_mult__right__le__imp__le,axiom,
% 5.44/5.63 ! [A: real,C: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_le_imp_le
% 5.44/5.63 thf(fact_2228_mult__right__le__imp__le,axiom,
% 5.44/5.63 ! [A: nat,C: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_le_imp_le
% 5.44/5.63 thf(fact_2229_mult__right__le__imp__le,axiom,
% 5.44/5.63 ! [A: int,C: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_le_imp_le
% 5.44/5.63 thf(fact_2230_mult__left__le__imp__le,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le_imp_le
% 5.44/5.63 thf(fact_2231_mult__left__le__imp__le,axiom,
% 5.44/5.63 ! [C: nat,A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le_imp_le
% 5.44/5.63 thf(fact_2232_mult__left__le__imp__le,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le_imp_le
% 5.44/5.63 thf(fact_2233_mult__le__cancel__left__pos,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left_pos
% 5.44/5.63 thf(fact_2234_mult__le__cancel__left__pos,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left_pos
% 5.44/5.63 thf(fact_2235_mult__le__cancel__left__neg,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left_neg
% 5.44/5.63 thf(fact_2236_mult__le__cancel__left__neg,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left_neg
% 5.44/5.63 thf(fact_2237_mult__less__cancel__right,axiom,
% 5.44/5.63 ! [A: real,C: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_right
% 5.44/5.63 thf(fact_2238_mult__less__cancel__right,axiom,
% 5.44/5.63 ! [A: int,C: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_right
% 5.44/5.63 thf(fact_2239_mult__strict__mono_H,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_real @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_mono'
% 5.44/5.63 thf(fact_2240_mult__strict__mono_H,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_nat @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_mono'
% 5.44/5.63 thf(fact_2241_mult__strict__mono_H,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_int @ C @ D )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_mono'
% 5.44/5.63 thf(fact_2242_mult__right__less__imp__less,axiom,
% 5.44/5.63 ! [A: real,C: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_less_imp_less
% 5.44/5.63 thf(fact_2243_mult__right__less__imp__less,axiom,
% 5.44/5.63 ! [A: nat,C: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_less_imp_less
% 5.44/5.63 thf(fact_2244_mult__right__less__imp__less,axiom,
% 5.44/5.63 ! [A: int,C: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_less_imp_less
% 5.44/5.63 thf(fact_2245_mult__less__cancel__left,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left
% 5.44/5.63 thf(fact_2246_mult__less__cancel__left,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left
% 5.44/5.63 thf(fact_2247_mult__strict__mono,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_real @ C @ D )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_mono
% 5.44/5.63 thf(fact_2248_mult__strict__mono,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( ( ord_less_nat @ C @ D )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_mono
% 5.44/5.63 thf(fact_2249_mult__strict__mono,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ B )
% 5.44/5.63 => ( ( ord_less_int @ C @ D )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_strict_mono
% 5.44/5.63 thf(fact_2250_mult__left__less__imp__less,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_less_imp_less
% 5.44/5.63 thf(fact_2251_mult__left__less__imp__less,axiom,
% 5.44/5.63 ! [C: nat,A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_less_imp_less
% 5.44/5.63 thf(fact_2252_mult__left__less__imp__less,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_less_imp_less
% 5.44/5.63 thf(fact_2253_mult__le__cancel__right,axiom,
% 5.44/5.63 ! [A: real,C: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_right
% 5.44/5.63 thf(fact_2254_mult__le__cancel__right,axiom,
% 5.44/5.63 ! [A: int,C: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_right
% 5.44/5.63 thf(fact_2255_mult__le__cancel__left,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left
% 5.44/5.63 thf(fact_2256_mult__le__cancel__left,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left
% 5.44/5.63 thf(fact_2257_add__strict__increasing2,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ B @ C )
% 5.44/5.63 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_strict_increasing2
% 5.44/5.63 thf(fact_2258_add__strict__increasing2,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ B @ C )
% 5.44/5.63 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_strict_increasing2
% 5.44/5.63 thf(fact_2259_add__strict__increasing2,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ B @ C )
% 5.44/5.63 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_strict_increasing2
% 5.44/5.63 thf(fact_2260_add__strict__increasing,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ C )
% 5.44/5.63 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_strict_increasing
% 5.44/5.63 thf(fact_2261_add__strict__increasing,axiom,
% 5.44/5.63 ! [A: nat,B: nat,C: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.63 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_strict_increasing
% 5.44/5.63 thf(fact_2262_add__strict__increasing,axiom,
% 5.44/5.63 ! [A: int,B: int,C: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.63 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_strict_increasing
% 5.44/5.63 thf(fact_2263_add__pos__nonneg,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B )
% 5.44/5.63 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_pos_nonneg
% 5.44/5.63 thf(fact_2264_add__pos__nonneg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_pos_nonneg
% 5.44/5.63 thf(fact_2265_add__pos__nonneg,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_pos_nonneg
% 5.44/5.63 thf(fact_2266_add__pos__nonneg,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_pos_nonneg
% 5.44/5.63 thf(fact_2267_add__nonpos__neg,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( ord_le72135733267957522d_enat @ B @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_neg
% 5.44/5.63 thf(fact_2268_add__nonpos__neg,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_neg
% 5.44/5.63 thf(fact_2269_add__nonpos__neg,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.44/5.63 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_neg
% 5.44/5.63 thf(fact_2270_add__nonpos__neg,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonpos_neg
% 5.44/5.63 thf(fact_2271_add__nonneg__pos,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B )
% 5.44/5.63 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_pos
% 5.44/5.63 thf(fact_2272_add__nonneg__pos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_pos
% 5.44/5.63 thf(fact_2273_add__nonneg__pos,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_pos
% 5.44/5.63 thf(fact_2274_add__nonneg__pos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_nonneg_pos
% 5.44/5.63 thf(fact_2275_add__neg__nonpos,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ B @ zero_z5237406670263579293d_enat )
% 5.44/5.63 => ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_neg_nonpos
% 5.44/5.63 thf(fact_2276_add__neg__nonpos,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_neg_nonpos
% 5.44/5.63 thf(fact_2277_add__neg__nonpos,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.44/5.63 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_neg_nonpos
% 5.44/5.63 thf(fact_2278_add__neg__nonpos,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_neg_nonpos
% 5.44/5.63 thf(fact_2279_field__le__epsilon,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ! [E2: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.44/5.63 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 5.44/5.63 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.63
% 5.44/5.63 % field_le_epsilon
% 5.44/5.63 thf(fact_2280_div__positive,axiom,
% 5.44/5.63 ! [B: code_integer,A: code_integer] :
% 5.44/5.63 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.44/5.63 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.44/5.63 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_positive
% 5.44/5.63 thf(fact_2281_div__positive,axiom,
% 5.44/5.63 ! [B: nat,A: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_positive
% 5.44/5.63 thf(fact_2282_div__positive,axiom,
% 5.44/5.63 ! [B: int,A: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ A )
% 5.44/5.63 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_positive
% 5.44/5.63 thf(fact_2283_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.44/5.63 ! [A: code_integer,B: code_integer] :
% 5.44/5.63 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.44/5.63 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.44/5.63 => ( ( divide6298287555418463151nteger @ A @ B )
% 5.44/5.63 = zero_z3403309356797280102nteger ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % unique_euclidean_semiring_numeral_class.div_less
% 5.44/5.63 thf(fact_2284_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( ( divide_divide_nat @ A @ B )
% 5.44/5.63 = zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % unique_euclidean_semiring_numeral_class.div_less
% 5.44/5.63 thf(fact_2285_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ A @ B )
% 5.44/5.63 => ( ( divide_divide_int @ A @ B )
% 5.44/5.63 = zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % unique_euclidean_semiring_numeral_class.div_less
% 5.44/5.63 thf(fact_2286_divide__nonpos__pos,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_nonpos_pos
% 5.44/5.63 thf(fact_2287_divide__nonpos__neg,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_nonpos_neg
% 5.44/5.63 thf(fact_2288_divide__nonneg__pos,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_nonneg_pos
% 5.44/5.63 thf(fact_2289_divide__nonneg__neg,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_nonneg_neg
% 5.44/5.63 thf(fact_2290_divide__le__cancel,axiom,
% 5.44/5.63 ! [A: real,C: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ A @ B ) )
% 5.44/5.63 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_le_cancel
% 5.44/5.63 thf(fact_2291_frac__less2,axiom,
% 5.44/5.63 ! [X: real,Y: real,W: real,Z: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.44/5.63 => ( ( ord_less_real @ W @ Z )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % frac_less2
% 5.44/5.63 thf(fact_2292_frac__less,axiom,
% 5.44/5.63 ! [X: real,Y: real,W: real,Z: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_real @ X @ Y )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.44/5.63 => ( ( ord_less_eq_real @ W @ Z )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % frac_less
% 5.44/5.63 thf(fact_2293_frac__le,axiom,
% 5.44/5.63 ! [Y: real,X: real,W: real,Z: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.44/5.63 => ( ( ord_less_eq_real @ W @ Z )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % frac_le
% 5.44/5.63 thf(fact_2294_sum__squares__ge__zero,axiom,
% 5.44/5.63 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_squares_ge_zero
% 5.44/5.63 thf(fact_2295_sum__squares__ge__zero,axiom,
% 5.44/5.63 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_squares_ge_zero
% 5.44/5.63 thf(fact_2296_sum__squares__le__zero__iff,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.44/5.63 = ( ( X = zero_zero_real )
% 5.44/5.63 & ( Y = zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_squares_le_zero_iff
% 5.44/5.63 thf(fact_2297_sum__squares__le__zero__iff,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.44/5.63 = ( ( X = zero_zero_int )
% 5.44/5.63 & ( Y = zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_squares_le_zero_iff
% 5.44/5.63 thf(fact_2298_mult__left__le__one__le,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le_one_le
% 5.44/5.63 thf(fact_2299_mult__left__le__one__le,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.63 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le_one_le
% 5.44/5.63 thf(fact_2300_mult__right__le__one__le,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_le_one_le
% 5.44/5.63 thf(fact_2301_mult__right__le__one__le,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.63 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_right_le_one_le
% 5.44/5.63 thf(fact_2302_mult__le__one,axiom,
% 5.44/5.63 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ A @ one_on7984719198319812577d_enat )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ B @ one_on7984719198319812577d_enat )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ B ) @ one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_one
% 5.44/5.63 thf(fact_2303_mult__le__one,axiom,
% 5.44/5.63 ! [A: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_one
% 5.44/5.63 thf(fact_2304_mult__le__one,axiom,
% 5.44/5.63 ! [A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_one
% 5.44/5.63 thf(fact_2305_mult__le__one,axiom,
% 5.44/5.63 ! [A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_one
% 5.44/5.63 thf(fact_2306_mult__left__le,axiom,
% 5.44/5.63 ! [C: extended_enat,A: extended_enat] :
% 5.44/5.63 ( ( ord_le2932123472753598470d_enat @ C @ one_on7984719198319812577d_enat )
% 5.44/5.63 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A )
% 5.44/5.63 => ( ord_le2932123472753598470d_enat @ ( times_7803423173614009249d_enat @ A @ C ) @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le
% 5.44/5.63 thf(fact_2307_mult__left__le,axiom,
% 5.44/5.63 ! [C: real,A: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le
% 5.44/5.63 thf(fact_2308_mult__left__le,axiom,
% 5.44/5.63 ! [C: nat,A: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le
% 5.44/5.63 thf(fact_2309_mult__left__le,axiom,
% 5.44/5.63 ! [C: int,A: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_left_le
% 5.44/5.63 thf(fact_2310_power__less__imp__less__base,axiom,
% 5.44/5.63 ! [A: real,N2: nat,B: real] :
% 5.44/5.63 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_less_imp_less_base
% 5.44/5.63 thf(fact_2311_power__less__imp__less__base,axiom,
% 5.44/5.63 ! [A: nat,N2: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_less_imp_less_base
% 5.44/5.63 thf(fact_2312_power__less__imp__less__base,axiom,
% 5.44/5.63 ! [A: int,N2: nat,B: int] :
% 5.44/5.63 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_less_imp_less_base
% 5.44/5.63 thf(fact_2313_not__sum__squares__lt__zero,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % not_sum_squares_lt_zero
% 5.44/5.63 thf(fact_2314_not__sum__squares__lt__zero,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % not_sum_squares_lt_zero
% 5.44/5.63 thf(fact_2315_sum__squares__gt__zero__iff,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 5.44/5.63 = ( ( X != zero_zero_real )
% 5.44/5.63 | ( Y != zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_squares_gt_zero_iff
% 5.44/5.63 thf(fact_2316_sum__squares__gt__zero__iff,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 5.44/5.63 = ( ( X != zero_zero_int )
% 5.44/5.63 | ( Y != zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_squares_gt_zero_iff
% 5.44/5.63 thf(fact_2317_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.44/5.63 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.63 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.44/5.63 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.44/5.63 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.44/5.63 thf(fact_2318_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.44/5.63 ! [C: nat,A: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.63 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.44/5.63 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.44/5.63 thf(fact_2319_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.44/5.63 ! [C: int,A: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.63 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.44/5.63 thf(fact_2320_zero__less__two,axiom,
% 5.44/5.63 ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_two
% 5.44/5.63 thf(fact_2321_zero__less__two,axiom,
% 5.44/5.63 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_two
% 5.44/5.63 thf(fact_2322_zero__less__two,axiom,
% 5.44/5.63 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_two
% 5.44/5.63 thf(fact_2323_zero__less__two,axiom,
% 5.44/5.63 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.44/5.63
% 5.44/5.63 % zero_less_two
% 5.44/5.63 thf(fact_2324_divide__strict__left__mono__neg,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_strict_left_mono_neg
% 5.44/5.63 thf(fact_2325_divide__strict__left__mono,axiom,
% 5.44/5.63 ! [B: real,A: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ B @ A )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_strict_left_mono
% 5.44/5.63 thf(fact_2326_mult__imp__less__div__pos,axiom,
% 5.44/5.63 ! [Y: real,Z: real,X: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X )
% 5.44/5.63 => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_imp_less_div_pos
% 5.44/5.63 thf(fact_2327_mult__imp__div__pos__less,axiom,
% 5.44/5.63 ! [Y: real,X: real,Z: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y ) )
% 5.44/5.63 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_imp_div_pos_less
% 5.44/5.63 thf(fact_2328_pos__less__divide__eq,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos_less_divide_eq
% 5.44/5.63 thf(fact_2329_pos__divide__less__eq,axiom,
% 5.44/5.63 ! [C: real,B: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.44/5.63 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos_divide_less_eq
% 5.44/5.63 thf(fact_2330_neg__less__divide__eq,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % neg_less_divide_eq
% 5.44/5.63 thf(fact_2331_neg__divide__less__eq,axiom,
% 5.44/5.63 ! [C: real,B: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.44/5.63 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % neg_divide_less_eq
% 5.44/5.63 thf(fact_2332_less__divide__eq,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_divide_eq
% 5.44/5.63 thf(fact_2333_divide__less__eq,axiom,
% 5.44/5.63 ! [B: real,C: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_less_eq
% 5.44/5.63 thf(fact_2334_power__le__one,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_le_one
% 5.44/5.63 thf(fact_2335_power__le__one,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.44/5.63 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_le_one
% 5.44/5.63 thf(fact_2336_power__le__one,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_le_one
% 5.44/5.63 thf(fact_2337_eq__divide__eq__numeral_I1_J,axiom,
% 5.44/5.63 ! [W: num,B: real,C: real] :
% 5.44/5.63 ( ( ( numeral_numeral_real @ W )
% 5.44/5.63 = ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( ( C != zero_zero_real )
% 5.44/5.63 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.44/5.63 = B ) )
% 5.44/5.63 & ( ( C = zero_zero_real )
% 5.44/5.63 => ( ( numeral_numeral_real @ W )
% 5.44/5.63 = zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % eq_divide_eq_numeral(1)
% 5.44/5.63 thf(fact_2338_eq__divide__eq__numeral_I1_J,axiom,
% 5.44/5.63 ! [W: num,B: complex,C: complex] :
% 5.44/5.63 ( ( ( numera6690914467698888265omplex @ W )
% 5.44/5.63 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.63 = ( ( ( C != zero_zero_complex )
% 5.44/5.63 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.44/5.63 = B ) )
% 5.44/5.63 & ( ( C = zero_zero_complex )
% 5.44/5.63 => ( ( numera6690914467698888265omplex @ W )
% 5.44/5.63 = zero_zero_complex ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % eq_divide_eq_numeral(1)
% 5.44/5.63 thf(fact_2339_divide__eq__eq__numeral_I1_J,axiom,
% 5.44/5.63 ! [B: real,C: real,W: num] :
% 5.44/5.63 ( ( ( divide_divide_real @ B @ C )
% 5.44/5.63 = ( numeral_numeral_real @ W ) )
% 5.44/5.63 = ( ( ( C != zero_zero_real )
% 5.44/5.63 => ( B
% 5.44/5.63 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.44/5.63 & ( ( C = zero_zero_real )
% 5.44/5.63 => ( ( numeral_numeral_real @ W )
% 5.44/5.63 = zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_eq_eq_numeral(1)
% 5.44/5.63 thf(fact_2340_divide__eq__eq__numeral_I1_J,axiom,
% 5.44/5.63 ! [B: complex,C: complex,W: num] :
% 5.44/5.63 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.44/5.63 = ( numera6690914467698888265omplex @ W ) )
% 5.44/5.63 = ( ( ( C != zero_zero_complex )
% 5.44/5.63 => ( B
% 5.44/5.63 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.44/5.63 & ( ( C = zero_zero_complex )
% 5.44/5.63 => ( ( numera6690914467698888265omplex @ W )
% 5.44/5.63 = zero_zero_complex ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_eq_eq_numeral(1)
% 5.44/5.63 thf(fact_2341_less__divide__eq__1,axiom,
% 5.44/5.63 ! [B: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_real @ A @ B ) )
% 5.44/5.63 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_divide_eq_1
% 5.44/5.63 thf(fact_2342_divide__less__eq__1,axiom,
% 5.44/5.63 ! [B: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_real @ B @ A ) )
% 5.44/5.63 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_real @ A @ B ) )
% 5.44/5.63 | ( A = zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_less_eq_1
% 5.44/5.63 thf(fact_2343_divide__add__eq__iff,axiom,
% 5.44/5.63 ! [Z: real,X: real,Y: real] :
% 5.44/5.63 ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 5.44/5.63 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_add_eq_iff
% 5.44/5.63 thf(fact_2344_divide__add__eq__iff,axiom,
% 5.44/5.63 ! [Z: complex,X: complex,Y: complex] :
% 5.44/5.63 ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_add_eq_iff
% 5.44/5.63 thf(fact_2345_add__divide__eq__iff,axiom,
% 5.44/5.63 ! [Z: real,X: real,Y: real] :
% 5.44/5.63 ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 5.44/5.63 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_divide_eq_iff
% 5.44/5.63 thf(fact_2346_add__divide__eq__iff,axiom,
% 5.44/5.63 ! [Z: complex,X: complex,Y: complex] :
% 5.44/5.63 ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_divide_eq_iff
% 5.44/5.63 thf(fact_2347_add__num__frac,axiom,
% 5.44/5.63 ! [Y: real,Z: real,X: real] :
% 5.44/5.63 ( ( Y != zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.63 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_num_frac
% 5.44/5.63 thf(fact_2348_add__num__frac,axiom,
% 5.44/5.63 ! [Y: complex,Z: complex,X: complex] :
% 5.44/5.63 ( ( Y != zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_num_frac
% 5.44/5.63 thf(fact_2349_add__frac__num,axiom,
% 5.44/5.63 ! [Y: real,X: real,Z: real] :
% 5.44/5.63 ( ( Y != zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z )
% 5.44/5.63 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_frac_num
% 5.44/5.63 thf(fact_2350_add__frac__num,axiom,
% 5.44/5.63 ! [Y: complex,X: complex,Z: complex] :
% 5.44/5.63 ( ( Y != zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_frac_num
% 5.44/5.63 thf(fact_2351_add__frac__eq,axiom,
% 5.44/5.63 ! [Y: real,Z: real,X: real,W: real] :
% 5.44/5.63 ( ( Y != zero_zero_real )
% 5.44/5.63 => ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.44/5.63 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_frac_eq
% 5.44/5.63 thf(fact_2352_add__frac__eq,axiom,
% 5.44/5.63 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.44/5.63 ( ( Y != zero_zero_complex )
% 5.44/5.63 => ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_frac_eq
% 5.44/5.63 thf(fact_2353_add__divide__eq__if__simps_I1_J,axiom,
% 5.44/5.63 ! [Z: real,A: real,B: real] :
% 5.44/5.63 ( ( ( Z = zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.44/5.63 = A ) )
% 5.44/5.63 & ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.44/5.63 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_divide_eq_if_simps(1)
% 5.44/5.63 thf(fact_2354_add__divide__eq__if__simps_I1_J,axiom,
% 5.44/5.63 ! [Z: complex,A: complex,B: complex] :
% 5.44/5.63 ( ( ( Z = zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.44/5.63 = A ) )
% 5.44/5.63 & ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_divide_eq_if_simps(1)
% 5.44/5.63 thf(fact_2355_add__divide__eq__if__simps_I2_J,axiom,
% 5.44/5.63 ! [Z: real,A: real,B: real] :
% 5.44/5.63 ( ( ( Z = zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.44/5.63 = B ) )
% 5.44/5.63 & ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.44/5.63 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_divide_eq_if_simps(2)
% 5.44/5.63 thf(fact_2356_add__divide__eq__if__simps_I2_J,axiom,
% 5.44/5.63 ! [Z: complex,A: complex,B: complex] :
% 5.44/5.63 ( ( ( Z = zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.44/5.63 = B ) )
% 5.44/5.63 & ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_divide_eq_if_simps(2)
% 5.44/5.63 thf(fact_2357_power__inject__base,axiom,
% 5.44/5.63 ! [A: real,N2: nat,B: real] :
% 5.44/5.63 ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.44/5.63 = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( A = B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_inject_base
% 5.44/5.63 thf(fact_2358_power__inject__base,axiom,
% 5.44/5.63 ! [A: nat,N2: nat,B: nat] :
% 5.44/5.63 ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.44/5.63 = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( A = B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_inject_base
% 5.44/5.63 thf(fact_2359_power__inject__base,axiom,
% 5.44/5.63 ! [A: int,N2: nat,B: int] :
% 5.44/5.63 ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.44/5.63 = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( A = B ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_inject_base
% 5.44/5.63 thf(fact_2360_power__le__imp__le__base,axiom,
% 5.44/5.63 ! [A: real,N2: nat,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.63 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_le_imp_le_base
% 5.44/5.63 thf(fact_2361_power__le__imp__le__base,axiom,
% 5.44/5.63 ! [A: nat,N2: nat,B: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.44/5.63 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_le_imp_le_base
% 5.44/5.63 thf(fact_2362_power__le__imp__le__base,axiom,
% 5.44/5.63 ! [A: int,N2: nat,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.63 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_le_imp_le_base
% 5.44/5.63 thf(fact_2363_div__add__self2,axiom,
% 5.44/5.63 ! [B: nat,A: nat] :
% 5.44/5.63 ( ( B != zero_zero_nat )
% 5.44/5.63 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.44/5.63 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_add_self2
% 5.44/5.63 thf(fact_2364_div__add__self2,axiom,
% 5.44/5.63 ! [B: int,A: int] :
% 5.44/5.63 ( ( B != zero_zero_int )
% 5.44/5.63 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.44/5.63 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_add_self2
% 5.44/5.63 thf(fact_2365_div__add__self2,axiom,
% 5.44/5.63 ! [B: code_integer,A: code_integer] :
% 5.44/5.63 ( ( B != zero_z3403309356797280102nteger )
% 5.44/5.63 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.44/5.63 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_add_self2
% 5.44/5.63 thf(fact_2366_div__add__self1,axiom,
% 5.44/5.63 ! [B: nat,A: nat] :
% 5.44/5.63 ( ( B != zero_zero_nat )
% 5.44/5.63 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.44/5.63 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_add_self1
% 5.44/5.63 thf(fact_2367_div__add__self1,axiom,
% 5.44/5.63 ! [B: int,A: int] :
% 5.44/5.63 ( ( B != zero_zero_int )
% 5.44/5.63 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.44/5.63 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_add_self1
% 5.44/5.63 thf(fact_2368_div__add__self1,axiom,
% 5.44/5.63 ! [B: code_integer,A: code_integer] :
% 5.44/5.63 ( ( B != zero_z3403309356797280102nteger )
% 5.44/5.63 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.44/5.63 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_add_self1
% 5.44/5.63 thf(fact_2369_divide__diff__eq__iff,axiom,
% 5.44/5.63 ! [Z: real,X: real,Y: real] :
% 5.44/5.63 ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 5.44/5.63 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_diff_eq_iff
% 5.44/5.63 thf(fact_2370_divide__diff__eq__iff,axiom,
% 5.44/5.63 ! [Z: complex,X: complex,Y: complex] :
% 5.44/5.63 ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_diff_eq_iff
% 5.44/5.63 thf(fact_2371_diff__divide__eq__iff,axiom,
% 5.44/5.63 ! [Z: real,X: real,Y: real] :
% 5.44/5.63 ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 5.44/5.63 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % diff_divide_eq_iff
% 5.44/5.63 thf(fact_2372_diff__divide__eq__iff,axiom,
% 5.44/5.63 ! [Z: complex,X: complex,Y: complex] :
% 5.44/5.63 ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % diff_divide_eq_iff
% 5.44/5.63 thf(fact_2373_diff__frac__eq,axiom,
% 5.44/5.63 ! [Y: real,Z: real,X: real,W: real] :
% 5.44/5.63 ( ( Y != zero_zero_real )
% 5.44/5.63 => ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.44/5.63 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % diff_frac_eq
% 5.44/5.63 thf(fact_2374_diff__frac__eq,axiom,
% 5.44/5.63 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.44/5.63 ( ( Y != zero_zero_complex )
% 5.44/5.63 => ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % diff_frac_eq
% 5.44/5.63 thf(fact_2375_add__divide__eq__if__simps_I4_J,axiom,
% 5.44/5.63 ! [Z: real,A: real,B: real] :
% 5.44/5.63 ( ( ( Z = zero_zero_real )
% 5.44/5.63 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.44/5.63 = A ) )
% 5.44/5.63 & ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.44/5.63 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_divide_eq_if_simps(4)
% 5.44/5.63 thf(fact_2376_add__divide__eq__if__simps_I4_J,axiom,
% 5.44/5.63 ! [Z: complex,A: complex,B: complex] :
% 5.44/5.63 ( ( ( Z = zero_zero_complex )
% 5.44/5.63 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.44/5.63 = A ) )
% 5.44/5.63 & ( ( Z != zero_zero_complex )
% 5.44/5.63 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_divide_eq_if_simps(4)
% 5.44/5.63 thf(fact_2377_vebt__member_Osimps_I4_J,axiom,
% 5.44/5.63 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.44/5.63 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_member.simps(4)
% 5.44/5.63 thf(fact_2378_vebt__delete_Osimps_I5_J,axiom,
% 5.44/5.63 ! [Mi: nat,Ma: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X: nat] :
% 5.44/5.63 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X )
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_delete.simps(5)
% 5.44/5.63 thf(fact_2379_numeral__1__eq__Suc__0,axiom,
% 5.44/5.63 ( ( numeral_numeral_nat @ one )
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % numeral_1_eq_Suc_0
% 5.44/5.63 thf(fact_2380_num_Osize_I5_J,axiom,
% 5.44/5.63 ! [X22: num] :
% 5.44/5.63 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.44/5.63 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % num.size(5)
% 5.44/5.63 thf(fact_2381_ex__least__nat__less,axiom,
% 5.44/5.63 ! [P: nat > $o,N2: nat] :
% 5.44/5.63 ( ( P @ N2 )
% 5.44/5.63 => ( ~ ( P @ zero_zero_nat )
% 5.44/5.63 => ? [K2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ K2 @ N2 )
% 5.44/5.63 & ! [I: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ I @ K2 )
% 5.44/5.63 => ~ ( P @ I ) )
% 5.44/5.63 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % ex_least_nat_less
% 5.44/5.63 thf(fact_2382_n__less__n__mult__m,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.44/5.63 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % n_less_n_mult_m
% 5.44/5.63 thf(fact_2383_n__less__m__mult__n,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.44/5.63 => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % n_less_m_mult_n
% 5.44/5.63 thf(fact_2384_one__less__mult,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.63 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.44/5.63 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % one_less_mult
% 5.44/5.63 thf(fact_2385_diff__Suc__less,axiom,
% 5.44/5.63 ! [N2: nat,I2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I2 ) ) @ N2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % diff_Suc_less
% 5.44/5.63 thf(fact_2386_power__gt__expt,axiom,
% 5.44/5.63 ! [N2: nat,K: nat] :
% 5.44/5.63 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.63 => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_gt_expt
% 5.44/5.63 thf(fact_2387_nat__mult__le__cancel1,axiom,
% 5.44/5.63 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.63 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.63 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_mult_le_cancel1
% 5.44/5.63 thf(fact_2388_nat__induct__non__zero,axiom,
% 5.44/5.63 ! [N2: nat,P: nat > $o] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( P @ one_one_nat )
% 5.44/5.63 => ( ! [N4: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.44/5.63 => ( ( P @ N4 )
% 5.44/5.63 => ( P @ ( suc @ N4 ) ) ) )
% 5.44/5.63 => ( P @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_induct_non_zero
% 5.44/5.63 thf(fact_2389_length__pos__if__in__set,axiom,
% 5.44/5.63 ! [X: real,Xs2: list_real] :
% 5.44/5.63 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % length_pos_if_in_set
% 5.44/5.63 thf(fact_2390_length__pos__if__in__set,axiom,
% 5.44/5.63 ! [X: complex,Xs2: list_complex] :
% 5.44/5.63 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % length_pos_if_in_set
% 5.44/5.63 thf(fact_2391_length__pos__if__in__set,axiom,
% 5.44/5.63 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.44/5.63 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % length_pos_if_in_set
% 5.44/5.63 thf(fact_2392_length__pos__if__in__set,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % length_pos_if_in_set
% 5.44/5.63 thf(fact_2393_length__pos__if__in__set,axiom,
% 5.44/5.63 ! [X: $o,Xs2: list_o] :
% 5.44/5.63 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % length_pos_if_in_set
% 5.44/5.63 thf(fact_2394_length__pos__if__in__set,axiom,
% 5.44/5.63 ! [X: nat,Xs2: list_nat] :
% 5.44/5.63 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % length_pos_if_in_set
% 5.44/5.63 thf(fact_2395_length__pos__if__in__set,axiom,
% 5.44/5.63 ! [X: int,Xs2: list_int] :
% 5.44/5.63 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % length_pos_if_in_set
% 5.44/5.63 thf(fact_2396_nat__one__le__power,axiom,
% 5.44/5.63 ! [I2: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 5.44/5.63 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_one_le_power
% 5.44/5.63 thf(fact_2397_nat__diff__split__asm,axiom,
% 5.44/5.63 ! [P: nat > $o,A: nat,B: nat] :
% 5.44/5.63 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.44/5.63 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.44/5.63 & ~ ( P @ zero_zero_nat ) )
% 5.44/5.63 | ? [D2: nat] :
% 5.44/5.63 ( ( A
% 5.44/5.63 = ( plus_plus_nat @ B @ D2 ) )
% 5.44/5.63 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_diff_split_asm
% 5.44/5.63 thf(fact_2398_nat__diff__split,axiom,
% 5.44/5.63 ! [P: nat > $o,A: nat,B: nat] :
% 5.44/5.63 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.44/5.63 = ( ( ( ord_less_nat @ A @ B )
% 5.44/5.63 => ( P @ zero_zero_nat ) )
% 5.44/5.63 & ! [D2: nat] :
% 5.44/5.63 ( ( A
% 5.44/5.63 = ( plus_plus_nat @ B @ D2 ) )
% 5.44/5.63 => ( P @ D2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_diff_split
% 5.44/5.63 thf(fact_2399_div__greater__zero__iff,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.44/5.63 = ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_greater_zero_iff
% 5.44/5.63 thf(fact_2400_div__le__mono2,axiom,
% 5.44/5.63 ! [M: nat,N2: nat,K: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.63 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.63 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_le_mono2
% 5.44/5.63 thf(fact_2401_nat__mult__div__cancel1,axiom,
% 5.44/5.63 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.63 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.63 = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_mult_div_cancel1
% 5.44/5.63 thf(fact_2402_div__less__iff__less__mult,axiom,
% 5.44/5.63 ! [Q2: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.44/5.63 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N2 )
% 5.44/5.63 = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_less_iff_less_mult
% 5.44/5.63 thf(fact_2403_div__eq__dividend__iff,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.63 => ( ( ( divide_divide_nat @ M @ N2 )
% 5.44/5.63 = M )
% 5.44/5.63 = ( N2 = one_one_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_eq_dividend_iff
% 5.44/5.63 thf(fact_2404_div__less__dividend,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.63 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_less_dividend
% 5.44/5.63 thf(fact_2405_vebt__insert_Osimps_I3_J,axiom,
% 5.44/5.63 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X: nat] :
% 5.44/5.63 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X )
% 5.44/5.63 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_insert.simps(3)
% 5.44/5.63 thf(fact_2406_vebt__mint_Ocases,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT] :
% 5.44/5.63 ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_mint.cases
% 5.44/5.63 thf(fact_2407_vebt__delete_Osimps_I6_J,axiom,
% 5.44/5.63 ! [Mi: nat,Ma: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X: nat] :
% 5.44/5.63 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X )
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_delete.simps(6)
% 5.44/5.63 thf(fact_2408_vebt__mint_Oelims,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.44/5.63 ( ( ( vEBT_vebt_mint @ X )
% 5.44/5.63 = Y )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ~ ( ( A3
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.63 & ( ~ A3
% 5.44/5.63 => ( ( B3
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.63 & ( ~ B3
% 5.44/5.63 => ( Y = none_nat ) ) ) ) ) )
% 5.44/5.63 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.63 => ( Y != none_nat ) )
% 5.44/5.63 => ~ ! [Mi2: nat] :
% 5.44/5.63 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_mint.elims
% 5.44/5.63 thf(fact_2409_vebt__maxt_Oelims,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.44/5.63 ( ( ( vEBT_vebt_maxt @ X )
% 5.44/5.63 = Y )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ~ ( ( B3
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.63 & ( ~ B3
% 5.44/5.63 => ( ( A3
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.63 & ( ~ A3
% 5.44/5.63 => ( Y = none_nat ) ) ) ) ) )
% 5.44/5.63 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.63 => ( Y != none_nat ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.44/5.63 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_maxt.elims
% 5.44/5.63 thf(fact_2410_mult__less__cancel__right2,axiom,
% 5.44/5.63 ! [A: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ A @ one_one_real ) )
% 5.44/5.63 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_right2
% 5.44/5.63 thf(fact_2411_mult__less__cancel__right2,axiom,
% 5.44/5.63 ! [A: int,C: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.44/5.63 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ A @ one_one_int ) )
% 5.44/5.63 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_right2
% 5.44/5.63 thf(fact_2412_mult__less__cancel__right1,axiom,
% 5.44/5.63 ! [C: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ one_one_real @ B ) )
% 5.44/5.63 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_right1
% 5.44/5.63 thf(fact_2413_mult__less__cancel__right1,axiom,
% 5.44/5.63 ! [C: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ one_one_int @ B ) )
% 5.44/5.63 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_right1
% 5.44/5.63 thf(fact_2414_mult__less__cancel__left2,axiom,
% 5.44/5.63 ! [C: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ A @ one_one_real ) )
% 5.44/5.63 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left2
% 5.44/5.63 thf(fact_2415_mult__less__cancel__left2,axiom,
% 5.44/5.63 ! [C: int,A: int] :
% 5.44/5.63 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.44/5.63 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ A @ one_one_int ) )
% 5.44/5.63 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left2
% 5.44/5.63 thf(fact_2416_mult__less__cancel__left1,axiom,
% 5.44/5.63 ! [C: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ one_one_real @ B ) )
% 5.44/5.63 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left1
% 5.44/5.63 thf(fact_2417_mult__less__cancel__left1,axiom,
% 5.44/5.63 ! [C: int,B: int] :
% 5.44/5.63 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_int @ one_one_int @ B ) )
% 5.44/5.63 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_less_cancel_left1
% 5.44/5.63 thf(fact_2418_mult__le__cancel__right2,axiom,
% 5.44/5.63 ! [A: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.44/5.63 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_right2
% 5.44/5.63 thf(fact_2419_mult__le__cancel__right2,axiom,
% 5.44/5.63 ! [A: int,C: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.44/5.63 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_right2
% 5.44/5.63 thf(fact_2420_mult__le__cancel__right1,axiom,
% 5.44/5.63 ! [C: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.44/5.63 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_right1
% 5.44/5.63 thf(fact_2421_mult__le__cancel__right1,axiom,
% 5.44/5.63 ! [C: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.44/5.63 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_right1
% 5.44/5.63 thf(fact_2422_mult__le__cancel__left2,axiom,
% 5.44/5.63 ! [C: real,A: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.44/5.63 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left2
% 5.44/5.63 thf(fact_2423_mult__le__cancel__left2,axiom,
% 5.44/5.63 ! [C: int,A: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.44/5.63 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left2
% 5.44/5.63 thf(fact_2424_mult__le__cancel__left1,axiom,
% 5.44/5.63 ! [C: real,B: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.44/5.63 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left1
% 5.44/5.63 thf(fact_2425_mult__le__cancel__left1,axiom,
% 5.44/5.63 ! [C: int,B: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.44/5.63 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.44/5.63 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.44/5.63 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.44/5.63 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_le_cancel_left1
% 5.44/5.63 thf(fact_2426_field__le__mult__one__interval,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ! [Z4: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ Z4 )
% 5.44/5.63 => ( ( ord_less_real @ Z4 @ one_one_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ Z4 @ X ) @ Y ) ) )
% 5.44/5.63 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.63
% 5.44/5.63 % field_le_mult_one_interval
% 5.44/5.63 thf(fact_2427_divide__left__mono__neg,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.63 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_left_mono_neg
% 5.44/5.63 thf(fact_2428_mult__imp__le__div__pos,axiom,
% 5.44/5.63 ! [Y: real,Z: real,X: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X )
% 5.44/5.63 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_imp_le_div_pos
% 5.44/5.63 thf(fact_2429_mult__imp__div__pos__le,axiom,
% 5.44/5.63 ! [Y: real,X: real,Z: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y ) )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_imp_div_pos_le
% 5.44/5.63 thf(fact_2430_pos__le__divide__eq,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos_le_divide_eq
% 5.44/5.63 thf(fact_2431_pos__divide__le__eq,axiom,
% 5.44/5.63 ! [C: real,B: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.44/5.63 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos_divide_le_eq
% 5.44/5.63 thf(fact_2432_neg__le__divide__eq,axiom,
% 5.44/5.63 ! [C: real,A: real,B: real] :
% 5.44/5.63 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % neg_le_divide_eq
% 5.44/5.63 thf(fact_2433_neg__divide__le__eq,axiom,
% 5.44/5.63 ! [C: real,B: real,A: real] :
% 5.44/5.63 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.44/5.63 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % neg_divide_le_eq
% 5.44/5.63 thf(fact_2434_divide__left__mono,axiom,
% 5.44/5.63 ! [B: real,A: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.63 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_left_mono
% 5.44/5.63 thf(fact_2435_le__divide__eq,axiom,
% 5.44/5.63 ! [A: real,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_divide_eq
% 5.44/5.63 thf(fact_2436_divide__le__eq,axiom,
% 5.44/5.63 ! [B: real,C: real,A: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_le_eq
% 5.44/5.63 thf(fact_2437_le__divide__eq__1,axiom,
% 5.44/5.63 ! [B: real,A: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_eq_real @ A @ B ) )
% 5.44/5.63 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_divide_eq_1
% 5.44/5.63 thf(fact_2438_divide__le__eq__1,axiom,
% 5.44/5.63 ! [B: real,A: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 & ( ord_less_eq_real @ B @ A ) )
% 5.44/5.63 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 & ( ord_less_eq_real @ A @ B ) )
% 5.44/5.63 | ( A = zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_le_eq_1
% 5.44/5.63 thf(fact_2439_convex__bound__le,axiom,
% 5.44/5.63 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ X @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ Y @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.44/5.63 => ( ( ( plus_plus_real @ U @ V )
% 5.44/5.63 = one_one_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % convex_bound_le
% 5.44/5.63 thf(fact_2440_convex__bound__le,axiom,
% 5.44/5.63 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ X @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ Y @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.44/5.63 => ( ( ( plus_plus_int @ U @ V )
% 5.44/5.63 = one_one_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % convex_bound_le
% 5.44/5.63 thf(fact_2441_less__divide__eq__numeral_I1_J,axiom,
% 5.44/5.63 ! [W: num,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_divide_eq_numeral(1)
% 5.44/5.63 thf(fact_2442_divide__less__eq__numeral_I1_J,axiom,
% 5.44/5.63 ! [B: real,C: real,W: num] :
% 5.44/5.63 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_less_eq_numeral(1)
% 5.44/5.63 thf(fact_2443_frac__le__eq,axiom,
% 5.44/5.63 ! [Y: real,Z: real,X: real,W: real] :
% 5.44/5.63 ( ( Y != zero_zero_real )
% 5.44/5.63 => ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.44/5.63 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % frac_le_eq
% 5.44/5.63 thf(fact_2444_power__Suc__less,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ A @ one_one_real )
% 5.44/5.63 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_less
% 5.44/5.63 thf(fact_2445_power__Suc__less,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.44/5.63 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_less
% 5.44/5.63 thf(fact_2446_power__Suc__less,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ A @ one_one_int )
% 5.44/5.63 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_less
% 5.44/5.63 thf(fact_2447_frac__less__eq,axiom,
% 5.44/5.63 ! [Y: real,Z: real,X: real,W: real] :
% 5.44/5.63 ( ( Y != zero_zero_real )
% 5.44/5.63 => ( ( Z != zero_zero_real )
% 5.44/5.63 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.44/5.63 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % frac_less_eq
% 5.44/5.63 thf(fact_2448_power__Suc__le__self,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_le_self
% 5.44/5.63 thf(fact_2449_power__Suc__le__self,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.44/5.63 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_le_self
% 5.44/5.63 thf(fact_2450_power__Suc__le__self,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_le_self
% 5.44/5.63 thf(fact_2451_power__Suc__less__one,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ A @ one_one_real )
% 5.44/5.63 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_less_one
% 5.44/5.63 thf(fact_2452_power__Suc__less__one,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.44/5.63 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_less_one
% 5.44/5.63 thf(fact_2453_power__Suc__less__one,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ A @ one_one_int )
% 5.44/5.63 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_Suc_less_one
% 5.44/5.63 thf(fact_2454_power__strict__decreasing,axiom,
% 5.44/5.63 ! [N2: nat,N3: nat,A: real] :
% 5.44/5.63 ( ( ord_less_nat @ N2 @ N3 )
% 5.44/5.63 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_real @ A @ one_one_real )
% 5.44/5.63 => ( ord_less_real @ ( power_power_real @ A @ N3 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_decreasing
% 5.44/5.63 thf(fact_2455_power__strict__decreasing,axiom,
% 5.44/5.63 ! [N2: nat,N3: nat,A: nat] :
% 5.44/5.63 ( ( ord_less_nat @ N2 @ N3 )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.44/5.63 => ( ord_less_nat @ ( power_power_nat @ A @ N3 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_decreasing
% 5.44/5.63 thf(fact_2456_power__strict__decreasing,axiom,
% 5.44/5.63 ! [N2: nat,N3: nat,A: int] :
% 5.44/5.63 ( ( ord_less_nat @ N2 @ N3 )
% 5.44/5.63 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_int @ A @ one_one_int )
% 5.44/5.63 => ( ord_less_int @ ( power_power_int @ A @ N3 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_strict_decreasing
% 5.44/5.63 thf(fact_2457_zero__power2,axiom,
% 5.44/5.63 ( ( power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power2
% 5.44/5.63 thf(fact_2458_zero__power2,axiom,
% 5.44/5.63 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_nat ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power2
% 5.44/5.63 thf(fact_2459_zero__power2,axiom,
% 5.44/5.63 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power2
% 5.44/5.63 thf(fact_2460_zero__power2,axiom,
% 5.44/5.63 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power2
% 5.44/5.63 thf(fact_2461_zero__power2,axiom,
% 5.44/5.63 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = zero_zero_complex ) ).
% 5.44/5.63
% 5.44/5.63 % zero_power2
% 5.44/5.63 thf(fact_2462_power__decreasing,axiom,
% 5.44/5.63 ! [N2: nat,N3: nat,A: real] :
% 5.44/5.63 ( ( ord_less_eq_nat @ N2 @ N3 )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( power_power_real @ A @ N3 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_decreasing
% 5.44/5.63 thf(fact_2463_power__decreasing,axiom,
% 5.44/5.63 ! [N2: nat,N3: nat,A: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ N2 @ N3 )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.63 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.44/5.63 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N3 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_decreasing
% 5.44/5.63 thf(fact_2464_power__decreasing,axiom,
% 5.44/5.63 ! [N2: nat,N3: nat,A: int] :
% 5.44/5.63 ( ( ord_less_eq_nat @ N2 @ N3 )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.44/5.63 => ( ord_less_eq_int @ ( power_power_int @ A @ N3 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_decreasing
% 5.44/5.63 thf(fact_2465_self__le__power,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % self_le_power
% 5.44/5.63 thf(fact_2466_self__le__power,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % self_le_power
% 5.44/5.63 thf(fact_2467_self__le__power,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % self_le_power
% 5.44/5.63 thf(fact_2468_one__less__power,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % one_less_power
% 5.44/5.63 thf(fact_2469_one__less__power,axiom,
% 5.44/5.63 ! [A: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ one_one_nat @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % one_less_power
% 5.44/5.63 thf(fact_2470_one__less__power,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_int @ one_one_int @ A )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % one_less_power
% 5.44/5.63 thf(fact_2471_numeral__2__eq__2,axiom,
% 5.44/5.63 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.44/5.63 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % numeral_2_eq_2
% 5.44/5.63 thf(fact_2472_pos2,axiom,
% 5.44/5.63 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.44/5.63
% 5.44/5.63 % pos2
% 5.44/5.63 thf(fact_2473_power__diff,axiom,
% 5.44/5.63 ! [A: nat,N2: nat,M: nat] :
% 5.44/5.63 ( ( A != zero_zero_nat )
% 5.44/5.63 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.63 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_diff
% 5.44/5.63 thf(fact_2474_power__diff,axiom,
% 5.44/5.63 ! [A: real,N2: nat,M: nat] :
% 5.44/5.63 ( ( A != zero_zero_real )
% 5.44/5.63 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.63 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_diff
% 5.44/5.63 thf(fact_2475_power__diff,axiom,
% 5.44/5.63 ! [A: int,N2: nat,M: nat] :
% 5.44/5.63 ( ( A != zero_zero_int )
% 5.44/5.63 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.63 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_diff
% 5.44/5.63 thf(fact_2476_power__diff,axiom,
% 5.44/5.63 ! [A: complex,N2: nat,M: nat] :
% 5.44/5.63 ( ( A != zero_zero_complex )
% 5.44/5.63 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.63 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_diff
% 5.44/5.63 thf(fact_2477_power__diff,axiom,
% 5.44/5.63 ! [A: code_integer,N2: nat,M: nat] :
% 5.44/5.63 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.63 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.63 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_diff
% 5.44/5.63 thf(fact_2478_div__if,axiom,
% 5.44/5.63 ( divide_divide_nat
% 5.44/5.63 = ( ^ [M6: nat,N: nat] :
% 5.44/5.63 ( if_nat
% 5.44/5.63 @ ( ( ord_less_nat @ M6 @ N )
% 5.44/5.63 | ( N = zero_zero_nat ) )
% 5.44/5.63 @ zero_zero_nat
% 5.44/5.63 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_if
% 5.44/5.63 thf(fact_2479_div__geq,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.44/5.63 => ( ( divide_divide_nat @ M @ N2 )
% 5.44/5.63 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_geq
% 5.44/5.63 thf(fact_2480_Suc__diff__eq__diff__pred,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.44/5.63 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % Suc_diff_eq_diff_pred
% 5.44/5.63 thf(fact_2481_Suc__pred_H,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( N2
% 5.44/5.63 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % Suc_pred'
% 5.44/5.63 thf(fact_2482_less__eq__div__iff__mult__less__eq,axiom,
% 5.44/5.63 ! [Q2: nat,M: nat,N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.44/5.63 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q2 ) )
% 5.44/5.63 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_eq_div_iff_mult_less_eq
% 5.44/5.63 thf(fact_2483_dividend__less__times__div,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % dividend_less_times_div
% 5.44/5.63 thf(fact_2484_dividend__less__div__times,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % dividend_less_div_times
% 5.44/5.63 thf(fact_2485_split__div,axiom,
% 5.44/5.63 ! [P: nat > $o,M: nat,N2: nat] :
% 5.44/5.63 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.44/5.63 = ( ( ( N2 = zero_zero_nat )
% 5.44/5.63 => ( P @ zero_zero_nat ) )
% 5.44/5.63 & ( ( N2 != zero_zero_nat )
% 5.44/5.63 => ! [I5: nat,J3: nat] :
% 5.44/5.63 ( ( ord_less_nat @ J3 @ N2 )
% 5.44/5.63 => ( ( M
% 5.44/5.63 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 5.44/5.63 => ( P @ I5 ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % split_div
% 5.44/5.63 thf(fact_2486_add__eq__if,axiom,
% 5.44/5.63 ( plus_plus_nat
% 5.44/5.63 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % add_eq_if
% 5.44/5.63 thf(fact_2487_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.44/5.63 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.44/5.63 = Y )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.63 => A3 )
% 5.44/5.63 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.63 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.63 => B3 )
% 5.44/5.63 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.44/5.63 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.44/5.63 => Y )
% 5.44/5.63 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [S2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.naive_member.elims(1)
% 5.44/5.63 thf(fact_2488_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.63 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.63 => A3 )
% 5.44/5.63 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.63 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.63 => B3 )
% 5.44/5.63 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.44/5.63 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [S2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.44/5.63 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.naive_member.elims(2)
% 5.44/5.63 thf(fact_2489_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.63 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.63 => A3 )
% 5.44/5.63 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.63 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.63 => B3 )
% 5.44/5.63 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.44/5.63 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.44/5.63 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [S2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.44/5.63 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.naive_member.elims(3)
% 5.44/5.63 thf(fact_2490_mult__eq__if,axiom,
% 5.44/5.63 ( times_times_nat
% 5.44/5.63 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % mult_eq_if
% 5.44/5.63 thf(fact_2491_vebt__succ_Osimps_I4_J,axiom,
% 5.44/5.63 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve2: nat] :
% 5.44/5.63 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve2 )
% 5.44/5.63 = none_nat ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_succ.simps(4)
% 5.44/5.63 thf(fact_2492_vebt__pred_Osimps_I5_J,axiom,
% 5.44/5.63 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.44/5.63 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve2 ) @ Vf2 )
% 5.44/5.63 = none_nat ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_pred.simps(5)
% 5.44/5.63 thf(fact_2493_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.44/5.63 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.44/5.63 = Y )
% 5.44/5.63 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.63 => Y )
% 5.44/5.63 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.44/5.63 => Y )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat] :
% 5.44/5.63 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( ~ ( ( Xa2 = Mi2 )
% 5.44/5.63 | ( Xa2 = Ma2 ) ) ) ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Vc2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( ~ ( ( Xa2 = Mi2 )
% 5.44/5.63 | ( Xa2 = Ma2 )
% 5.44/5.63 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.44/5.63 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Vd2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.membermima.elims(1)
% 5.44/5.63 thf(fact_2494_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.63 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.44/5.63 => ( ! [Uu2: $o,Uv2: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.63 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat] :
% 5.44/5.63 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.44/5.63 => ( ( Xa2 = Mi2 )
% 5.44/5.63 | ( Xa2 = Ma2 ) ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Vc2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.44/5.63 => ( ( Xa2 = Mi2 )
% 5.44/5.63 | ( Xa2 = Ma2 )
% 5.44/5.63 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.44/5.63 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Vd2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.44/5.63 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.membermima.elims(3)
% 5.44/5.63 thf(fact_2495_le__divide__eq__numeral_I1_J,axiom,
% 5.44/5.63 ! [W: num,B: real,C: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_divide_eq_numeral(1)
% 5.44/5.63 thf(fact_2496_divide__le__eq__numeral_I1_J,axiom,
% 5.44/5.63 ! [B: real,C: real,W: num] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.44/5.63 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.63 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.44/5.63 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % divide_le_eq_numeral(1)
% 5.44/5.63 thf(fact_2497_convex__bound__lt,axiom,
% 5.44/5.63 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.44/5.63 ( ( ord_less_real @ X @ A )
% 5.44/5.63 => ( ( ord_less_real @ Y @ A )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.44/5.63 => ( ( ( plus_plus_real @ U @ V )
% 5.44/5.63 = one_one_real )
% 5.44/5.63 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % convex_bound_lt
% 5.44/5.63 thf(fact_2498_convex__bound__lt,axiom,
% 5.44/5.63 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.44/5.63 ( ( ord_less_int @ X @ A )
% 5.44/5.63 => ( ( ord_less_int @ Y @ A )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.44/5.63 => ( ( ( plus_plus_int @ U @ V )
% 5.44/5.63 = one_one_int )
% 5.44/5.63 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % convex_bound_lt
% 5.44/5.63 thf(fact_2499_half__gt__zero__iff,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.63 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.44/5.63
% 5.44/5.63 % half_gt_zero_iff
% 5.44/5.63 thf(fact_2500_half__gt__zero,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.63 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % half_gt_zero
% 5.44/5.63 thf(fact_2501_scaling__mono,axiom,
% 5.44/5.63 ! [U: real,V: real,R: real,S3: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ U @ V )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.44/5.63 => ( ( ord_less_eq_real @ R @ S3 )
% 5.44/5.63 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S3 ) ) @ V ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % scaling_mono
% 5.44/5.63 thf(fact_2502_power2__le__imp__le,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_le_imp_le
% 5.44/5.63 thf(fact_2503_power2__le__imp__le,axiom,
% 5.44/5.63 ! [X: nat,Y: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.44/5.63 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_le_imp_le
% 5.44/5.63 thf(fact_2504_power2__le__imp__le,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.63 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_le_imp_le
% 5.44/5.63 thf(fact_2505_power2__eq__imp__eq,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( X = Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_eq_imp_eq
% 5.44/5.63 thf(fact_2506_power2__eq__imp__eq,axiom,
% 5.44/5.63 ! [X: nat,Y: nat] :
% 5.44/5.63 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.44/5.63 => ( X = Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_eq_imp_eq
% 5.44/5.63 thf(fact_2507_power2__eq__imp__eq,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.63 => ( X = Y ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_eq_imp_eq
% 5.44/5.63 thf(fact_2508_zero__le__power2,axiom,
% 5.44/5.63 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_power2
% 5.44/5.63 thf(fact_2509_zero__le__power2,axiom,
% 5.44/5.63 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_power2
% 5.44/5.63 thf(fact_2510_power2__less__0,axiom,
% 5.44/5.63 ! [A: real] :
% 5.44/5.63 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % power2_less_0
% 5.44/5.63 thf(fact_2511_power2__less__0,axiom,
% 5.44/5.63 ! [A: int] :
% 5.44/5.63 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % power2_less_0
% 5.44/5.63 thf(fact_2512_exp__add__not__zero__imp__right,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.63 != zero_zero_nat )
% 5.44/5.63 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.63 != zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % exp_add_not_zero_imp_right
% 5.44/5.63 thf(fact_2513_exp__add__not__zero__imp__right,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.63 != zero_zero_int )
% 5.44/5.63 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.63 != zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % exp_add_not_zero_imp_right
% 5.44/5.63 thf(fact_2514_exp__add__not__zero__imp__left,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.63 != zero_zero_nat )
% 5.44/5.63 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.44/5.63 != zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % exp_add_not_zero_imp_left
% 5.44/5.63 thf(fact_2515_exp__add__not__zero__imp__left,axiom,
% 5.44/5.63 ! [M: nat,N2: nat] :
% 5.44/5.63 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.63 != zero_zero_int )
% 5.44/5.63 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.44/5.63 != zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % exp_add_not_zero_imp_left
% 5.44/5.63 thf(fact_2516_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.63 != zero_zero_nat )
% 5.44/5.63 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.44/5.63 != zero_zero_nat ) ) ).
% 5.44/5.63
% 5.44/5.63 % exp_not_zero_imp_exp_diff_not_zero
% 5.44/5.63 thf(fact_2517_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.63 != zero_zero_int )
% 5.44/5.63 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.44/5.63 != zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % exp_not_zero_imp_exp_diff_not_zero
% 5.44/5.63 thf(fact_2518_power__diff__power__eq,axiom,
% 5.44/5.63 ! [A: nat,N2: nat,M: nat] :
% 5.44/5.63 ( ( A != zero_zero_nat )
% 5.44/5.63 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.44/5.63 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.44/5.63 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.44/5.63 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_diff_power_eq
% 5.44/5.63 thf(fact_2519_power__diff__power__eq,axiom,
% 5.44/5.63 ! [A: int,N2: nat,M: nat] :
% 5.44/5.63 ( ( A != zero_zero_int )
% 5.44/5.63 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.44/5.63 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.44/5.63 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.44/5.63 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_diff_power_eq
% 5.44/5.63 thf(fact_2520_power__diff__power__eq,axiom,
% 5.44/5.63 ! [A: code_integer,N2: nat,M: nat] :
% 5.44/5.63 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.63 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.44/5.63 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.44/5.63 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.44/5.63 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_diff_power_eq
% 5.44/5.63 thf(fact_2521_less__2__cases__iff,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = ( ( N2 = zero_zero_nat )
% 5.44/5.63 | ( N2
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_2_cases_iff
% 5.44/5.63 thf(fact_2522_less__2__cases,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 => ( ( N2 = zero_zero_nat )
% 5.44/5.63 | ( N2
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % less_2_cases
% 5.44/5.63 thf(fact_2523_nat__induct2,axiom,
% 5.44/5.63 ! [P: nat > $o,N2: nat] :
% 5.44/5.63 ( ( P @ zero_zero_nat )
% 5.44/5.63 => ( ( P @ one_one_nat )
% 5.44/5.63 => ( ! [N4: nat] :
% 5.44/5.63 ( ( P @ N4 )
% 5.44/5.63 => ( P @ ( plus_plus_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.63 => ( P @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_induct2
% 5.44/5.63 thf(fact_2524_power__eq__if,axiom,
% 5.44/5.63 ( power_8040749407984259932d_enat
% 5.44/5.63 = ( ^ [P4: extended_enat,M6: nat] : ( if_Extended_enat @ ( M6 = zero_zero_nat ) @ one_on7984719198319812577d_enat @ ( times_7803423173614009249d_enat @ P4 @ ( power_8040749407984259932d_enat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_if
% 5.44/5.63 thf(fact_2525_power__eq__if,axiom,
% 5.44/5.63 ( power_power_complex
% 5.44/5.63 = ( ^ [P4: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P4 @ ( power_power_complex @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_if
% 5.44/5.63 thf(fact_2526_power__eq__if,axiom,
% 5.44/5.63 ( power_power_real
% 5.44/5.63 = ( ^ [P4: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P4 @ ( power_power_real @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_if
% 5.44/5.63 thf(fact_2527_power__eq__if,axiom,
% 5.44/5.63 ( power_power_nat
% 5.44/5.63 = ( ^ [P4: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P4 @ ( power_power_nat @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_if
% 5.44/5.63 thf(fact_2528_power__eq__if,axiom,
% 5.44/5.63 ( power_power_int
% 5.44/5.63 = ( ^ [P4: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P4 @ ( power_power_int @ P4 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_eq_if
% 5.44/5.63 thf(fact_2529_power__minus__mult,axiom,
% 5.44/5.63 ! [N2: nat,A: complex] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.44/5.63 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_minus_mult
% 5.44/5.63 thf(fact_2530_power__minus__mult,axiom,
% 5.44/5.63 ! [N2: nat,A: real] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.44/5.63 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_minus_mult
% 5.44/5.63 thf(fact_2531_power__minus__mult,axiom,
% 5.44/5.63 ! [N2: nat,A: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.44/5.63 = ( power_power_nat @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_minus_mult
% 5.44/5.63 thf(fact_2532_power__minus__mult,axiom,
% 5.44/5.63 ! [N2: nat,A: int] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.44/5.63 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power_minus_mult
% 5.44/5.63 thf(fact_2533_split__div_H,axiom,
% 5.44/5.63 ! [P: nat > $o,M: nat,N2: nat] :
% 5.44/5.63 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.44/5.63 = ( ( ( N2 = zero_zero_nat )
% 5.44/5.63 & ( P @ zero_zero_nat ) )
% 5.44/5.63 | ? [Q4: nat] :
% 5.44/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q4 ) @ M )
% 5.44/5.63 & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q4 ) ) )
% 5.44/5.63 & ( P @ Q4 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % split_div'
% 5.44/5.63 thf(fact_2534_le__div__geq,axiom,
% 5.44/5.63 ! [N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.63 => ( ( divide_divide_nat @ M @ N2 )
% 5.44/5.63 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % le_div_geq
% 5.44/5.63 thf(fact_2535_vebt__pred_Osimps_I6_J,axiom,
% 5.44/5.63 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.44/5.63 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.44/5.63 = none_nat ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_pred.simps(6)
% 5.44/5.63 thf(fact_2536_vebt__succ_Osimps_I5_J,axiom,
% 5.44/5.63 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.44/5.63 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.44/5.63 = none_nat ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_succ.simps(5)
% 5.44/5.63 thf(fact_2537_power2__less__imp__less,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_real @ X @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_less_imp_less
% 5.44/5.63 thf(fact_2538_power2__less__imp__less,axiom,
% 5.44/5.63 ! [X: nat,Y: nat] :
% 5.44/5.63 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.44/5.63 => ( ord_less_nat @ X @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_less_imp_less
% 5.44/5.63 thf(fact_2539_power2__less__imp__less,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.63 => ( ord_less_int @ X @ Y ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % power2_less_imp_less
% 5.44/5.63 thf(fact_2540_sum__power2__le__zero__iff,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.44/5.63 = ( ( X = zero_zero_real )
% 5.44/5.63 & ( Y = zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_power2_le_zero_iff
% 5.44/5.63 thf(fact_2541_sum__power2__le__zero__iff,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.44/5.63 = ( ( X = zero_zero_int )
% 5.44/5.63 & ( Y = zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_power2_le_zero_iff
% 5.44/5.63 thf(fact_2542_sum__power2__ge__zero,axiom,
% 5.44/5.63 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_power2_ge_zero
% 5.44/5.63 thf(fact_2543_sum__power2__ge__zero,axiom,
% 5.44/5.63 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_power2_ge_zero
% 5.44/5.63 thf(fact_2544_sum__power2__gt__zero__iff,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.63 = ( ( X != zero_zero_real )
% 5.44/5.63 | ( Y != zero_zero_real ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_power2_gt_zero_iff
% 5.44/5.63 thf(fact_2545_sum__power2__gt__zero__iff,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.63 = ( ( X != zero_zero_int )
% 5.44/5.63 | ( Y != zero_zero_int ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % sum_power2_gt_zero_iff
% 5.44/5.63 thf(fact_2546_not__sum__power2__lt__zero,axiom,
% 5.44/5.63 ! [X: real,Y: real] :
% 5.44/5.63 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.44/5.63
% 5.44/5.63 % not_sum_power2_lt_zero
% 5.44/5.63 thf(fact_2547_not__sum__power2__lt__zero,axiom,
% 5.44/5.63 ! [X: int,Y: int] :
% 5.44/5.63 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.44/5.63
% 5.44/5.63 % not_sum_power2_lt_zero
% 5.44/5.63 thf(fact_2548_zero__le__even__power_H,axiom,
% 5.44/5.63 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_even_power'
% 5.44/5.63 thf(fact_2549_zero__le__even__power_H,axiom,
% 5.44/5.63 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % zero_le_even_power'
% 5.44/5.63 thf(fact_2550_nat__bit__induct,axiom,
% 5.44/5.63 ! [P: nat > $o,N2: nat] :
% 5.44/5.63 ( ( P @ zero_zero_nat )
% 5.44/5.63 => ( ! [N4: nat] :
% 5.44/5.63 ( ( P @ N4 )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.44/5.63 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.44/5.63 => ( ! [N4: nat] :
% 5.44/5.63 ( ( P @ N4 )
% 5.44/5.63 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.44/5.63 => ( P @ N2 ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % nat_bit_induct
% 5.44/5.63 thf(fact_2551_Suc__n__div__2__gt__zero,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % Suc_n_div_2_gt_zero
% 5.44/5.63 thf(fact_2552_div__2__gt__zero,axiom,
% 5.44/5.63 ! [N2: nat] :
% 5.44/5.63 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.63 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % div_2_gt_zero
% 5.44/5.63 thf(fact_2553_vebt__member_Oelims_I2_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.63 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.63 => A3 )
% 5.44/5.63 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.63 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.63 => B3 )
% 5.44/5.63 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Summary2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ~ ( ( Xa2 != Mi2 )
% 5.44/5.63 => ( ( Xa2 != Ma2 )
% 5.44/5.63 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.63 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.63 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.63 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.63 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_member.elims(2)
% 5.44/5.63 thf(fact_2554_vebt__member_Oelims_I1_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.44/5.63 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.44/5.63 = Y )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.63 => A3 )
% 5.44/5.63 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.63 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.63 => B3 )
% 5.44/5.63 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.44/5.63 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.63 => Y )
% 5.44/5.63 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.44/5.63 => Y )
% 5.44/5.63 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.44/5.63 => Y )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Summary2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( ~ ( ( Xa2 != Mi2 )
% 5.44/5.63 => ( ( Xa2 != Ma2 )
% 5.44/5.63 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.63 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.63 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.63 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.63 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_member.elims(1)
% 5.44/5.63 thf(fact_2555_vebt__member_Oelims_I3_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.63 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.63 => A3 )
% 5.44/5.63 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.63 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.63 => B3 )
% 5.44/5.63 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.44/5.63 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.63 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.44/5.63 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Summary2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( ( Xa2 != Mi2 )
% 5.44/5.63 => ( ( Xa2 != Ma2 )
% 5.44/5.63 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.63 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.63 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.63 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.63 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_member.elims(3)
% 5.44/5.63 thf(fact_2556_odd__0__le__power__imp__0__le,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.63 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.44/5.63
% 5.44/5.63 % odd_0_le_power_imp_0_le
% 5.44/5.63 thf(fact_2557_odd__0__le__power__imp__0__le,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.63 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.44/5.63
% 5.44/5.63 % odd_0_le_power_imp_0_le
% 5.44/5.63 thf(fact_2558_odd__power__less__zero,axiom,
% 5.44/5.63 ! [A: real,N2: nat] :
% 5.44/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.63 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 5.44/5.63
% 5.44/5.63 % odd_power_less_zero
% 5.44/5.63 thf(fact_2559_odd__power__less__zero,axiom,
% 5.44/5.63 ! [A: int,N2: nat] :
% 5.44/5.63 ( ( ord_less_int @ A @ zero_zero_int )
% 5.44/5.63 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 5.44/5.63
% 5.44/5.63 % odd_power_less_zero
% 5.44/5.63 thf(fact_2560_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.44/5.63 ! [X: nat,N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.63 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.exp_split_high_low(1)
% 5.44/5.63 thf(fact_2561_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.44/5.63 ! [X: nat,N2: nat,M: nat] :
% 5.44/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.63 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.63 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.exp_split_high_low(2)
% 5.44/5.63 thf(fact_2562_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.63 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat] :
% 5.44/5.63 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.44/5.63 => ~ ( ( Xa2 = Mi2 )
% 5.44/5.63 | ( Xa2 = Ma2 ) ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Vc2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.44/5.63 => ~ ( ( Xa2 = Mi2 )
% 5.44/5.63 | ( Xa2 = Ma2 )
% 5.44/5.63 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.44/5.63 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.44/5.63 ( ? [Vd2: vEBT_VEBT] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.44/5.63 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % VEBT_internal.membermima.elims(2)
% 5.44/5.63 thf(fact_2563_arith__geo__mean,axiom,
% 5.44/5.63 ! [U: real,X: real,Y: real] :
% 5.44/5.63 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.63 = ( times_times_real @ X @ Y ) )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.63 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % arith_geo_mean
% 5.44/5.63 thf(fact_2564_invar__vebt_Osimps,axiom,
% 5.44/5.63 ( vEBT_invar_vebt
% 5.44/5.63 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 5.44/5.63 ( ( ? [A4: $o,B4: $o] :
% 5.44/5.63 ( A1
% 5.44/5.63 = ( vEBT_Leaf @ A4 @ B4 ) )
% 5.44/5.63 & ( A22
% 5.44/5.63 = ( suc @ zero_zero_nat ) ) )
% 5.44/5.63 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 5.44/5.63 ( ( A1
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 5.44/5.63 & ! [X2: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.44/5.63 => ( vEBT_invar_vebt @ X2 @ N ) )
% 5.44/5.63 & ( vEBT_invar_vebt @ Summary3 @ N )
% 5.44/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.44/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.44/5.63 & ( A22
% 5.44/5.63 = ( plus_plus_nat @ N @ N ) )
% 5.44/5.63 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 5.44/5.63 & ! [X2: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.44/5.63 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.63 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 5.44/5.63 ( ( A1
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 5.44/5.63 & ! [X2: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.44/5.63 => ( vEBT_invar_vebt @ X2 @ N ) )
% 5.44/5.63 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 5.44/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.44/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.44/5.63 & ( A22
% 5.44/5.63 = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 5.44/5.63 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 5.44/5.63 & ! [X2: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.44/5.63 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.63 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.44/5.63 ( ( A1
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 5.44/5.63 & ! [X2: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.44/5.63 => ( vEBT_invar_vebt @ X2 @ N ) )
% 5.44/5.63 & ( vEBT_invar_vebt @ Summary3 @ N )
% 5.44/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.44/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.44/5.63 & ( A22
% 5.44/5.63 = ( plus_plus_nat @ N @ N ) )
% 5.44/5.63 & ! [I5: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.44/5.63 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X4 ) )
% 5.44/5.63 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 5.44/5.63 & ( ( Mi3 = Ma3 )
% 5.44/5.63 => ! [X2: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.44/5.63 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.63 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.63 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.44/5.63 & ( ( Mi3 != Ma3 )
% 5.44/5.63 => ! [I5: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.44/5.63 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 5.44/5.63 = I5 )
% 5.44/5.63 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 5.44/5.63 & ! [X2: nat] :
% 5.44/5.63 ( ( ( ( vEBT_VEBT_high @ X2 @ N )
% 5.44/5.63 = I5 )
% 5.44/5.63 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N ) ) )
% 5.44/5.63 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.63 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 5.44/5.63 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.44/5.63 ( ( A1
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 5.44/5.63 & ! [X2: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.44/5.63 => ( vEBT_invar_vebt @ X2 @ N ) )
% 5.44/5.63 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 5.44/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.44/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.44/5.63 & ( A22
% 5.44/5.63 = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 5.44/5.63 & ! [I5: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.44/5.63 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X4 ) )
% 5.44/5.63 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 5.44/5.63 & ( ( Mi3 = Ma3 )
% 5.44/5.63 => ! [X2: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.44/5.63 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.63 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.63 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.44/5.63 & ( ( Mi3 != Ma3 )
% 5.44/5.63 => ! [I5: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.44/5.63 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 5.44/5.63 = I5 )
% 5.44/5.63 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 5.44/5.63 & ! [X2: nat] :
% 5.44/5.63 ( ( ( ( vEBT_VEBT_high @ X2 @ N )
% 5.44/5.63 = I5 )
% 5.44/5.63 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N ) ) )
% 5.44/5.63 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.63 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % invar_vebt.simps
% 5.44/5.63 thf(fact_2565_invar__vebt_Ocases,axiom,
% 5.44/5.63 ! [A12: vEBT_VEBT,A23: nat] :
% 5.44/5.63 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.44/5.63 => ( ( ? [A3: $o,B3: $o] :
% 5.44/5.63 ( A12
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( A23
% 5.44/5.63 != ( suc @ zero_zero_nat ) ) )
% 5.44/5.63 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.44/5.63 ( ( A12
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( ( A23 = Deg2 )
% 5.44/5.63 => ( ! [X3: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.44/5.63 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.44/5.63 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.44/5.63 => ( ( M5 = N4 )
% 5.44/5.63 => ( ( Deg2
% 5.44/5.63 = ( plus_plus_nat @ N4 @ M5 ) )
% 5.44/5.63 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.44/5.63 => ~ ! [X3: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.63 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.44/5.63 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.44/5.63 ( ( A12
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( ( A23 = Deg2 )
% 5.44/5.63 => ( ! [X3: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.44/5.63 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.44/5.63 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.44/5.63 => ( ( M5
% 5.44/5.63 = ( suc @ N4 ) )
% 5.44/5.63 => ( ( Deg2
% 5.44/5.63 = ( plus_plus_nat @ N4 @ M5 ) )
% 5.44/5.63 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.44/5.63 => ~ ! [X3: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.63 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.44/5.63 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.44/5.63 ( ( A12
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( ( A23 = Deg2 )
% 5.44/5.63 => ( ! [X3: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.44/5.63 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.44/5.63 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.44/5.63 => ( ( M5 = N4 )
% 5.44/5.63 => ( ( Deg2
% 5.44/5.63 = ( plus_plus_nat @ N4 @ M5 ) )
% 5.44/5.63 => ( ! [I: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.44/5.63 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X4 ) )
% 5.44/5.63 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.44/5.63 => ( ( ( Mi2 = Ma2 )
% 5.44/5.63 => ! [X3: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.63 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.44/5.63 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.63 => ~ ( ( Mi2 != Ma2 )
% 5.44/5.63 => ! [I: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.44/5.63 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N4 )
% 5.44/5.63 = I )
% 5.44/5.63 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N4 ) ) )
% 5.44/5.63 & ! [X3: nat] :
% 5.44/5.63 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 5.44/5.63 = I )
% 5.44/5.63 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 5.44/5.63 => ( ( ord_less_nat @ Mi2 @ X3 )
% 5.44/5.63 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.63 => ~ ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.44/5.63 ( ( A12
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( ( A23 = Deg2 )
% 5.44/5.63 => ( ! [X3: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.63 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.44/5.63 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 5.44/5.63 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.44/5.63 => ( ( M5
% 5.44/5.63 = ( suc @ N4 ) )
% 5.44/5.63 => ( ( Deg2
% 5.44/5.63 = ( plus_plus_nat @ N4 @ M5 ) )
% 5.44/5.63 => ( ! [I: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.44/5.63 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X4 ) )
% 5.44/5.63 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.44/5.63 => ( ( ( Mi2 = Ma2 )
% 5.44/5.63 => ! [X3: vEBT_VEBT] :
% 5.44/5.63 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.63 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 5.44/5.63 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.44/5.63 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.63 => ~ ( ( Mi2 != Ma2 )
% 5.44/5.63 => ! [I: nat] :
% 5.44/5.63 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.44/5.63 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N4 )
% 5.44/5.63 = I )
% 5.44/5.63 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N4 ) ) )
% 5.44/5.63 & ! [X3: nat] :
% 5.44/5.63 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 5.44/5.63 = I )
% 5.44/5.63 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 5.44/5.63 => ( ( ord_less_nat @ Mi2 @ X3 )
% 5.44/5.63 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % invar_vebt.cases
% 5.44/5.63 thf(fact_2566_vebt__insert_Oelims,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.44/5.63 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.44/5.63 = Y )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 5.44/5.63 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.63 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.44/5.63 & ( ( Xa2 != one_one_nat )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) ) )
% 5.44/5.63 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S2 ) ) )
% 5.44/5.63 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) ) )
% 5.44/5.63 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( if_VEBT_VEBT
% 5.44/5.63 @ ( ( 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 @ TreeList3 ) )
% 5.44/5.63 & ~ ( ( Xa2 = Mi2 )
% 5.44/5.63 | ( Xa2 = Ma2 ) ) )
% 5.44/5.63 @ ( 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 @ TreeList3 @ ( 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 @ TreeList3 @ ( 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 @ TreeList3 @ ( 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 ) )
% 5.44/5.63 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.63
% 5.44/5.63 % vebt_insert.elims
% 5.44/5.63 thf(fact_2567_vebt__delete_Oelims,axiom,
% 5.44/5.63 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.44/5.63 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 5.44/5.63 = Y )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( ( Xa2 = zero_zero_nat )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 5.44/5.63 => ( ! [A3: $o] :
% 5.44/5.63 ( ? [B3: $o] :
% 5.44/5.63 ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( ( Xa2
% 5.44/5.63 = ( suc @ zero_zero_nat ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Leaf @ A3 @ $false ) ) ) )
% 5.44/5.63 => ( ! [A3: $o,B3: $o] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.63 => ( ? [N4: nat] :
% 5.44/5.63 ( Xa2
% 5.44/5.63 = ( suc @ ( suc @ N4 ) ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.44/5.63 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) ) )
% 5.44/5.63 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) )
% 5.44/5.63 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.63 ( ( X
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.63 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.63 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.44/5.63 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.63 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.44/5.63 => ( ( ( ( Xa2 = Mi2 )
% 5.44/5.63 & ( Xa2 = Ma2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.44/5.63 & ( ~ ( ( Xa2 = Mi2 )
% 5.44/5.63 & ( Xa2 = Ma2 ) )
% 5.44/5.63 => ( Y
% 5.44/5.63 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.63 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 @ ( vEBT_Node
% 5.44/5.63 @ ( some_P7363390416028606310at_nat
% 5.44/5.63 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.44/5.63 @ ( if_nat
% 5.44/5.63 @ ( ( ( Xa2 = Mi2 )
% 5.44/5.63 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.44/5.63 = Ma2 ) )
% 5.44/5.63 & ( ( Xa2 != Mi2 )
% 5.44/5.63 => ( Xa2 = Ma2 ) ) )
% 5.44/5.63 @ ( if_nat
% 5.44/5.63 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 = none_nat )
% 5.44/5.63 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.44/5.63 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.63 @ Ma2 ) ) )
% 5.44/5.63 @ ( suc @ ( suc @ Va2 ) )
% 5.44/5.63 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.63 @ ( vEBT_Node
% 5.44/5.63 @ ( some_P7363390416028606310at_nat
% 5.44/5.63 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.44/5.63 @ ( if_nat
% 5.44/5.63 @ ( ( ( Xa2 = Mi2 )
% 5.44/5.63 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.44/5.63 = Ma2 ) )
% 5.44/5.63 & ( ( Xa2 != Mi2 )
% 5.44/5.63 => ( Xa2 = Ma2 ) ) )
% 5.44/5.63 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.63 @ Ma2 ) ) )
% 5.44/5.63 @ ( suc @ ( suc @ Va2 ) )
% 5.44/5.63 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 @ Summary2 ) )
% 5.44/5.64 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_delete.elims
% 5.44/5.64 thf(fact_2568_vebt__delete_Osimps_I4_J,axiom,
% 5.44/5.64 ! [Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 5.44/5.64 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Uu )
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_delete.simps(4)
% 5.44/5.64 thf(fact_2569_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.44/5.64 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.44/5.64 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.44/5.64
% 5.44/5.64 % VEBT_internal.minNull.simps(5)
% 5.44/5.64 thf(fact_2570_vebt__member_Osimps_I2_J,axiom,
% 5.44/5.64 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.44/5.64 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_member.simps(2)
% 5.44/5.64 thf(fact_2571_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.44/5.64 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.44/5.64
% 5.44/5.64 % VEBT_internal.minNull.simps(4)
% 5.44/5.64 thf(fact_2572_vebt__succ_Oelims,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.44/5.64 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.44/5.64 = Y )
% 5.44/5.64 => ( ! [Uu2: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.44/5.64 => ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => ~ ( ( B3
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.64 & ( ~ B3
% 5.44/5.64 => ( Y = none_nat ) ) ) ) )
% 5.44/5.64 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.44/5.64 ( X
% 5.44/5.64 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.44/5.64 => ( ? [N4: nat] :
% 5.44/5.64 ( Xa2
% 5.44/5.64 = ( suc @ N4 ) )
% 5.44/5.64 => ( Y != none_nat ) ) )
% 5.44/5.64 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.64 ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.44/5.64 => ( Y != none_nat ) )
% 5.44/5.64 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.44/5.64 ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.44/5.64 => ( Y != none_nat ) )
% 5.44/5.64 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.44/5.64 ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.44/5.64 => ( Y != none_nat ) )
% 5.44/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( some_nat @ Mi2 ) ) )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 @ ( if_option_nat
% 5.44/5.64 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 != none_nat )
% 5.44/5.64 & ( 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 @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.64 @ ( 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 @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.64 @ ( if_option_nat
% 5.44/5.64 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.64 = none_nat )
% 5.44/5.64 @ none_nat
% 5.44/5.64 @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.64 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_succ.elims
% 5.44/5.64 thf(fact_2573_buildup__gives__valid,axiom,
% 5.44/5.64 ! [N2: nat] :
% 5.44/5.64 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.64 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % buildup_gives_valid
% 5.44/5.64 thf(fact_2574_inrange,axiom,
% 5.44/5.64 ! [T: vEBT_VEBT,N2: nat] :
% 5.44/5.64 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.64 => ( 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 ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % inrange
% 5.44/5.64 thf(fact_2575_buildup__gives__empty,axiom,
% 5.44/5.64 ! [N2: nat] :
% 5.44/5.64 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N2 ) )
% 5.44/5.64 = bot_bot_set_nat ) ).
% 5.44/5.64
% 5.44/5.64 % buildup_gives_empty
% 5.44/5.64 thf(fact_2576_set__bit__0,axiom,
% 5.44/5.64 ! [A: code_integer] :
% 5.44/5.64 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 5.44/5.64 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % set_bit_0
% 5.44/5.64 thf(fact_2577_set__bit__0,axiom,
% 5.44/5.64 ! [A: int] :
% 5.44/5.64 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.44/5.64 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % set_bit_0
% 5.44/5.64 thf(fact_2578_set__bit__0,axiom,
% 5.44/5.64 ! [A: nat] :
% 5.44/5.64 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.44/5.64 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % set_bit_0
% 5.44/5.64 thf(fact_2579_max__bot,axiom,
% 5.44/5.64 ! [X: set_nat] :
% 5.44/5.64 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot
% 5.44/5.64 thf(fact_2580_max__bot,axiom,
% 5.44/5.64 ! [X: set_int] :
% 5.44/5.64 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot
% 5.44/5.64 thf(fact_2581_max__bot,axiom,
% 5.44/5.64 ! [X: set_real] :
% 5.44/5.64 ( ( ord_max_set_real @ bot_bot_set_real @ X )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot
% 5.44/5.64 thf(fact_2582_max__bot,axiom,
% 5.44/5.64 ! [X: nat] :
% 5.44/5.64 ( ( ord_max_nat @ bot_bot_nat @ X )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot
% 5.44/5.64 thf(fact_2583_max__bot,axiom,
% 5.44/5.64 ! [X: extended_enat] :
% 5.44/5.64 ( ( ord_ma741700101516333627d_enat @ bot_bo4199563552545308370d_enat @ X )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot
% 5.44/5.64 thf(fact_2584_max__bot2,axiom,
% 5.44/5.64 ! [X: set_nat] :
% 5.44/5.64 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot2
% 5.44/5.64 thf(fact_2585_max__bot2,axiom,
% 5.44/5.64 ! [X: set_int] :
% 5.44/5.64 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot2
% 5.44/5.64 thf(fact_2586_max__bot2,axiom,
% 5.44/5.64 ! [X: set_real] :
% 5.44/5.64 ( ( ord_max_set_real @ X @ bot_bot_set_real )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot2
% 5.44/5.64 thf(fact_2587_max__bot2,axiom,
% 5.44/5.64 ! [X: nat] :
% 5.44/5.64 ( ( ord_max_nat @ X @ bot_bot_nat )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot2
% 5.44/5.64 thf(fact_2588_max__bot2,axiom,
% 5.44/5.64 ! [X: extended_enat] :
% 5.44/5.64 ( ( ord_ma741700101516333627d_enat @ X @ bot_bo4199563552545308370d_enat )
% 5.44/5.64 = X ) ).
% 5.44/5.64
% 5.44/5.64 % max_bot2
% 5.44/5.64 thf(fact_2589_vebt__succ_Opelims,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.44/5.64 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.44/5.64 = Y )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [Uu2: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 5.44/5.64 => ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => ( ( ( B3
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.64 & ( ~ B3
% 5.44/5.64 => ( Y = none_nat ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.44/5.64 => ( ! [Uv2: $o,Uw2: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.44/5.64 => ! [N4: nat] :
% 5.44/5.64 ( ( Xa2
% 5.44/5.64 = ( suc @ N4 ) )
% 5.44/5.64 => ( ( Y = none_nat )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N4 ) ) ) ) ) )
% 5.44/5.64 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.44/5.64 => ( ( Y = none_nat )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.44/5.64 => ( ( Y = none_nat )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.44/5.64 => ( ( Y = none_nat )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 5.44/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( some_nat @ Mi2 ) ) )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 @ ( if_option_nat
% 5.44/5.64 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 != none_nat )
% 5.44/5.64 & ( 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 @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.64 @ ( 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 @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.64 @ ( if_option_nat
% 5.44/5.64 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.64 = none_nat )
% 5.44/5.64 @ none_nat
% 5.44/5.64 @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.64 @ none_nat ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_succ.pelims
% 5.44/5.64 thf(fact_2590_Diff__eq__empty__iff,axiom,
% 5.44/5.64 ! [A2: set_int,B2: set_int] :
% 5.44/5.64 ( ( ( minus_minus_set_int @ A2 @ B2 )
% 5.44/5.64 = bot_bot_set_int )
% 5.44/5.64 = ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % Diff_eq_empty_iff
% 5.44/5.64 thf(fact_2591_Diff__eq__empty__iff,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ( ( minus_minus_set_real @ A2 @ B2 )
% 5.44/5.64 = bot_bot_set_real )
% 5.44/5.64 = ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % Diff_eq_empty_iff
% 5.44/5.64 thf(fact_2592_Diff__eq__empty__iff,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 5.44/5.64 = bot_bot_set_nat )
% 5.44/5.64 = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % Diff_eq_empty_iff
% 5.44/5.64 thf(fact_2593_subset__empty,axiom,
% 5.44/5.64 ! [A2: set_int] :
% 5.44/5.64 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.44/5.64 = ( A2 = bot_bot_set_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_empty
% 5.44/5.64 thf(fact_2594_subset__empty,axiom,
% 5.44/5.64 ! [A2: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 5.44/5.64 = ( A2 = bot_bot_set_real ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_empty
% 5.44/5.64 thf(fact_2595_subset__empty,axiom,
% 5.44/5.64 ! [A2: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.44/5.64 = ( A2 = bot_bot_set_nat ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_empty
% 5.44/5.64 thf(fact_2596_empty__subsetI,axiom,
% 5.44/5.64 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % empty_subsetI
% 5.44/5.64 thf(fact_2597_empty__subsetI,axiom,
% 5.44/5.64 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % empty_subsetI
% 5.44/5.64 thf(fact_2598_empty__subsetI,axiom,
% 5.44/5.64 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % empty_subsetI
% 5.44/5.64 thf(fact_2599_buildup__nothing__in__min__max,axiom,
% 5.44/5.64 ! [N2: nat,X: nat] :
% 5.44/5.64 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X ) ).
% 5.44/5.64
% 5.44/5.64 % buildup_nothing_in_min_max
% 5.44/5.64 thf(fact_2600_buildup__nothing__in__leaf,axiom,
% 5.44/5.64 ! [N2: nat,X: nat] :
% 5.44/5.64 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X ) ).
% 5.44/5.64
% 5.44/5.64 % buildup_nothing_in_leaf
% 5.44/5.64 thf(fact_2601_dual__order_Orefl,axiom,
% 5.44/5.64 ! [A: set_real] : ( ord_less_eq_set_real @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.refl
% 5.44/5.64 thf(fact_2602_dual__order_Orefl,axiom,
% 5.44/5.64 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.refl
% 5.44/5.64 thf(fact_2603_dual__order_Orefl,axiom,
% 5.44/5.64 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.refl
% 5.44/5.64 thf(fact_2604_dual__order_Orefl,axiom,
% 5.44/5.64 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.refl
% 5.44/5.64 thf(fact_2605_dual__order_Orefl,axiom,
% 5.44/5.64 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.refl
% 5.44/5.64 thf(fact_2606_order__refl,axiom,
% 5.44/5.64 ! [X: set_real] : ( ord_less_eq_set_real @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_refl
% 5.44/5.64 thf(fact_2607_order__refl,axiom,
% 5.44/5.64 ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_refl
% 5.44/5.64 thf(fact_2608_order__refl,axiom,
% 5.44/5.64 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_refl
% 5.44/5.64 thf(fact_2609_order__refl,axiom,
% 5.44/5.64 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_refl
% 5.44/5.64 thf(fact_2610_order__refl,axiom,
% 5.44/5.64 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_refl
% 5.44/5.64 thf(fact_2611_subset__antisym,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.64 => ( A2 = B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_antisym
% 5.44/5.64 thf(fact_2612_subset__antisym,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.64 => ( A2 = B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_antisym
% 5.44/5.64 thf(fact_2613_psubsetI,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ( A2 != B2 )
% 5.44/5.64 => ( ord_less_set_real @ A2 @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubsetI
% 5.44/5.64 thf(fact_2614_psubsetI,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( A2 != B2 )
% 5.44/5.64 => ( ord_less_set_nat @ A2 @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubsetI
% 5.44/5.64 thf(fact_2615_subsetI,axiom,
% 5.44/5.64 ! [A2: set_int,B2: set_int] :
% 5.44/5.64 ( ! [X5: int] :
% 5.44/5.64 ( ( member_int @ X5 @ A2 )
% 5.44/5.64 => ( member_int @ X5 @ B2 ) )
% 5.44/5.64 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetI
% 5.44/5.64 thf(fact_2616_subsetI,axiom,
% 5.44/5.64 ! [A2: set_complex,B2: set_complex] :
% 5.44/5.64 ( ! [X5: complex] :
% 5.44/5.64 ( ( member_complex @ X5 @ A2 )
% 5.44/5.64 => ( member_complex @ X5 @ B2 ) )
% 5.44/5.64 => ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetI
% 5.44/5.64 thf(fact_2617_subsetI,axiom,
% 5.44/5.64 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.44/5.64 ( ! [X5: product_prod_nat_nat] :
% 5.44/5.64 ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 5.44/5.64 => ( member8440522571783428010at_nat @ X5 @ B2 ) )
% 5.44/5.64 => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetI
% 5.44/5.64 thf(fact_2618_subsetI,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ! [X5: real] :
% 5.44/5.64 ( ( member_real @ X5 @ A2 )
% 5.44/5.64 => ( member_real @ X5 @ B2 ) )
% 5.44/5.64 => ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetI
% 5.44/5.64 thf(fact_2619_subsetI,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ! [X5: nat] :
% 5.44/5.64 ( ( member_nat @ X5 @ A2 )
% 5.44/5.64 => ( member_nat @ X5 @ B2 ) )
% 5.44/5.64 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetI
% 5.44/5.64 thf(fact_2620_div__pos__pos__trivial,axiom,
% 5.44/5.64 ! [K: int,L2: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.64 => ( ( ord_less_int @ K @ L2 )
% 5.44/5.64 => ( ( divide_divide_int @ K @ L2 )
% 5.44/5.64 = zero_zero_int ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % div_pos_pos_trivial
% 5.44/5.64 thf(fact_2621_div__neg__neg__trivial,axiom,
% 5.44/5.64 ! [K: int,L2: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.44/5.64 => ( ( ord_less_int @ L2 @ K )
% 5.44/5.64 => ( ( divide_divide_int @ K @ L2 )
% 5.44/5.64 = zero_zero_int ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % div_neg_neg_trivial
% 5.44/5.64 thf(fact_2622_i0__less,axiom,
% 5.44/5.64 ! [N2: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.44/5.64 = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.64
% 5.44/5.64 % i0_less
% 5.44/5.64 thf(fact_2623_idiff__0,axiom,
% 5.44/5.64 ! [N2: extended_enat] :
% 5.44/5.64 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.44/5.64 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.64
% 5.44/5.64 % idiff_0
% 5.44/5.64 thf(fact_2624_idiff__0__right,axiom,
% 5.44/5.64 ! [N2: extended_enat] :
% 5.44/5.64 ( ( minus_3235023915231533773d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.44/5.64 = N2 ) ).
% 5.44/5.64
% 5.44/5.64 % idiff_0_right
% 5.44/5.64 thf(fact_2625_not__real__square__gt__zero,axiom,
% 5.44/5.64 ! [X: real] :
% 5.44/5.64 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 5.44/5.64 = ( X = zero_zero_real ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_real_square_gt_zero
% 5.44/5.64 thf(fact_2626_half__nonnegative__int__iff,axiom,
% 5.44/5.64 ! [K: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.44/5.64 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.44/5.64
% 5.44/5.64 % half_nonnegative_int_iff
% 5.44/5.64 thf(fact_2627_half__negative__int__iff,axiom,
% 5.44/5.64 ! [K: int] :
% 5.44/5.64 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.44/5.64 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % half_negative_int_iff
% 5.44/5.64 thf(fact_2628_bot__nat__def,axiom,
% 5.44/5.64 bot_bot_nat = zero_zero_nat ).
% 5.44/5.64
% 5.44/5.64 % bot_nat_def
% 5.44/5.64 thf(fact_2629_zdiv__zmult2__eq,axiom,
% 5.44/5.64 ! [C: int,A: int,B: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.64 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.64 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % zdiv_zmult2_eq
% 5.44/5.64 thf(fact_2630_enat__0__less__mult__iff,axiom,
% 5.44/5.64 ! [M: extended_enat,N2: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 5.44/5.64 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.44/5.64 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % enat_0_less_mult_iff
% 5.44/5.64 thf(fact_2631_not__iless0,axiom,
% 5.44/5.64 ! [N2: extended_enat] :
% 5.44/5.64 ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 5.44/5.64
% 5.44/5.64 % not_iless0
% 5.44/5.64 thf(fact_2632_iadd__is__0,axiom,
% 5.44/5.64 ! [M: extended_enat,N2: extended_enat] :
% 5.44/5.64 ( ( ( plus_p3455044024723400733d_enat @ M @ N2 )
% 5.44/5.64 = zero_z5237406670263579293d_enat )
% 5.44/5.64 = ( ( M = zero_z5237406670263579293d_enat )
% 5.44/5.64 & ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % iadd_is_0
% 5.44/5.64 thf(fact_2633_i0__lb,axiom,
% 5.44/5.64 ! [N2: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N2 ) ).
% 5.44/5.64
% 5.44/5.64 % i0_lb
% 5.44/5.64 thf(fact_2634_ile0__eq,axiom,
% 5.44/5.64 ! [N2: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.44/5.64 = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.64
% 5.44/5.64 % ile0_eq
% 5.44/5.64 thf(fact_2635_ex__nat__less,axiom,
% 5.44/5.64 ! [N2: nat,P: nat > $o] :
% 5.44/5.64 ( ( ? [M6: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.44/5.64 & ( P @ M6 ) ) )
% 5.44/5.64 = ( ? [X2: nat] :
% 5.44/5.64 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.64 & ( P @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ex_nat_less
% 5.44/5.64 thf(fact_2636_all__nat__less,axiom,
% 5.44/5.64 ! [N2: nat,P: nat > $o] :
% 5.44/5.64 ( ( ! [M6: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.44/5.64 => ( P @ M6 ) ) )
% 5.44/5.64 = ( ! [X2: nat] :
% 5.44/5.64 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.64 => ( P @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % all_nat_less
% 5.44/5.64 thf(fact_2637_vebt__buildup_Osimps_I1_J,axiom,
% 5.44/5.64 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.44/5.64 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_buildup.simps(1)
% 5.44/5.64 thf(fact_2638_order__antisym__conv,axiom,
% 5.44/5.64 ! [Y: set_real,X: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ Y @ X )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym_conv
% 5.44/5.64 thf(fact_2639_order__antisym__conv,axiom,
% 5.44/5.64 ! [Y: set_nat,X: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym_conv
% 5.44/5.64 thf(fact_2640_order__antisym__conv,axiom,
% 5.44/5.64 ! [Y: num,X: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ Y @ X )
% 5.44/5.64 => ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym_conv
% 5.44/5.64 thf(fact_2641_order__antisym__conv,axiom,
% 5.44/5.64 ! [Y: nat,X: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ Y @ X )
% 5.44/5.64 => ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym_conv
% 5.44/5.64 thf(fact_2642_order__antisym__conv,axiom,
% 5.44/5.64 ! [Y: int,X: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ Y @ X )
% 5.44/5.64 => ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym_conv
% 5.44/5.64 thf(fact_2643_linorder__le__cases,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ~ ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_le_cases
% 5.44/5.64 thf(fact_2644_linorder__le__cases,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ~ ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_le_cases
% 5.44/5.64 thf(fact_2645_linorder__le__cases,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ~ ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_le_cases
% 5.44/5.64 thf(fact_2646_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2647_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2648_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2649_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2650_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2651_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2652_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: int,B: int,F: int > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2653_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: int,B: int,F: int > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2654_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: int,B: int,F: int > int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2655_ord__le__eq__subst,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,F: set_real > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: set_real,Y5: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_subst
% 5.44/5.64 thf(fact_2656_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: num,F: num > num,B: num,C: num] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2657_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2658_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: int,F: num > int,B: num,C: num] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2659_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2660_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2661_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: int,F: nat > int,B: nat,C: nat] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2662_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: num,F: int > num,B: int,C: int] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2663_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: nat,F: int > nat,B: int,C: int] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2664_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: int,F: int > int,B: int,C: int] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2665_ord__eq__le__subst,axiom,
% 5.44/5.64 ! [A: num,F: set_real > num,B: set_real,C: set_real] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B @ C )
% 5.44/5.64 => ( ! [X5: set_real,Y5: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_subst
% 5.44/5.64 thf(fact_2666_linorder__linear,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 | ( ord_less_eq_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_linear
% 5.44/5.64 thf(fact_2667_linorder__linear,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_linear
% 5.44/5.64 thf(fact_2668_linorder__linear,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 | ( ord_less_eq_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_linear
% 5.44/5.64 thf(fact_2669_order__eq__refl,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real] :
% 5.44/5.64 ( ( X = Y )
% 5.44/5.64 => ( ord_less_eq_set_real @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_eq_refl
% 5.44/5.64 thf(fact_2670_order__eq__refl,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat] :
% 5.44/5.64 ( ( X = Y )
% 5.44/5.64 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_eq_refl
% 5.44/5.64 thf(fact_2671_order__eq__refl,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( X = Y )
% 5.44/5.64 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_eq_refl
% 5.44/5.64 thf(fact_2672_order__eq__refl,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( X = Y )
% 5.44/5.64 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_eq_refl
% 5.44/5.64 thf(fact_2673_order__eq__refl,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( X = Y )
% 5.44/5.64 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_eq_refl
% 5.44/5.64 thf(fact_2674_order__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2675_order__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2676_order__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2677_order__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2678_order__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2679_order__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2680_order__subst2,axiom,
% 5.44/5.64 ! [A: int,B: int,F: int > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2681_order__subst2,axiom,
% 5.44/5.64 ! [A: int,B: int,F: int > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2682_order__subst2,axiom,
% 5.44/5.64 ! [A: int,B: int,F: int > int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2683_order__subst2,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,F: set_real > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: set_real,Y5: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst2
% 5.44/5.64 thf(fact_2684_order__subst1,axiom,
% 5.44/5.64 ! [A: num,F: num > num,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2685_order__subst1,axiom,
% 5.44/5.64 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2686_order__subst1,axiom,
% 5.44/5.64 ! [A: num,F: int > num,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2687_order__subst1,axiom,
% 5.44/5.64 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2688_order__subst1,axiom,
% 5.44/5.64 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2689_order__subst1,axiom,
% 5.44/5.64 ! [A: nat,F: int > nat,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2690_order__subst1,axiom,
% 5.44/5.64 ! [A: int,F: num > int,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2691_order__subst1,axiom,
% 5.44/5.64 ! [A: int,F: nat > int,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2692_order__subst1,axiom,
% 5.44/5.64 ! [A: int,F: int > int,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2693_order__subst1,axiom,
% 5.44/5.64 ! [A: set_real,F: num > set_real,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_set_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_eq_set_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_subst1
% 5.44/5.64 thf(fact_2694_Orderings_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: set_real,Z2: set_real] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: set_real,B4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.44/5.64 & ( ord_less_eq_set_real @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Orderings.order_eq_iff
% 5.44/5.64 thf(fact_2695_Orderings_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 5.44/5.64 & ( ord_less_eq_set_nat @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Orderings.order_eq_iff
% 5.44/5.64 thf(fact_2696_Orderings_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: num,B4: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.44/5.64 & ( ord_less_eq_num @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Orderings.order_eq_iff
% 5.44/5.64 thf(fact_2697_Orderings_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: nat,B4: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.44/5.64 & ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Orderings.order_eq_iff
% 5.44/5.64 thf(fact_2698_Orderings_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: int,B4: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.44/5.64 & ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Orderings.order_eq_iff
% 5.44/5.64 thf(fact_2699_antisym,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B @ A )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym
% 5.44/5.64 thf(fact_2700_antisym,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ B @ A )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym
% 5.44/5.64 thf(fact_2701_antisym,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ A )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym
% 5.44/5.64 thf(fact_2702_antisym,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym
% 5.44/5.64 thf(fact_2703_antisym,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ A )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym
% 5.44/5.64 thf(fact_2704_dual__order_Otrans,axiom,
% 5.44/5.64 ! [B: set_real,A: set_real,C: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ C @ B )
% 5.44/5.64 => ( ord_less_eq_set_real @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.trans
% 5.44/5.64 thf(fact_2705_dual__order_Otrans,axiom,
% 5.44/5.64 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.44/5.64 => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.trans
% 5.44/5.64 thf(fact_2706_dual__order_Otrans,axiom,
% 5.44/5.64 ! [B: num,A: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_num @ C @ B )
% 5.44/5.64 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.trans
% 5.44/5.64 thf(fact_2707_dual__order_Otrans,axiom,
% 5.44/5.64 ! [B: nat,A: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_nat @ C @ B )
% 5.44/5.64 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.trans
% 5.44/5.64 thf(fact_2708_dual__order_Otrans,axiom,
% 5.44/5.64 ! [B: int,A: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_int @ C @ B )
% 5.44/5.64 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.trans
% 5.44/5.64 thf(fact_2709_dual__order_Oantisym,axiom,
% 5.44/5.64 ! [B: set_real,A: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.antisym
% 5.44/5.64 thf(fact_2710_dual__order_Oantisym,axiom,
% 5.44/5.64 ! [B: set_nat,A: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.antisym
% 5.44/5.64 thf(fact_2711_dual__order_Oantisym,axiom,
% 5.44/5.64 ! [B: num,A: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.antisym
% 5.44/5.64 thf(fact_2712_dual__order_Oantisym,axiom,
% 5.44/5.64 ! [B: nat,A: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.antisym
% 5.44/5.64 thf(fact_2713_dual__order_Oantisym,axiom,
% 5.44/5.64 ! [B: int,A: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.antisym
% 5.44/5.64 thf(fact_2714_dual__order_Oeq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: set_real,Z2: set_real] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: set_real,B4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ B4 @ A4 )
% 5.44/5.64 & ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.eq_iff
% 5.44/5.64 thf(fact_2715_dual__order_Oeq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 5.44/5.64 & ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.eq_iff
% 5.44/5.64 thf(fact_2716_dual__order_Oeq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: num,B4: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.44/5.64 & ( ord_less_eq_num @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.eq_iff
% 5.44/5.64 thf(fact_2717_dual__order_Oeq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: nat,B4: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.44/5.64 & ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.eq_iff
% 5.44/5.64 thf(fact_2718_dual__order_Oeq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A4: int,B4: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.44/5.64 & ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.eq_iff
% 5.44/5.64 thf(fact_2719_linorder__wlog,axiom,
% 5.44/5.64 ! [P: num > num > $o,A: num,B: num] :
% 5.44/5.64 ( ! [A3: num,B3: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A3 @ B3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( ! [A3: num,B3: num] :
% 5.44/5.64 ( ( P @ B3 @ A3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_wlog
% 5.44/5.64 thf(fact_2720_linorder__wlog,axiom,
% 5.44/5.64 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.44/5.64 ( ! [A3: nat,B3: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A3 @ B3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( ! [A3: nat,B3: nat] :
% 5.44/5.64 ( ( P @ B3 @ A3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_wlog
% 5.44/5.64 thf(fact_2721_linorder__wlog,axiom,
% 5.44/5.64 ! [P: int > int > $o,A: int,B: int] :
% 5.44/5.64 ( ! [A3: int,B3: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A3 @ B3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( ! [A3: int,B3: int] :
% 5.44/5.64 ( ( P @ B3 @ A3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_wlog
% 5.44/5.64 thf(fact_2722_order__trans,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real,Z: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ Y @ Z )
% 5.44/5.64 => ( ord_less_eq_set_real @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_trans
% 5.44/5.64 thf(fact_2723_order__trans,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ Y @ Z )
% 5.44/5.64 => ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_trans
% 5.44/5.64 thf(fact_2724_order__trans,axiom,
% 5.44/5.64 ! [X: num,Y: num,Z: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_num @ Y @ Z )
% 5.44/5.64 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_trans
% 5.44/5.64 thf(fact_2725_order__trans,axiom,
% 5.44/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.44/5.64 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_trans
% 5.44/5.64 thf(fact_2726_order__trans,axiom,
% 5.44/5.64 ! [X: int,Y: int,Z: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_int @ Y @ Z )
% 5.44/5.64 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_trans
% 5.44/5.64 thf(fact_2727_order_Otrans,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,C: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B @ C )
% 5.44/5.64 => ( ord_less_eq_set_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.trans
% 5.44/5.64 thf(fact_2728_order_Otrans,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.44/5.64 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.trans
% 5.44/5.64 thf(fact_2729_order_Otrans,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.trans
% 5.44/5.64 thf(fact_2730_order_Otrans,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.trans
% 5.44/5.64 thf(fact_2731_order_Otrans,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.trans
% 5.44/5.64 thf(fact_2732_order__antisym,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ Y @ X )
% 5.44/5.64 => ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym
% 5.44/5.64 thf(fact_2733_order__antisym,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ Y @ X )
% 5.44/5.64 => ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym
% 5.44/5.64 thf(fact_2734_order__antisym,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_num @ Y @ X )
% 5.44/5.64 => ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym
% 5.44/5.64 thf(fact_2735_order__antisym,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_nat @ Y @ X )
% 5.44/5.64 => ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym
% 5.44/5.64 thf(fact_2736_order__antisym,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_int @ Y @ X )
% 5.44/5.64 => ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_antisym
% 5.44/5.64 thf(fact_2737_ord__le__eq__trans,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,C: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_eq_set_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_trans
% 5.44/5.64 thf(fact_2738_ord__le__eq__trans,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_trans
% 5.44/5.64 thf(fact_2739_ord__le__eq__trans,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_trans
% 5.44/5.64 thf(fact_2740_ord__le__eq__trans,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_trans
% 5.44/5.64 thf(fact_2741_ord__le__eq__trans,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_le_eq_trans
% 5.44/5.64 thf(fact_2742_ord__eq__le__trans,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,C: set_real] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B @ C )
% 5.44/5.64 => ( ord_less_eq_set_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_trans
% 5.44/5.64 thf(fact_2743_ord__eq__le__trans,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.44/5.64 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_trans
% 5.44/5.64 thf(fact_2744_ord__eq__le__trans,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_trans
% 5.44/5.64 thf(fact_2745_ord__eq__le__trans,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_trans
% 5.44/5.64 thf(fact_2746_ord__eq__le__trans,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_le_trans
% 5.44/5.64 thf(fact_2747_order__class_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: set_real,Z2: set_real] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [X2: set_real,Y3: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X2 @ Y3 )
% 5.44/5.64 & ( ord_less_eq_set_real @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_class.order_eq_iff
% 5.44/5.64 thf(fact_2748_order__class_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [X2: set_nat,Y3: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 5.44/5.64 & ( ord_less_eq_set_nat @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_class.order_eq_iff
% 5.44/5.64 thf(fact_2749_order__class_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [X2: num,Y3: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.44/5.64 & ( ord_less_eq_num @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_class.order_eq_iff
% 5.44/5.64 thf(fact_2750_order__class_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [X2: nat,Y3: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.44/5.64 & ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_class.order_eq_iff
% 5.44/5.64 thf(fact_2751_order__class_Oorder__eq__iff,axiom,
% 5.44/5.64 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [X2: int,Y3: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.44/5.64 & ( ord_less_eq_int @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_class.order_eq_iff
% 5.44/5.64 thf(fact_2752_le__cases3,axiom,
% 5.44/5.64 ! [X: num,Y: num,Z: num] :
% 5.44/5.64 ( ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 5.44/5.64 => ( ( ( ord_less_eq_num @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_eq_num @ X @ Z ) )
% 5.44/5.64 => ( ( ( ord_less_eq_num @ X @ Z )
% 5.44/5.64 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 5.44/5.64 => ( ( ( ord_less_eq_num @ Z @ Y )
% 5.44/5.64 => ~ ( ord_less_eq_num @ Y @ X ) )
% 5.44/5.64 => ( ( ( ord_less_eq_num @ Y @ Z )
% 5.44/5.64 => ~ ( ord_less_eq_num @ Z @ X ) )
% 5.44/5.64 => ~ ( ( ord_less_eq_num @ Z @ X )
% 5.44/5.64 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % le_cases3
% 5.44/5.64 thf(fact_2753_le__cases3,axiom,
% 5.44/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.64 ( ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 5.44/5.64 => ( ( ( ord_less_eq_nat @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 5.44/5.64 => ( ( ( ord_less_eq_nat @ X @ Z )
% 5.44/5.64 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 5.44/5.64 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 5.44/5.64 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 5.44/5.64 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 5.44/5.64 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 5.44/5.64 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 5.44/5.64 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % le_cases3
% 5.44/5.64 thf(fact_2754_le__cases3,axiom,
% 5.44/5.64 ! [X: int,Y: int,Z: int] :
% 5.44/5.64 ( ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 5.44/5.64 => ( ( ( ord_less_eq_int @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_eq_int @ X @ Z ) )
% 5.44/5.64 => ( ( ( ord_less_eq_int @ X @ Z )
% 5.44/5.64 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 5.44/5.64 => ( ( ( ord_less_eq_int @ Z @ Y )
% 5.44/5.64 => ~ ( ord_less_eq_int @ Y @ X ) )
% 5.44/5.64 => ( ( ( ord_less_eq_int @ Y @ Z )
% 5.44/5.64 => ~ ( ord_less_eq_int @ Z @ X ) )
% 5.44/5.64 => ~ ( ( ord_less_eq_int @ Z @ X )
% 5.44/5.64 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % le_cases3
% 5.44/5.64 thf(fact_2755_nle__le,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.44/5.64 = ( ( ord_less_eq_num @ B @ A )
% 5.44/5.64 & ( B != A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nle_le
% 5.44/5.64 thf(fact_2756_nle__le,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.44/5.64 = ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.64 & ( B != A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nle_le
% 5.44/5.64 thf(fact_2757_nle__le,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.44/5.64 = ( ( ord_less_eq_int @ B @ A )
% 5.44/5.64 & ( B != A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nle_le
% 5.44/5.64 thf(fact_2758_lt__ex,axiom,
% 5.44/5.64 ! [X: real] :
% 5.44/5.64 ? [Y5: real] : ( ord_less_real @ Y5 @ X ) ).
% 5.44/5.64
% 5.44/5.64 % lt_ex
% 5.44/5.64 thf(fact_2759_lt__ex,axiom,
% 5.44/5.64 ! [X: int] :
% 5.44/5.64 ? [Y5: int] : ( ord_less_int @ Y5 @ X ) ).
% 5.44/5.64
% 5.44/5.64 % lt_ex
% 5.44/5.64 thf(fact_2760_gt__ex,axiom,
% 5.44/5.64 ! [X: real] :
% 5.44/5.64 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 5.44/5.64
% 5.44/5.64 % gt_ex
% 5.44/5.64 thf(fact_2761_gt__ex,axiom,
% 5.44/5.64 ! [X: nat] :
% 5.44/5.64 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 5.44/5.64
% 5.44/5.64 % gt_ex
% 5.44/5.64 thf(fact_2762_gt__ex,axiom,
% 5.44/5.64 ! [X: int] :
% 5.44/5.64 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 5.44/5.64
% 5.44/5.64 % gt_ex
% 5.44/5.64 thf(fact_2763_dense,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ? [Z4: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Z4 )
% 5.44/5.64 & ( ord_less_real @ Z4 @ Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dense
% 5.44/5.64 thf(fact_2764_less__imp__neq,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_imp_neq
% 5.44/5.64 thf(fact_2765_less__imp__neq,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_imp_neq
% 5.44/5.64 thf(fact_2766_less__imp__neq,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_imp_neq
% 5.44/5.64 thf(fact_2767_less__imp__neq,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_imp_neq
% 5.44/5.64 thf(fact_2768_less__imp__neq,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_imp_neq
% 5.44/5.64 thf(fact_2769_order_Oasym,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ~ ( ord_le72135733267957522d_enat @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.asym
% 5.44/5.64 thf(fact_2770_order_Oasym,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.asym
% 5.44/5.64 thf(fact_2771_order_Oasym,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.asym
% 5.44/5.64 thf(fact_2772_order_Oasym,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.asym
% 5.44/5.64 thf(fact_2773_order_Oasym,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.asym
% 5.44/5.64 thf(fact_2774_ord__eq__less__trans,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_trans
% 5.44/5.64 thf(fact_2775_ord__eq__less__trans,axiom,
% 5.44/5.64 ! [A: real,B: real,C: real] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ord_less_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_trans
% 5.44/5.64 thf(fact_2776_ord__eq__less__trans,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_num @ B @ C )
% 5.44/5.64 => ( ord_less_num @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_trans
% 5.44/5.64 thf(fact_2777_ord__eq__less__trans,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_nat @ B @ C )
% 5.44/5.64 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_trans
% 5.44/5.64 thf(fact_2778_ord__eq__less__trans,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int] :
% 5.44/5.64 ( ( A = B )
% 5.44/5.64 => ( ( ord_less_int @ B @ C )
% 5.44/5.64 => ( ord_less_int @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_trans
% 5.44/5.64 thf(fact_2779_ord__less__eq__trans,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_trans
% 5.44/5.64 thf(fact_2780_ord__less__eq__trans,axiom,
% 5.44/5.64 ! [A: real,B: real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_trans
% 5.44/5.64 thf(fact_2781_ord__less__eq__trans,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_num @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_trans
% 5.44/5.64 thf(fact_2782_ord__less__eq__trans,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_trans
% 5.44/5.64 thf(fact_2783_ord__less__eq__trans,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ( ( B = C )
% 5.44/5.64 => ( ord_less_int @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_trans
% 5.44/5.64 thf(fact_2784_less__induct,axiom,
% 5.44/5.64 ! [P: extended_enat > $o,A: extended_enat] :
% 5.44/5.64 ( ! [X5: extended_enat] :
% 5.44/5.64 ( ! [Y2: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ Y2 @ X5 )
% 5.44/5.64 => ( P @ Y2 ) )
% 5.44/5.64 => ( P @ X5 ) )
% 5.44/5.64 => ( P @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_induct
% 5.44/5.64 thf(fact_2785_less__induct,axiom,
% 5.44/5.64 ! [P: nat > $o,A: nat] :
% 5.44/5.64 ( ! [X5: nat] :
% 5.44/5.64 ( ! [Y2: nat] :
% 5.44/5.64 ( ( ord_less_nat @ Y2 @ X5 )
% 5.44/5.64 => ( P @ Y2 ) )
% 5.44/5.64 => ( P @ X5 ) )
% 5.44/5.64 => ( P @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_induct
% 5.44/5.64 thf(fact_2786_antisym__conv3,axiom,
% 5.44/5.64 ! [Y: extended_enat,X: extended_enat] :
% 5.44/5.64 ( ~ ( ord_le72135733267957522d_enat @ Y @ X )
% 5.44/5.64 => ( ( ~ ( ord_le72135733267957522d_enat @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv3
% 5.44/5.64 thf(fact_2787_antisym__conv3,axiom,
% 5.44/5.64 ! [Y: real,X: real] :
% 5.44/5.64 ( ~ ( ord_less_real @ Y @ X )
% 5.44/5.64 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv3
% 5.44/5.64 thf(fact_2788_antisym__conv3,axiom,
% 5.44/5.64 ! [Y: num,X: num] :
% 5.44/5.64 ( ~ ( ord_less_num @ Y @ X )
% 5.44/5.64 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv3
% 5.44/5.64 thf(fact_2789_antisym__conv3,axiom,
% 5.44/5.64 ! [Y: nat,X: nat] :
% 5.44/5.64 ( ~ ( ord_less_nat @ Y @ X )
% 5.44/5.64 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv3
% 5.44/5.64 thf(fact_2790_antisym__conv3,axiom,
% 5.44/5.64 ! [Y: int,X: int] :
% 5.44/5.64 ( ~ ( ord_less_int @ Y @ X )
% 5.44/5.64 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv3
% 5.44/5.64 thf(fact_2791_linorder__cases,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ~ ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( ( X != Y )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_cases
% 5.44/5.64 thf(fact_2792_linorder__cases,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ~ ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ( X != Y )
% 5.44/5.64 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_cases
% 5.44/5.64 thf(fact_2793_linorder__cases,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ~ ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( ( X != Y )
% 5.44/5.64 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_cases
% 5.44/5.64 thf(fact_2794_linorder__cases,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ~ ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( ( X != Y )
% 5.44/5.64 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_cases
% 5.44/5.64 thf(fact_2795_linorder__cases,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ~ ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( ( X != Y )
% 5.44/5.64 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_cases
% 5.44/5.64 thf(fact_2796_dual__order_Oasym,axiom,
% 5.44/5.64 ! [B: extended_enat,A: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.44/5.64 => ~ ( ord_le72135733267957522d_enat @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.asym
% 5.44/5.64 thf(fact_2797_dual__order_Oasym,axiom,
% 5.44/5.64 ! [B: real,A: real] :
% 5.44/5.64 ( ( ord_less_real @ B @ A )
% 5.44/5.64 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.asym
% 5.44/5.64 thf(fact_2798_dual__order_Oasym,axiom,
% 5.44/5.64 ! [B: num,A: num] :
% 5.44/5.64 ( ( ord_less_num @ B @ A )
% 5.44/5.64 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.asym
% 5.44/5.64 thf(fact_2799_dual__order_Oasym,axiom,
% 5.44/5.64 ! [B: nat,A: nat] :
% 5.44/5.64 ( ( ord_less_nat @ B @ A )
% 5.44/5.64 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.asym
% 5.44/5.64 thf(fact_2800_dual__order_Oasym,axiom,
% 5.44/5.64 ! [B: int,A: int] :
% 5.44/5.64 ( ( ord_less_int @ B @ A )
% 5.44/5.64 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.asym
% 5.44/5.64 thf(fact_2801_dual__order_Oirrefl,axiom,
% 5.44/5.64 ! [A: extended_enat] :
% 5.44/5.64 ~ ( ord_le72135733267957522d_enat @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.irrefl
% 5.44/5.64 thf(fact_2802_dual__order_Oirrefl,axiom,
% 5.44/5.64 ! [A: real] :
% 5.44/5.64 ~ ( ord_less_real @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.irrefl
% 5.44/5.64 thf(fact_2803_dual__order_Oirrefl,axiom,
% 5.44/5.64 ! [A: num] :
% 5.44/5.64 ~ ( ord_less_num @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.irrefl
% 5.44/5.64 thf(fact_2804_dual__order_Oirrefl,axiom,
% 5.44/5.64 ! [A: nat] :
% 5.44/5.64 ~ ( ord_less_nat @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.irrefl
% 5.44/5.64 thf(fact_2805_dual__order_Oirrefl,axiom,
% 5.44/5.64 ! [A: int] :
% 5.44/5.64 ~ ( ord_less_int @ A @ A ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.irrefl
% 5.44/5.64 thf(fact_2806_exists__least__iff,axiom,
% 5.44/5.64 ( ( ^ [P2: extended_enat > $o] :
% 5.44/5.64 ? [X7: extended_enat] : ( P2 @ X7 ) )
% 5.44/5.64 = ( ^ [P3: extended_enat > $o] :
% 5.44/5.64 ? [N: extended_enat] :
% 5.44/5.64 ( ( P3 @ N )
% 5.44/5.64 & ! [M6: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ M6 @ N )
% 5.44/5.64 => ~ ( P3 @ M6 ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % exists_least_iff
% 5.44/5.64 thf(fact_2807_exists__least__iff,axiom,
% 5.44/5.64 ( ( ^ [P2: nat > $o] :
% 5.44/5.64 ? [X7: nat] : ( P2 @ X7 ) )
% 5.44/5.64 = ( ^ [P3: nat > $o] :
% 5.44/5.64 ? [N: nat] :
% 5.44/5.64 ( ( P3 @ N )
% 5.44/5.64 & ! [M6: nat] :
% 5.44/5.64 ( ( ord_less_nat @ M6 @ N )
% 5.44/5.64 => ~ ( P3 @ M6 ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % exists_least_iff
% 5.44/5.64 thf(fact_2808_linorder__less__wlog,axiom,
% 5.44/5.64 ! [P: extended_enat > extended_enat > $o,A: extended_enat,B: extended_enat] :
% 5.44/5.64 ( ! [A3: extended_enat,B3: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A3 @ B3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( ! [A3: extended_enat] : ( P @ A3 @ A3 )
% 5.44/5.64 => ( ! [A3: extended_enat,B3: extended_enat] :
% 5.44/5.64 ( ( P @ B3 @ A3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_wlog
% 5.44/5.64 thf(fact_2809_linorder__less__wlog,axiom,
% 5.44/5.64 ! [P: real > real > $o,A: real,B: real] :
% 5.44/5.64 ( ! [A3: real,B3: real] :
% 5.44/5.64 ( ( ord_less_real @ A3 @ B3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( ! [A3: real] : ( P @ A3 @ A3 )
% 5.44/5.64 => ( ! [A3: real,B3: real] :
% 5.44/5.64 ( ( P @ B3 @ A3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_wlog
% 5.44/5.64 thf(fact_2810_linorder__less__wlog,axiom,
% 5.44/5.64 ! [P: num > num > $o,A: num,B: num] :
% 5.44/5.64 ( ! [A3: num,B3: num] :
% 5.44/5.64 ( ( ord_less_num @ A3 @ B3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( ! [A3: num] : ( P @ A3 @ A3 )
% 5.44/5.64 => ( ! [A3: num,B3: num] :
% 5.44/5.64 ( ( P @ B3 @ A3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_wlog
% 5.44/5.64 thf(fact_2811_linorder__less__wlog,axiom,
% 5.44/5.64 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.44/5.64 ( ! [A3: nat,B3: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A3 @ B3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 5.44/5.64 => ( ! [A3: nat,B3: nat] :
% 5.44/5.64 ( ( P @ B3 @ A3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_wlog
% 5.44/5.64 thf(fact_2812_linorder__less__wlog,axiom,
% 5.44/5.64 ! [P: int > int > $o,A: int,B: int] :
% 5.44/5.64 ( ! [A3: int,B3: int] :
% 5.44/5.64 ( ( ord_less_int @ A3 @ B3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( ! [A3: int] : ( P @ A3 @ A3 )
% 5.44/5.64 => ( ! [A3: int,B3: int] :
% 5.44/5.64 ( ( P @ B3 @ A3 )
% 5.44/5.64 => ( P @ A3 @ B3 ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_wlog
% 5.44/5.64 thf(fact_2813_order_Ostrict__trans,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans
% 5.44/5.64 thf(fact_2814_order_Ostrict__trans,axiom,
% 5.44/5.64 ! [A: real,B: real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ord_less_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans
% 5.44/5.64 thf(fact_2815_order_Ostrict__trans,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_num @ B @ C )
% 5.44/5.64 => ( ord_less_num @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans
% 5.44/5.64 thf(fact_2816_order_Ostrict__trans,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_nat @ B @ C )
% 5.44/5.64 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans
% 5.44/5.64 thf(fact_2817_order_Ostrict__trans,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_int @ B @ C )
% 5.44/5.64 => ( ord_less_int @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans
% 5.44/5.64 thf(fact_2818_not__less__iff__gr__or__eq,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ~ ( ord_le72135733267957522d_enat @ X @ Y ) )
% 5.44/5.64 = ( ( ord_le72135733267957522d_enat @ Y @ X )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_less_iff_gr_or_eq
% 5.44/5.64 thf(fact_2819_not__less__iff__gr__or__eq,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.44/5.64 = ( ( ord_less_real @ Y @ X )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_less_iff_gr_or_eq
% 5.44/5.64 thf(fact_2820_not__less__iff__gr__or__eq,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.44/5.64 = ( ( ord_less_num @ Y @ X )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_less_iff_gr_or_eq
% 5.44/5.64 thf(fact_2821_not__less__iff__gr__or__eq,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.44/5.64 = ( ( ord_less_nat @ Y @ X )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_less_iff_gr_or_eq
% 5.44/5.64 thf(fact_2822_not__less__iff__gr__or__eq,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.44/5.64 = ( ( ord_less_int @ Y @ X )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_less_iff_gr_or_eq
% 5.44/5.64 thf(fact_2823_dual__order_Ostrict__trans,axiom,
% 5.44/5.64 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans
% 5.44/5.64 thf(fact_2824_dual__order_Ostrict__trans,axiom,
% 5.44/5.64 ! [B: real,A: real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ B @ A )
% 5.44/5.64 => ( ( ord_less_real @ C @ B )
% 5.44/5.64 => ( ord_less_real @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans
% 5.44/5.64 thf(fact_2825_dual__order_Ostrict__trans,axiom,
% 5.44/5.64 ! [B: num,A: num,C: num] :
% 5.44/5.64 ( ( ord_less_num @ B @ A )
% 5.44/5.64 => ( ( ord_less_num @ C @ B )
% 5.44/5.64 => ( ord_less_num @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans
% 5.44/5.64 thf(fact_2826_dual__order_Ostrict__trans,axiom,
% 5.44/5.64 ! [B: nat,A: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_nat @ C @ B )
% 5.44/5.64 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans
% 5.44/5.64 thf(fact_2827_dual__order_Ostrict__trans,axiom,
% 5.44/5.64 ! [B: int,A: int,C: int] :
% 5.44/5.64 ( ( ord_less_int @ B @ A )
% 5.44/5.64 => ( ( ord_less_int @ C @ B )
% 5.44/5.64 => ( ord_less_int @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans
% 5.44/5.64 thf(fact_2828_order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2829_order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2830_order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2831_order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2832_order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2833_dual__order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [B: extended_enat,A: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2834_dual__order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [B: real,A: real] :
% 5.44/5.64 ( ( ord_less_real @ B @ A )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2835_dual__order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [B: num,A: num] :
% 5.44/5.64 ( ( ord_less_num @ B @ A )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2836_dual__order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [B: nat,A: nat] :
% 5.44/5.64 ( ( ord_less_nat @ B @ A )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2837_dual__order_Ostrict__implies__not__eq,axiom,
% 5.44/5.64 ! [B: int,A: int] :
% 5.44/5.64 ( ( ord_less_int @ B @ A )
% 5.44/5.64 => ( A != B ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_not_eq
% 5.44/5.64 thf(fact_2838_linorder__neqE,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 => ( ~ ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neqE
% 5.44/5.64 thf(fact_2839_linorder__neqE,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 => ( ~ ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neqE
% 5.44/5.64 thf(fact_2840_linorder__neqE,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 => ( ~ ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neqE
% 5.44/5.64 thf(fact_2841_linorder__neqE,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 => ( ~ ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neqE
% 5.44/5.64 thf(fact_2842_linorder__neqE,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 => ( ~ ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neqE
% 5.44/5.64 thf(fact_2843_order__less__asym,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ~ ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym
% 5.44/5.64 thf(fact_2844_order__less__asym,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym
% 5.44/5.64 thf(fact_2845_order__less__asym,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym
% 5.44/5.64 thf(fact_2846_order__less__asym,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym
% 5.44/5.64 thf(fact_2847_order__less__asym,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym
% 5.44/5.64 thf(fact_2848_linorder__neq__iff,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 = ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 | ( ord_le72135733267957522d_enat @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neq_iff
% 5.44/5.64 thf(fact_2849_linorder__neq__iff,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 = ( ( ord_less_real @ X @ Y )
% 5.44/5.64 | ( ord_less_real @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neq_iff
% 5.44/5.64 thf(fact_2850_linorder__neq__iff,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 = ( ( ord_less_num @ X @ Y )
% 5.44/5.64 | ( ord_less_num @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neq_iff
% 5.44/5.64 thf(fact_2851_linorder__neq__iff,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 = ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 | ( ord_less_nat @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neq_iff
% 5.44/5.64 thf(fact_2852_linorder__neq__iff,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( X != Y )
% 5.44/5.64 = ( ( ord_less_int @ X @ Y )
% 5.44/5.64 | ( ord_less_int @ Y @ X ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_neq_iff
% 5.44/5.64 thf(fact_2853_order__less__asym_H,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ~ ( ord_le72135733267957522d_enat @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym'
% 5.44/5.64 thf(fact_2854_order__less__asym_H,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym'
% 5.44/5.64 thf(fact_2855_order__less__asym_H,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym'
% 5.44/5.64 thf(fact_2856_order__less__asym_H,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym'
% 5.44/5.64 thf(fact_2857_order__less__asym_H,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_asym'
% 5.44/5.64 thf(fact_2858_order__less__trans,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ Y @ Z )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_trans
% 5.44/5.64 thf(fact_2859_order__less__trans,axiom,
% 5.44/5.64 ! [X: real,Y: real,Z: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_real @ Y @ Z )
% 5.44/5.64 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_trans
% 5.44/5.64 thf(fact_2860_order__less__trans,axiom,
% 5.44/5.64 ! [X: num,Y: num,Z: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( ( ord_less_num @ Y @ Z )
% 5.44/5.64 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_trans
% 5.44/5.64 thf(fact_2861_order__less__trans,axiom,
% 5.44/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_nat @ Y @ Z )
% 5.44/5.64 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_trans
% 5.44/5.64 thf(fact_2862_order__less__trans,axiom,
% 5.44/5.64 ! [X: int,Y: int,Z: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( ( ord_less_int @ Y @ Z )
% 5.44/5.64 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_trans
% 5.44/5.64 thf(fact_2863_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: extended_enat,F: extended_enat > extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2864_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: real,F: extended_enat > real,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2865_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: num,F: extended_enat > num,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2866_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: nat,F: extended_enat > nat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2867_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: int,F: extended_enat > int,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2868_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: extended_enat,F: real > extended_enat,B: real,C: real] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2869_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: real,F: real > real,B: real,C: real] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2870_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: num,F: real > num,B: real,C: real] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2871_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2872_ord__eq__less__subst,axiom,
% 5.44/5.64 ! [A: int,F: real > int,B: real,C: real] :
% 5.44/5.64 ( ( A
% 5.44/5.64 = ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_eq_less_subst
% 5.44/5.64 thf(fact_2873_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2874_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > real,C: real] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2875_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > num,C: num] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2876_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > nat,C: nat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2877_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > int,C: int] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2878_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2879_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2880_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > num,C: num] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2881_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2882_ord__less__eq__subst,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > int,C: int] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ( F @ B )
% 5.44/5.64 = C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % ord_less_eq_subst
% 5.44/5.64 thf(fact_2883_order__less__irrefl,axiom,
% 5.44/5.64 ! [X: extended_enat] :
% 5.44/5.64 ~ ( ord_le72135733267957522d_enat @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_irrefl
% 5.44/5.64 thf(fact_2884_order__less__irrefl,axiom,
% 5.44/5.64 ! [X: real] :
% 5.44/5.64 ~ ( ord_less_real @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_irrefl
% 5.44/5.64 thf(fact_2885_order__less__irrefl,axiom,
% 5.44/5.64 ! [X: num] :
% 5.44/5.64 ~ ( ord_less_num @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_irrefl
% 5.44/5.64 thf(fact_2886_order__less__irrefl,axiom,
% 5.44/5.64 ! [X: nat] :
% 5.44/5.64 ~ ( ord_less_nat @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_irrefl
% 5.44/5.64 thf(fact_2887_order__less__irrefl,axiom,
% 5.44/5.64 ! [X: int] :
% 5.44/5.64 ~ ( ord_less_int @ X @ X ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_irrefl
% 5.44/5.64 thf(fact_2888_order__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: extended_enat > extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2889_order__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: real > extended_enat,B: real,C: real] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2890_order__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: num > extended_enat,B: num,C: num] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2891_order__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: nat > extended_enat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2892_order__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: int > extended_enat,B: int,C: int] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2893_order__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: extended_enat > real,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2894_order__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: real > real,B: real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2895_order__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: num > real,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2896_order__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2897_order__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: int > real,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst1
% 5.44/5.64 thf(fact_2898_order__less__subst2,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2899_order__less__subst2,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > real,C: real] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2900_order__less__subst2,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > num,C: num] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2901_order__less__subst2,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > nat,C: nat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2902_order__less__subst2,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > int,C: int] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2903_order__less__subst2,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2904_order__less__subst2,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2905_order__less__subst2,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > num,C: num] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2906_order__less__subst2,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2907_order__less__subst2,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > int,C: int] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_subst2
% 5.44/5.64 thf(fact_2908_order__less__not__sym,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ~ ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_not_sym
% 5.44/5.64 thf(fact_2909_order__less__not__sym,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_not_sym
% 5.44/5.64 thf(fact_2910_order__less__not__sym,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_not_sym
% 5.44/5.64 thf(fact_2911_order__less__not__sym,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_not_sym
% 5.44/5.64 thf(fact_2912_order__less__not__sym,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_not_sym
% 5.44/5.64 thf(fact_2913_order__less__imp__triv,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat,P: $o] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ Y @ X )
% 5.44/5.64 => P ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_triv
% 5.44/5.64 thf(fact_2914_order__less__imp__triv,axiom,
% 5.44/5.64 ! [X: real,Y: real,P: $o] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_real @ Y @ X )
% 5.44/5.64 => P ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_triv
% 5.44/5.64 thf(fact_2915_order__less__imp__triv,axiom,
% 5.44/5.64 ! [X: num,Y: num,P: $o] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( ( ord_less_num @ Y @ X )
% 5.44/5.64 => P ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_triv
% 5.44/5.64 thf(fact_2916_order__less__imp__triv,axiom,
% 5.44/5.64 ! [X: nat,Y: nat,P: $o] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_nat @ Y @ X )
% 5.44/5.64 => P ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_triv
% 5.44/5.64 thf(fact_2917_order__less__imp__triv,axiom,
% 5.44/5.64 ! [X: int,Y: int,P: $o] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( ( ord_less_int @ Y @ X )
% 5.44/5.64 => P ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_triv
% 5.44/5.64 thf(fact_2918_linorder__less__linear,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 | ( X = Y )
% 5.44/5.64 | ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_linear
% 5.44/5.64 thf(fact_2919_linorder__less__linear,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 | ( X = Y )
% 5.44/5.64 | ( ord_less_real @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_linear
% 5.44/5.64 thf(fact_2920_linorder__less__linear,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 | ( X = Y )
% 5.44/5.64 | ( ord_less_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_linear
% 5.44/5.64 thf(fact_2921_linorder__less__linear,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 | ( X = Y )
% 5.44/5.64 | ( ord_less_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_linear
% 5.44/5.64 thf(fact_2922_linorder__less__linear,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 | ( X = Y )
% 5.44/5.64 | ( ord_less_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_less_linear
% 5.44/5.64 thf(fact_2923_order__less__imp__not__eq,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq
% 5.44/5.64 thf(fact_2924_order__less__imp__not__eq,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq
% 5.44/5.64 thf(fact_2925_order__less__imp__not__eq,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq
% 5.44/5.64 thf(fact_2926_order__less__imp__not__eq,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq
% 5.44/5.64 thf(fact_2927_order__less__imp__not__eq,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( X != Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq
% 5.44/5.64 thf(fact_2928_order__less__imp__not__eq2,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( Y != X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq2
% 5.44/5.64 thf(fact_2929_order__less__imp__not__eq2,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( Y != X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq2
% 5.44/5.64 thf(fact_2930_order__less__imp__not__eq2,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( Y != X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq2
% 5.44/5.64 thf(fact_2931_order__less__imp__not__eq2,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( Y != X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq2
% 5.44/5.64 thf(fact_2932_order__less__imp__not__eq2,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( Y != X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_eq2
% 5.44/5.64 thf(fact_2933_order__less__imp__not__less,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ~ ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_less
% 5.44/5.64 thf(fact_2934_order__less__imp__not__less,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_less
% 5.44/5.64 thf(fact_2935_order__less__imp__not__less,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_less
% 5.44/5.64 thf(fact_2936_order__less__imp__not__less,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_less
% 5.44/5.64 thf(fact_2937_order__less__imp__not__less,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_not_less
% 5.44/5.64 thf(fact_2938_subset__iff__psubset__eq,axiom,
% 5.44/5.64 ( ord_less_eq_set_real
% 5.44/5.64 = ( ^ [A5: set_real,B5: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ A5 @ B5 )
% 5.44/5.64 | ( A5 = B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_iff_psubset_eq
% 5.44/5.64 thf(fact_2939_subset__iff__psubset__eq,axiom,
% 5.44/5.64 ( ord_less_eq_set_nat
% 5.44/5.64 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ A5 @ B5 )
% 5.44/5.64 | ( A5 = B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_iff_psubset_eq
% 5.44/5.64 thf(fact_2940_subset__psubset__trans,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real,C4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_set_real @ B2 @ C4 )
% 5.44/5.64 => ( ord_less_set_real @ A2 @ C4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_psubset_trans
% 5.44/5.64 thf(fact_2941_subset__psubset__trans,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat,C4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_set_nat @ B2 @ C4 )
% 5.44/5.64 => ( ord_less_set_nat @ A2 @ C4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_psubset_trans
% 5.44/5.64 thf(fact_2942_subset__not__subset__eq,axiom,
% 5.44/5.64 ( ord_less_set_real
% 5.44/5.64 = ( ^ [A5: set_real,B5: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A5 @ B5 )
% 5.44/5.64 & ~ ( ord_less_eq_set_real @ B5 @ A5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_not_subset_eq
% 5.44/5.64 thf(fact_2943_subset__not__subset__eq,axiom,
% 5.44/5.64 ( ord_less_set_nat
% 5.44/5.64 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 5.44/5.64 & ~ ( ord_less_eq_set_nat @ B5 @ A5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_not_subset_eq
% 5.44/5.64 thf(fact_2944_psubset__subset__trans,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real,C4: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.64 => ( ord_less_set_real @ A2 @ C4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubset_subset_trans
% 5.44/5.64 thf(fact_2945_psubset__subset__trans,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat,C4: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ B2 @ C4 )
% 5.44/5.64 => ( ord_less_set_nat @ A2 @ C4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubset_subset_trans
% 5.44/5.64 thf(fact_2946_psubset__imp__subset,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubset_imp_subset
% 5.44/5.64 thf(fact_2947_psubset__imp__subset,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubset_imp_subset
% 5.44/5.64 thf(fact_2948_Collect__mono__iff,axiom,
% 5.44/5.64 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.44/5.64 ( ( ord_le3146513528884898305at_nat @ ( collec3392354462482085612at_nat @ P ) @ ( collec3392354462482085612at_nat @ Q ) )
% 5.44/5.64 = ( ! [X2: product_prod_nat_nat] :
% 5.44/5.64 ( ( P @ X2 )
% 5.44/5.64 => ( Q @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono_iff
% 5.44/5.64 thf(fact_2949_Collect__mono__iff,axiom,
% 5.44/5.64 ! [P: complex > $o,Q: complex > $o] :
% 5.44/5.64 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 5.44/5.64 = ( ! [X2: complex] :
% 5.44/5.64 ( ( P @ X2 )
% 5.44/5.64 => ( Q @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono_iff
% 5.44/5.64 thf(fact_2950_Collect__mono__iff,axiom,
% 5.44/5.64 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.44/5.64 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.44/5.64 = ( ! [X2: list_nat] :
% 5.44/5.64 ( ( P @ X2 )
% 5.44/5.64 => ( Q @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono_iff
% 5.44/5.64 thf(fact_2951_Collect__mono__iff,axiom,
% 5.44/5.64 ! [P: real > $o,Q: real > $o] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 5.44/5.64 = ( ! [X2: real] :
% 5.44/5.64 ( ( P @ X2 )
% 5.44/5.64 => ( Q @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono_iff
% 5.44/5.64 thf(fact_2952_Collect__mono__iff,axiom,
% 5.44/5.64 ! [P: nat > $o,Q: nat > $o] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.44/5.64 = ( ! [X2: nat] :
% 5.44/5.64 ( ( P @ X2 )
% 5.44/5.64 => ( Q @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono_iff
% 5.44/5.64 thf(fact_2953_set__eq__subset,axiom,
% 5.44/5.64 ( ( ^ [Y4: set_real,Z2: set_real] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A5: set_real,B5: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A5 @ B5 )
% 5.44/5.64 & ( ord_less_eq_set_real @ B5 @ A5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % set_eq_subset
% 5.44/5.64 thf(fact_2954_set__eq__subset,axiom,
% 5.44/5.64 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 5.44/5.64 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 5.44/5.64 & ( ord_less_eq_set_nat @ B5 @ A5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % set_eq_subset
% 5.44/5.64 thf(fact_2955_subset__trans,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real,C4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.64 => ( ord_less_eq_set_real @ A2 @ C4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_trans
% 5.44/5.64 thf(fact_2956_subset__trans,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat,C4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ B2 @ C4 )
% 5.44/5.64 => ( ord_less_eq_set_nat @ A2 @ C4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_trans
% 5.44/5.64 thf(fact_2957_Collect__mono,axiom,
% 5.44/5.64 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.44/5.64 ( ! [X5: product_prod_nat_nat] :
% 5.44/5.64 ( ( P @ X5 )
% 5.44/5.64 => ( Q @ X5 ) )
% 5.44/5.64 => ( ord_le3146513528884898305at_nat @ ( collec3392354462482085612at_nat @ P ) @ ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono
% 5.44/5.64 thf(fact_2958_Collect__mono,axiom,
% 5.44/5.64 ! [P: complex > $o,Q: complex > $o] :
% 5.44/5.64 ( ! [X5: complex] :
% 5.44/5.64 ( ( P @ X5 )
% 5.44/5.64 => ( Q @ X5 ) )
% 5.44/5.64 => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono
% 5.44/5.64 thf(fact_2959_Collect__mono,axiom,
% 5.44/5.64 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.44/5.64 ( ! [X5: list_nat] :
% 5.44/5.64 ( ( P @ X5 )
% 5.44/5.64 => ( Q @ X5 ) )
% 5.44/5.64 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono
% 5.44/5.64 thf(fact_2960_Collect__mono,axiom,
% 5.44/5.64 ! [P: real > $o,Q: real > $o] :
% 5.44/5.64 ( ! [X5: real] :
% 5.44/5.64 ( ( P @ X5 )
% 5.44/5.64 => ( Q @ X5 ) )
% 5.44/5.64 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono
% 5.44/5.64 thf(fact_2961_Collect__mono,axiom,
% 5.44/5.64 ! [P: nat > $o,Q: nat > $o] :
% 5.44/5.64 ( ! [X5: nat] :
% 5.44/5.64 ( ( P @ X5 )
% 5.44/5.64 => ( Q @ X5 ) )
% 5.44/5.64 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_mono
% 5.44/5.64 thf(fact_2962_subset__refl,axiom,
% 5.44/5.64 ! [A2: set_real] : ( ord_less_eq_set_real @ A2 @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % subset_refl
% 5.44/5.64 thf(fact_2963_subset__refl,axiom,
% 5.44/5.64 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % subset_refl
% 5.44/5.64 thf(fact_2964_subset__iff,axiom,
% 5.44/5.64 ( ord_less_eq_set_int
% 5.44/5.64 = ( ^ [A5: set_int,B5: set_int] :
% 5.44/5.64 ! [T2: int] :
% 5.44/5.64 ( ( member_int @ T2 @ A5 )
% 5.44/5.64 => ( member_int @ T2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_iff
% 5.44/5.64 thf(fact_2965_subset__iff,axiom,
% 5.44/5.64 ( ord_le211207098394363844omplex
% 5.44/5.64 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.44/5.64 ! [T2: complex] :
% 5.44/5.64 ( ( member_complex @ T2 @ A5 )
% 5.44/5.64 => ( member_complex @ T2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_iff
% 5.44/5.64 thf(fact_2966_subset__iff,axiom,
% 5.44/5.64 ( ord_le3146513528884898305at_nat
% 5.44/5.64 = ( ^ [A5: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.44/5.64 ! [T2: product_prod_nat_nat] :
% 5.44/5.64 ( ( member8440522571783428010at_nat @ T2 @ A5 )
% 5.44/5.64 => ( member8440522571783428010at_nat @ T2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_iff
% 5.44/5.64 thf(fact_2967_subset__iff,axiom,
% 5.44/5.64 ( ord_less_eq_set_real
% 5.44/5.64 = ( ^ [A5: set_real,B5: set_real] :
% 5.44/5.64 ! [T2: real] :
% 5.44/5.64 ( ( member_real @ T2 @ A5 )
% 5.44/5.64 => ( member_real @ T2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_iff
% 5.44/5.64 thf(fact_2968_subset__iff,axiom,
% 5.44/5.64 ( ord_less_eq_set_nat
% 5.44/5.64 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.44/5.64 ! [T2: nat] :
% 5.44/5.64 ( ( member_nat @ T2 @ A5 )
% 5.44/5.64 => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_iff
% 5.44/5.64 thf(fact_2969_psubset__eq,axiom,
% 5.44/5.64 ( ord_less_set_real
% 5.44/5.64 = ( ^ [A5: set_real,B5: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A5 @ B5 )
% 5.44/5.64 & ( A5 != B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubset_eq
% 5.44/5.64 thf(fact_2970_psubset__eq,axiom,
% 5.44/5.64 ( ord_less_set_nat
% 5.44/5.64 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 5.44/5.64 & ( A5 != B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubset_eq
% 5.44/5.64 thf(fact_2971_equalityD2,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ( A2 = B2 )
% 5.44/5.64 => ( ord_less_eq_set_real @ B2 @ A2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % equalityD2
% 5.44/5.64 thf(fact_2972_equalityD2,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( A2 = B2 )
% 5.44/5.64 => ( ord_less_eq_set_nat @ B2 @ A2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % equalityD2
% 5.44/5.64 thf(fact_2973_equalityD1,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ( A2 = B2 )
% 5.44/5.64 => ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % equalityD1
% 5.44/5.64 thf(fact_2974_equalityD1,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( A2 = B2 )
% 5.44/5.64 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 5.44/5.64
% 5.44/5.64 % equalityD1
% 5.44/5.64 thf(fact_2975_subset__eq,axiom,
% 5.44/5.64 ( ord_less_eq_set_int
% 5.44/5.64 = ( ^ [A5: set_int,B5: set_int] :
% 5.44/5.64 ! [X2: int] :
% 5.44/5.64 ( ( member_int @ X2 @ A5 )
% 5.44/5.64 => ( member_int @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_eq
% 5.44/5.64 thf(fact_2976_subset__eq,axiom,
% 5.44/5.64 ( ord_le211207098394363844omplex
% 5.44/5.64 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.44/5.64 ! [X2: complex] :
% 5.44/5.64 ( ( member_complex @ X2 @ A5 )
% 5.44/5.64 => ( member_complex @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_eq
% 5.44/5.64 thf(fact_2977_subset__eq,axiom,
% 5.44/5.64 ( ord_le3146513528884898305at_nat
% 5.44/5.64 = ( ^ [A5: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.44/5.64 ! [X2: product_prod_nat_nat] :
% 5.44/5.64 ( ( member8440522571783428010at_nat @ X2 @ A5 )
% 5.44/5.64 => ( member8440522571783428010at_nat @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_eq
% 5.44/5.64 thf(fact_2978_subset__eq,axiom,
% 5.44/5.64 ( ord_less_eq_set_real
% 5.44/5.64 = ( ^ [A5: set_real,B5: set_real] :
% 5.44/5.64 ! [X2: real] :
% 5.44/5.64 ( ( member_real @ X2 @ A5 )
% 5.44/5.64 => ( member_real @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_eq
% 5.44/5.64 thf(fact_2979_subset__eq,axiom,
% 5.44/5.64 ( ord_less_eq_set_nat
% 5.44/5.64 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.44/5.64 ! [X2: nat] :
% 5.44/5.64 ( ( member_nat @ X2 @ A5 )
% 5.44/5.64 => ( member_nat @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subset_eq
% 5.44/5.64 thf(fact_2980_equalityE,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ( A2 = B2 )
% 5.44/5.64 => ~ ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ~ ( ord_less_eq_set_real @ B2 @ A2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % equalityE
% 5.44/5.64 thf(fact_2981_equalityE,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( A2 = B2 )
% 5.44/5.64 => ~ ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ~ ( ord_less_eq_set_nat @ B2 @ A2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % equalityE
% 5.44/5.64 thf(fact_2982_psubsetE,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ A2 @ B2 )
% 5.44/5.64 => ~ ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ord_less_eq_set_real @ B2 @ A2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubsetE
% 5.44/5.64 thf(fact_2983_psubsetE,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ A2 @ B2 )
% 5.44/5.64 => ~ ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ord_less_eq_set_nat @ B2 @ A2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % psubsetE
% 5.44/5.64 thf(fact_2984_subsetD,axiom,
% 5.44/5.64 ! [A2: set_int,B2: set_int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.64 => ( ( member_int @ C @ A2 )
% 5.44/5.64 => ( member_int @ C @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetD
% 5.44/5.64 thf(fact_2985_subsetD,axiom,
% 5.44/5.64 ! [A2: set_complex,B2: set_complex,C: complex] :
% 5.44/5.64 ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.64 => ( ( member_complex @ C @ A2 )
% 5.44/5.64 => ( member_complex @ C @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetD
% 5.44/5.64 thf(fact_2986_subsetD,axiom,
% 5.44/5.64 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.44/5.64 ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.44/5.64 => ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetD
% 5.44/5.64 thf(fact_2987_subsetD,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real,C: real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ( member_real @ C @ A2 )
% 5.44/5.64 => ( member_real @ C @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetD
% 5.44/5.64 thf(fact_2988_subsetD,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( member_nat @ C @ A2 )
% 5.44/5.64 => ( member_nat @ C @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % subsetD
% 5.44/5.64 thf(fact_2989_in__mono,axiom,
% 5.44/5.64 ! [A2: set_int,B2: set_int,X: int] :
% 5.44/5.64 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.64 => ( ( member_int @ X @ A2 )
% 5.44/5.64 => ( member_int @ X @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % in_mono
% 5.44/5.64 thf(fact_2990_in__mono,axiom,
% 5.44/5.64 ! [A2: set_complex,B2: set_complex,X: complex] :
% 5.44/5.64 ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.64 => ( ( member_complex @ X @ A2 )
% 5.44/5.64 => ( member_complex @ X @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % in_mono
% 5.44/5.64 thf(fact_2991_in__mono,axiom,
% 5.44/5.64 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 5.44/5.64 ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.44/5.64 => ( member8440522571783428010at_nat @ X @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % in_mono
% 5.44/5.64 thf(fact_2992_in__mono,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real,X: real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ( member_real @ X @ A2 )
% 5.44/5.64 => ( member_real @ X @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % in_mono
% 5.44/5.64 thf(fact_2993_in__mono,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat,X: nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( member_nat @ X @ A2 )
% 5.44/5.64 => ( member_nat @ X @ B2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % in_mono
% 5.44/5.64 thf(fact_2994_double__diff,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real,C4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.64 => ( ( minus_minus_set_real @ B2 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.44/5.64 = A2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % double_diff
% 5.44/5.64 thf(fact_2995_double__diff,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat,C4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ B2 @ C4 )
% 5.44/5.64 => ( ( minus_minus_set_nat @ B2 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.44/5.64 = A2 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % double_diff
% 5.44/5.64 thf(fact_2996_Diff__subset,axiom,
% 5.44/5.64 ! [A2: set_real,B2: set_real] : ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % Diff_subset
% 5.44/5.64 thf(fact_2997_Diff__subset,axiom,
% 5.44/5.64 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % Diff_subset
% 5.44/5.64 thf(fact_2998_Diff__mono,axiom,
% 5.44/5.64 ! [A2: set_real,C4: set_real,D4: set_real,B2: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ D4 @ B2 )
% 5.44/5.64 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ ( minus_minus_set_real @ C4 @ D4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Diff_mono
% 5.44/5.64 thf(fact_2999_Diff__mono,axiom,
% 5.44/5.64 ! [A2: set_nat,C4: set_nat,D4: set_nat,B2: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ D4 @ B2 )
% 5.44/5.64 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Diff_mono
% 5.44/5.64 thf(fact_3000_not__exp__less__eq__0__int,axiom,
% 5.44/5.64 ! [N2: nat] :
% 5.44/5.64 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 5.44/5.64
% 5.44/5.64 % not_exp_less_eq_0_int
% 5.44/5.64 thf(fact_3001_realpow__pos__nth2,axiom,
% 5.44/5.64 ! [A: real,N2: nat] :
% 5.44/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.64 => ? [R3: real] :
% 5.44/5.64 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.44/5.64 & ( ( power_power_real @ R3 @ ( suc @ N2 ) )
% 5.44/5.64 = A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % realpow_pos_nth2
% 5.44/5.64 thf(fact_3002_real__arch__pow__inv,axiom,
% 5.44/5.64 ! [Y: real,X: real] :
% 5.44/5.64 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.64 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.64 => ? [N4: nat] : ( ord_less_real @ ( power_power_real @ X @ N4 ) @ Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % real_arch_pow_inv
% 5.44/5.64 thf(fact_3003_vebt__buildup_Osimps_I2_J,axiom,
% 5.44/5.64 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.44/5.64 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_buildup.simps(2)
% 5.44/5.64 thf(fact_3004_realpow__pos__nth,axiom,
% 5.44/5.64 ! [N2: nat,A: real] :
% 5.44/5.64 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.64 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.64 => ? [R3: real] :
% 5.44/5.64 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.44/5.64 & ( ( power_power_real @ R3 @ N2 )
% 5.44/5.64 = A ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % realpow_pos_nth
% 5.44/5.64 thf(fact_3005_realpow__pos__nth__unique,axiom,
% 5.44/5.64 ! [N2: nat,A: real] :
% 5.44/5.64 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.64 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.64 => ? [X5: real] :
% 5.44/5.64 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.44/5.64 & ( ( power_power_real @ X5 @ N2 )
% 5.44/5.64 = A )
% 5.44/5.64 & ! [Y2: real] :
% 5.44/5.64 ( ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.44/5.64 & ( ( power_power_real @ Y2 @ N2 )
% 5.44/5.64 = A ) )
% 5.44/5.64 => ( Y2 = X5 ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % realpow_pos_nth_unique
% 5.44/5.64 thf(fact_3006_neg__zdiv__mult__2,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.64 => ( ( 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 ) )
% 5.44/5.64 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % neg_zdiv_mult_2
% 5.44/5.64 thf(fact_3007_pos__zdiv__mult__2,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.64 => ( ( 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 ) )
% 5.44/5.64 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % pos_zdiv_mult_2
% 5.44/5.64 thf(fact_3008_less__eq__set__def,axiom,
% 5.44/5.64 ( ord_less_eq_set_int
% 5.44/5.64 = ( ^ [A5: set_int,B5: set_int] :
% 5.44/5.64 ( ord_less_eq_int_o
% 5.44/5.64 @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 5.44/5.64 @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_eq_set_def
% 5.44/5.64 thf(fact_3009_less__eq__set__def,axiom,
% 5.44/5.64 ( ord_le211207098394363844omplex
% 5.44/5.64 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.44/5.64 ( ord_le4573692005234683329plex_o
% 5.44/5.64 @ ^ [X2: complex] : ( member_complex @ X2 @ A5 )
% 5.44/5.64 @ ^ [X2: complex] : ( member_complex @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_eq_set_def
% 5.44/5.64 thf(fact_3010_less__eq__set__def,axiom,
% 5.44/5.64 ( ord_le3146513528884898305at_nat
% 5.44/5.64 = ( ^ [A5: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.44/5.64 ( ord_le704812498762024988_nat_o
% 5.44/5.64 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A5 )
% 5.44/5.64 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_eq_set_def
% 5.44/5.64 thf(fact_3011_less__eq__set__def,axiom,
% 5.44/5.64 ( ord_less_eq_set_real
% 5.44/5.64 = ( ^ [A5: set_real,B5: set_real] :
% 5.44/5.64 ( ord_less_eq_real_o
% 5.44/5.64 @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 5.44/5.64 @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_eq_set_def
% 5.44/5.64 thf(fact_3012_less__eq__set__def,axiom,
% 5.44/5.64 ( ord_less_eq_set_nat
% 5.44/5.64 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.44/5.64 ( ord_less_eq_nat_o
% 5.44/5.64 @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 5.44/5.64 @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_eq_set_def
% 5.44/5.64 thf(fact_3013_Collect__subset,axiom,
% 5.44/5.64 ! [A2: set_int,P: int > $o] :
% 5.44/5.64 ( ord_less_eq_set_int
% 5.44/5.64 @ ( collect_int
% 5.44/5.64 @ ^ [X2: int] :
% 5.44/5.64 ( ( member_int @ X2 @ A2 )
% 5.44/5.64 & ( P @ X2 ) ) )
% 5.44/5.64 @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_subset
% 5.44/5.64 thf(fact_3014_Collect__subset,axiom,
% 5.44/5.64 ! [A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.44/5.64 ( ord_le3146513528884898305at_nat
% 5.44/5.64 @ ( collec3392354462482085612at_nat
% 5.44/5.64 @ ^ [X2: product_prod_nat_nat] :
% 5.44/5.64 ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 5.44/5.64 & ( P @ X2 ) ) )
% 5.44/5.64 @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_subset
% 5.44/5.64 thf(fact_3015_Collect__subset,axiom,
% 5.44/5.64 ! [A2: set_complex,P: complex > $o] :
% 5.44/5.64 ( ord_le211207098394363844omplex
% 5.44/5.64 @ ( collect_complex
% 5.44/5.64 @ ^ [X2: complex] :
% 5.44/5.64 ( ( member_complex @ X2 @ A2 )
% 5.44/5.64 & ( P @ X2 ) ) )
% 5.44/5.64 @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_subset
% 5.44/5.64 thf(fact_3016_Collect__subset,axiom,
% 5.44/5.64 ! [A2: set_list_nat,P: list_nat > $o] :
% 5.44/5.64 ( ord_le6045566169113846134st_nat
% 5.44/5.64 @ ( collect_list_nat
% 5.44/5.64 @ ^ [X2: list_nat] :
% 5.44/5.64 ( ( member_list_nat @ X2 @ A2 )
% 5.44/5.64 & ( P @ X2 ) ) )
% 5.44/5.64 @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_subset
% 5.44/5.64 thf(fact_3017_Collect__subset,axiom,
% 5.44/5.64 ! [A2: set_real,P: real > $o] :
% 5.44/5.64 ( ord_less_eq_set_real
% 5.44/5.64 @ ( collect_real
% 5.44/5.64 @ ^ [X2: real] :
% 5.44/5.64 ( ( member_real @ X2 @ A2 )
% 5.44/5.64 & ( P @ X2 ) ) )
% 5.44/5.64 @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_subset
% 5.44/5.64 thf(fact_3018_Collect__subset,axiom,
% 5.44/5.64 ! [A2: set_nat,P: nat > $o] :
% 5.44/5.64 ( ord_less_eq_set_nat
% 5.44/5.64 @ ( collect_nat
% 5.44/5.64 @ ^ [X2: nat] :
% 5.44/5.64 ( ( member_nat @ X2 @ A2 )
% 5.44/5.64 & ( P @ X2 ) ) )
% 5.44/5.64 @ A2 ) ).
% 5.44/5.64
% 5.44/5.64 % Collect_subset
% 5.44/5.64 thf(fact_3019_int__power__div__base,axiom,
% 5.44/5.64 ! [M: nat,K: int] :
% 5.44/5.64 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.64 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.44/5.64 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.44/5.64 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % int_power_div_base
% 5.44/5.64 thf(fact_3020_leD,axiom,
% 5.44/5.64 ! [Y: extended_enat,X: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ Y @ X )
% 5.44/5.64 => ~ ( ord_le72135733267957522d_enat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % leD
% 5.44/5.64 thf(fact_3021_leD,axiom,
% 5.44/5.64 ! [Y: real,X: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % leD
% 5.44/5.64 thf(fact_3022_leD,axiom,
% 5.44/5.64 ! [Y: set_real,X: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_set_real @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % leD
% 5.44/5.64 thf(fact_3023_leD,axiom,
% 5.44/5.64 ! [Y: set_nat,X: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % leD
% 5.44/5.64 thf(fact_3024_leD,axiom,
% 5.44/5.64 ! [Y: num,X: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_num @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % leD
% 5.44/5.64 thf(fact_3025_leD,axiom,
% 5.44/5.64 ! [Y: nat,X: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % leD
% 5.44/5.64 thf(fact_3026_leD,axiom,
% 5.44/5.64 ! [Y: int,X: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ Y @ X )
% 5.44/5.64 => ~ ( ord_less_int @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % leD
% 5.44/5.64 thf(fact_3027_leI,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ~ ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( ord_le2932123472753598470d_enat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % leI
% 5.44/5.64 thf(fact_3028_leI,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ~ ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_real @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % leI
% 5.44/5.64 thf(fact_3029_leI,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ~ ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % leI
% 5.44/5.64 thf(fact_3030_leI,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ~ ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % leI
% 5.44/5.64 thf(fact_3031_leI,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ~ ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % leI
% 5.44/5.64 thf(fact_3032_nless__le,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.64 ( ( ~ ( ord_le72135733267957522d_enat @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.64 | ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nless_le
% 5.44/5.64 thf(fact_3033_nless__le,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.44/5.64 | ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nless_le
% 5.44/5.64 thf(fact_3034_nless__le,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real] :
% 5.44/5.64 ( ( ~ ( ord_less_set_real @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 | ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nless_le
% 5.44/5.64 thf(fact_3035_nless__le,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat] :
% 5.44/5.64 ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 | ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nless_le
% 5.44/5.64 thf(fact_3036_nless__le,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.44/5.64 | ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nless_le
% 5.44/5.64 thf(fact_3037_nless__le,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 | ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nless_le
% 5.44/5.64 thf(fact_3038_nless__le,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.44/5.64 | ( A = B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % nless_le
% 5.44/5.64 thf(fact_3039_antisym__conv1,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ~ ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv1
% 5.44/5.64 thf(fact_3040_antisym__conv1,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ~ ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv1
% 5.44/5.64 thf(fact_3041_antisym__conv1,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real] :
% 5.44/5.64 ( ~ ( ord_less_set_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv1
% 5.44/5.64 thf(fact_3042_antisym__conv1,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat] :
% 5.44/5.64 ( ~ ( ord_less_set_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv1
% 5.44/5.64 thf(fact_3043_antisym__conv1,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ~ ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv1
% 5.44/5.64 thf(fact_3044_antisym__conv1,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ~ ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv1
% 5.44/5.64 thf(fact_3045_antisym__conv1,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ~ ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv1
% 5.44/5.64 thf(fact_3046_antisym__conv2,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 5.44/5.64 => ( ( ~ ( ord_le72135733267957522d_enat @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv2
% 5.44/5.64 thf(fact_3047_antisym__conv2,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.64 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv2
% 5.44/5.64 thf(fact_3048_antisym__conv2,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.64 => ( ( ~ ( ord_less_set_real @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv2
% 5.44/5.64 thf(fact_3049_antisym__conv2,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.64 => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv2
% 5.44/5.64 thf(fact_3050_antisym__conv2,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv2
% 5.44/5.64 thf(fact_3051_antisym__conv2,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv2
% 5.44/5.64 thf(fact_3052_antisym__conv2,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.44/5.64 = ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % antisym_conv2
% 5.44/5.64 thf(fact_3053_dense__ge,axiom,
% 5.44/5.64 ! [Z: real,Y: real] :
% 5.44/5.64 ( ! [X5: real] :
% 5.44/5.64 ( ( ord_less_real @ Z @ X5 )
% 5.44/5.64 => ( ord_less_eq_real @ Y @ X5 ) )
% 5.44/5.64 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.44/5.64
% 5.44/5.64 % dense_ge
% 5.44/5.64 thf(fact_3054_dense__le,axiom,
% 5.44/5.64 ! [Y: real,Z: real] :
% 5.44/5.64 ( ! [X5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y )
% 5.44/5.64 => ( ord_less_eq_real @ X5 @ Z ) )
% 5.44/5.64 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.44/5.64
% 5.44/5.64 % dense_le
% 5.44/5.64 thf(fact_3055_less__le__not__le,axiom,
% 5.44/5.64 ( ord_le72135733267957522d_enat
% 5.44/5.64 = ( ^ [X2: extended_enat,Y3: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ X2 @ Y3 )
% 5.44/5.64 & ~ ( ord_le2932123472753598470d_enat @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_le_not_le
% 5.44/5.64 thf(fact_3056_less__le__not__le,axiom,
% 5.44/5.64 ( ord_less_real
% 5.44/5.64 = ( ^ [X2: real,Y3: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.44/5.64 & ~ ( ord_less_eq_real @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_le_not_le
% 5.44/5.64 thf(fact_3057_less__le__not__le,axiom,
% 5.44/5.64 ( ord_less_set_real
% 5.44/5.64 = ( ^ [X2: set_real,Y3: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X2 @ Y3 )
% 5.44/5.64 & ~ ( ord_less_eq_set_real @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_le_not_le
% 5.44/5.64 thf(fact_3058_less__le__not__le,axiom,
% 5.44/5.64 ( ord_less_set_nat
% 5.44/5.64 = ( ^ [X2: set_nat,Y3: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 5.44/5.64 & ~ ( ord_less_eq_set_nat @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_le_not_le
% 5.44/5.64 thf(fact_3059_less__le__not__le,axiom,
% 5.44/5.64 ( ord_less_num
% 5.44/5.64 = ( ^ [X2: num,Y3: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.44/5.64 & ~ ( ord_less_eq_num @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_le_not_le
% 5.44/5.64 thf(fact_3060_less__le__not__le,axiom,
% 5.44/5.64 ( ord_less_nat
% 5.44/5.64 = ( ^ [X2: nat,Y3: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.44/5.64 & ~ ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_le_not_le
% 5.44/5.64 thf(fact_3061_less__le__not__le,axiom,
% 5.44/5.64 ( ord_less_int
% 5.44/5.64 = ( ^ [X2: int,Y3: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.44/5.64 & ~ ( ord_less_eq_int @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % less_le_not_le
% 5.44/5.64 thf(fact_3062_not__le__imp__less,axiom,
% 5.44/5.64 ! [Y: extended_enat,X: extended_enat] :
% 5.44/5.64 ( ~ ( ord_le2932123472753598470d_enat @ Y @ X )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_le_imp_less
% 5.44/5.64 thf(fact_3063_not__le__imp__less,axiom,
% 5.44/5.64 ! [Y: real,X: real] :
% 5.44/5.64 ( ~ ( ord_less_eq_real @ Y @ X )
% 5.44/5.64 => ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_le_imp_less
% 5.44/5.64 thf(fact_3064_not__le__imp__less,axiom,
% 5.44/5.64 ! [Y: num,X: num] :
% 5.44/5.64 ( ~ ( ord_less_eq_num @ Y @ X )
% 5.44/5.64 => ( ord_less_num @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_le_imp_less
% 5.44/5.64 thf(fact_3065_not__le__imp__less,axiom,
% 5.44/5.64 ! [Y: nat,X: nat] :
% 5.44/5.64 ( ~ ( ord_less_eq_nat @ Y @ X )
% 5.44/5.64 => ( ord_less_nat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_le_imp_less
% 5.44/5.64 thf(fact_3066_not__le__imp__less,axiom,
% 5.44/5.64 ! [Y: int,X: int] :
% 5.44/5.64 ( ~ ( ord_less_eq_int @ Y @ X )
% 5.44/5.64 => ( ord_less_int @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % not_le_imp_less
% 5.44/5.64 thf(fact_3067_order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_le2932123472753598470d_enat
% 5.44/5.64 = ( ^ [A4: extended_enat,B4: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A4 @ B4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.order_iff_strict
% 5.44/5.64 thf(fact_3068_order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_real
% 5.44/5.64 = ( ^ [A4: real,B4: real] :
% 5.44/5.64 ( ( ord_less_real @ A4 @ B4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.order_iff_strict
% 5.44/5.64 thf(fact_3069_order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_set_real
% 5.44/5.64 = ( ^ [A4: set_real,B4: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ A4 @ B4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.order_iff_strict
% 5.44/5.64 thf(fact_3070_order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_set_nat
% 5.44/5.64 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ A4 @ B4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.order_iff_strict
% 5.44/5.64 thf(fact_3071_order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_num
% 5.44/5.64 = ( ^ [A4: num,B4: num] :
% 5.44/5.64 ( ( ord_less_num @ A4 @ B4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.order_iff_strict
% 5.44/5.64 thf(fact_3072_order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_nat
% 5.44/5.64 = ( ^ [A4: nat,B4: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A4 @ B4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.order_iff_strict
% 5.44/5.64 thf(fact_3073_order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_int
% 5.44/5.64 = ( ^ [A4: int,B4: int] :
% 5.44/5.64 ( ( ord_less_int @ A4 @ B4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.order_iff_strict
% 5.44/5.64 thf(fact_3074_order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_le72135733267957522d_enat
% 5.44/5.64 = ( ^ [A4: extended_enat,B4: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A4 @ B4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_order
% 5.44/5.64 thf(fact_3075_order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_real
% 5.44/5.64 = ( ^ [A4: real,B4: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ A4 @ B4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_order
% 5.44/5.64 thf(fact_3076_order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_set_real
% 5.44/5.64 = ( ^ [A4: set_real,B4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_order
% 5.44/5.64 thf(fact_3077_order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_set_nat
% 5.44/5.64 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_order
% 5.44/5.64 thf(fact_3078_order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_num
% 5.44/5.64 = ( ^ [A4: num,B4: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_order
% 5.44/5.64 thf(fact_3079_order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_nat
% 5.44/5.64 = ( ^ [A4: nat,B4: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_order
% 5.44/5.64 thf(fact_3080_order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_int
% 5.44/5.64 = ( ^ [A4: int,B4: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_order
% 5.44/5.64 thf(fact_3081_order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans1
% 5.44/5.64 thf(fact_3082_order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [A: real,B: real,C: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ord_less_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans1
% 5.44/5.64 thf(fact_3083_order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,C: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_set_real @ B @ C )
% 5.44/5.64 => ( ord_less_set_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans1
% 5.44/5.64 thf(fact_3084_order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_set_nat @ B @ C )
% 5.44/5.64 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans1
% 5.44/5.64 thf(fact_3085_order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_num @ B @ C )
% 5.44/5.64 => ( ord_less_num @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans1
% 5.44/5.64 thf(fact_3086_order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_nat @ B @ C )
% 5.44/5.64 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans1
% 5.44/5.64 thf(fact_3087_order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_int @ B @ C )
% 5.44/5.64 => ( ord_less_int @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans1
% 5.44/5.64 thf(fact_3088_order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ B @ C )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans2
% 5.44/5.64 thf(fact_3089_order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [A: real,B: real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_real @ B @ C )
% 5.44/5.64 => ( ord_less_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans2
% 5.44/5.64 thf(fact_3090_order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,C: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ B @ C )
% 5.44/5.64 => ( ord_less_set_real @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans2
% 5.44/5.64 thf(fact_3091_order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.44/5.64 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans2
% 5.44/5.64 thf(fact_3092_order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ord_less_num @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans2
% 5.44/5.64 thf(fact_3093_order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans2
% 5.44/5.64 thf(fact_3094_order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.44/5.64 => ( ord_less_int @ A @ C ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_trans2
% 5.44/5.64 thf(fact_3095_order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_le72135733267957522d_enat
% 5.44/5.64 = ( ^ [A4: extended_enat,B4: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A4 @ B4 )
% 5.44/5.64 & ~ ( ord_le2932123472753598470d_enat @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_not
% 5.44/5.64 thf(fact_3096_order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_real
% 5.44/5.64 = ( ^ [A4: real,B4: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ A4 @ B4 )
% 5.44/5.64 & ~ ( ord_less_eq_real @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_not
% 5.44/5.64 thf(fact_3097_order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_set_real
% 5.44/5.64 = ( ^ [A4: set_real,B4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.44/5.64 & ~ ( ord_less_eq_set_real @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_not
% 5.44/5.64 thf(fact_3098_order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_set_nat
% 5.44/5.64 = ( ^ [A4: set_nat,B4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 5.44/5.64 & ~ ( ord_less_eq_set_nat @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_not
% 5.44/5.64 thf(fact_3099_order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_num
% 5.44/5.64 = ( ^ [A4: num,B4: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.44/5.64 & ~ ( ord_less_eq_num @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_not
% 5.44/5.64 thf(fact_3100_order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_nat
% 5.44/5.64 = ( ^ [A4: nat,B4: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.44/5.64 & ~ ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_not
% 5.44/5.64 thf(fact_3101_order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_int
% 5.44/5.64 = ( ^ [A4: int,B4: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.44/5.64 & ~ ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_iff_not
% 5.44/5.64 thf(fact_3102_dense__ge__bounded,axiom,
% 5.44/5.64 ! [Z: real,X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ Z @ X )
% 5.44/5.64 => ( ! [W2: real] :
% 5.44/5.64 ( ( ord_less_real @ Z @ W2 )
% 5.44/5.64 => ( ( ord_less_real @ W2 @ X )
% 5.44/5.64 => ( ord_less_eq_real @ Y @ W2 ) ) )
% 5.44/5.64 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dense_ge_bounded
% 5.44/5.64 thf(fact_3103_dense__le__bounded,axiom,
% 5.44/5.64 ! [X: real,Y: real,Z: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ! [W2: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ W2 )
% 5.44/5.64 => ( ( ord_less_real @ W2 @ Y )
% 5.44/5.64 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.44/5.64 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dense_le_bounded
% 5.44/5.64 thf(fact_3104_dual__order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_le2932123472753598470d_enat
% 5.44/5.64 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ B4 @ A4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.order_iff_strict
% 5.44/5.64 thf(fact_3105_dual__order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_real
% 5.44/5.64 = ( ^ [B4: real,A4: real] :
% 5.44/5.64 ( ( ord_less_real @ B4 @ A4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.order_iff_strict
% 5.44/5.64 thf(fact_3106_dual__order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_set_real
% 5.44/5.64 = ( ^ [B4: set_real,A4: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ B4 @ A4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.order_iff_strict
% 5.44/5.64 thf(fact_3107_dual__order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_set_nat
% 5.44/5.64 = ( ^ [B4: set_nat,A4: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ B4 @ A4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.order_iff_strict
% 5.44/5.64 thf(fact_3108_dual__order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_num
% 5.44/5.64 = ( ^ [B4: num,A4: num] :
% 5.44/5.64 ( ( ord_less_num @ B4 @ A4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.order_iff_strict
% 5.44/5.64 thf(fact_3109_dual__order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_nat
% 5.44/5.64 = ( ^ [B4: nat,A4: nat] :
% 5.44/5.64 ( ( ord_less_nat @ B4 @ A4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.order_iff_strict
% 5.44/5.64 thf(fact_3110_dual__order_Oorder__iff__strict,axiom,
% 5.44/5.64 ( ord_less_eq_int
% 5.44/5.64 = ( ^ [B4: int,A4: int] :
% 5.44/5.64 ( ( ord_less_int @ B4 @ A4 )
% 5.44/5.64 | ( A4 = B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.order_iff_strict
% 5.44/5.64 thf(fact_3111_dual__order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_le72135733267957522d_enat
% 5.44/5.64 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ B4 @ A4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_order
% 5.44/5.64 thf(fact_3112_dual__order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_real
% 5.44/5.64 = ( ^ [B4: real,A4: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ B4 @ A4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_order
% 5.44/5.64 thf(fact_3113_dual__order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_set_real
% 5.44/5.64 = ( ^ [B4: set_real,A4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ B4 @ A4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_order
% 5.44/5.64 thf(fact_3114_dual__order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_set_nat
% 5.44/5.64 = ( ^ [B4: set_nat,A4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_order
% 5.44/5.64 thf(fact_3115_dual__order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_num
% 5.44/5.64 = ( ^ [B4: num,A4: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_order
% 5.44/5.64 thf(fact_3116_dual__order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_nat
% 5.44/5.64 = ( ^ [B4: nat,A4: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_order
% 5.44/5.64 thf(fact_3117_dual__order_Ostrict__iff__order,axiom,
% 5.44/5.64 ( ord_less_int
% 5.44/5.64 = ( ^ [B4: int,A4: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.44/5.64 & ( A4 != B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_order
% 5.44/5.64 thf(fact_3118_dual__order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans1
% 5.44/5.64 thf(fact_3119_dual__order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [B: real,A: real,C: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.64 => ( ( ord_less_real @ C @ B )
% 5.44/5.64 => ( ord_less_real @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans1
% 5.44/5.64 thf(fact_3120_dual__order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [B: set_real,A: set_real,C: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ B @ A )
% 5.44/5.64 => ( ( ord_less_set_real @ C @ B )
% 5.44/5.64 => ( ord_less_set_real @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans1
% 5.44/5.64 thf(fact_3121_dual__order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_set_nat @ C @ B )
% 5.44/5.64 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans1
% 5.44/5.64 thf(fact_3122_dual__order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [B: num,A: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ B @ A )
% 5.44/5.64 => ( ( ord_less_num @ C @ B )
% 5.44/5.64 => ( ord_less_num @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans1
% 5.44/5.64 thf(fact_3123_dual__order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [B: nat,A: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_nat @ C @ B )
% 5.44/5.64 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans1
% 5.44/5.64 thf(fact_3124_dual__order_Ostrict__trans1,axiom,
% 5.44/5.64 ! [B: int,A: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ B @ A )
% 5.44/5.64 => ( ( ord_less_int @ C @ B )
% 5.44/5.64 => ( ord_less_int @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans1
% 5.44/5.64 thf(fact_3125_dual__order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans2
% 5.44/5.64 thf(fact_3126_dual__order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [B: real,A: real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_real @ C @ B )
% 5.44/5.64 => ( ord_less_real @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans2
% 5.44/5.64 thf(fact_3127_dual__order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [B: set_real,A: set_real,C: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ C @ B )
% 5.44/5.64 => ( ord_less_set_real @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans2
% 5.44/5.64 thf(fact_3128_dual__order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.44/5.64 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans2
% 5.44/5.64 thf(fact_3129_dual__order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [B: num,A: num,C: num] :
% 5.44/5.64 ( ( ord_less_num @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_num @ C @ B )
% 5.44/5.64 => ( ord_less_num @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans2
% 5.44/5.64 thf(fact_3130_dual__order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [B: nat,A: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_nat @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_nat @ C @ B )
% 5.44/5.64 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans2
% 5.44/5.64 thf(fact_3131_dual__order_Ostrict__trans2,axiom,
% 5.44/5.64 ! [B: int,A: int,C: int] :
% 5.44/5.64 ( ( ord_less_int @ B @ A )
% 5.44/5.64 => ( ( ord_less_eq_int @ C @ B )
% 5.44/5.64 => ( ord_less_int @ C @ A ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_trans2
% 5.44/5.64 thf(fact_3132_dual__order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_le72135733267957522d_enat
% 5.44/5.64 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ B4 @ A4 )
% 5.44/5.64 & ~ ( ord_le2932123472753598470d_enat @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_not
% 5.44/5.64 thf(fact_3133_dual__order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_real
% 5.44/5.64 = ( ^ [B4: real,A4: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ B4 @ A4 )
% 5.44/5.64 & ~ ( ord_less_eq_real @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_not
% 5.44/5.64 thf(fact_3134_dual__order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_set_real
% 5.44/5.64 = ( ^ [B4: set_real,A4: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ B4 @ A4 )
% 5.44/5.64 & ~ ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_not
% 5.44/5.64 thf(fact_3135_dual__order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_set_nat
% 5.44/5.64 = ( ^ [B4: set_nat,A4: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 5.44/5.64 & ~ ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_not
% 5.44/5.64 thf(fact_3136_dual__order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_num
% 5.44/5.64 = ( ^ [B4: num,A4: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.44/5.64 & ~ ( ord_less_eq_num @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_not
% 5.44/5.64 thf(fact_3137_dual__order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_nat
% 5.44/5.64 = ( ^ [B4: nat,A4: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.44/5.64 & ~ ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_not
% 5.44/5.64 thf(fact_3138_dual__order_Ostrict__iff__not,axiom,
% 5.44/5.64 ( ord_less_int
% 5.44/5.64 = ( ^ [B4: int,A4: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.44/5.64 & ~ ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_iff_not
% 5.44/5.64 thf(fact_3139_order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ord_le2932123472753598470d_enat @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_order
% 5.44/5.64 thf(fact_3140_order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_order
% 5.44/5.64 thf(fact_3141_order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ A @ B )
% 5.44/5.64 => ( ord_less_eq_set_real @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_order
% 5.44/5.64 thf(fact_3142_order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ A @ B )
% 5.44/5.64 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_order
% 5.44/5.64 thf(fact_3143_order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_order
% 5.44/5.64 thf(fact_3144_order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_order
% 5.44/5.64 thf(fact_3145_order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % order.strict_implies_order
% 5.44/5.64 thf(fact_3146_dual__order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [B: extended_enat,A: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.44/5.64 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_order
% 5.44/5.64 thf(fact_3147_dual__order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [B: real,A: real] :
% 5.44/5.64 ( ( ord_less_real @ B @ A )
% 5.44/5.64 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_order
% 5.44/5.64 thf(fact_3148_dual__order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [B: set_real,A: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ B @ A )
% 5.44/5.64 => ( ord_less_eq_set_real @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_order
% 5.44/5.64 thf(fact_3149_dual__order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [B: set_nat,A: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ B @ A )
% 5.44/5.64 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_order
% 5.44/5.64 thf(fact_3150_dual__order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [B: num,A: num] :
% 5.44/5.64 ( ( ord_less_num @ B @ A )
% 5.44/5.64 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_order
% 5.44/5.64 thf(fact_3151_dual__order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [B: nat,A: nat] :
% 5.44/5.64 ( ( ord_less_nat @ B @ A )
% 5.44/5.64 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_order
% 5.44/5.64 thf(fact_3152_dual__order_Ostrict__implies__order,axiom,
% 5.44/5.64 ! [B: int,A: int] :
% 5.44/5.64 ( ( ord_less_int @ B @ A )
% 5.44/5.64 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % dual_order.strict_implies_order
% 5.44/5.64 thf(fact_3153_order__le__less,axiom,
% 5.44/5.64 ( ord_le2932123472753598470d_enat
% 5.44/5.64 = ( ^ [X2: extended_enat,Y3: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X2 @ Y3 )
% 5.44/5.64 | ( X2 = Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less
% 5.44/5.64 thf(fact_3154_order__le__less,axiom,
% 5.44/5.64 ( ord_less_eq_real
% 5.44/5.64 = ( ^ [X2: real,Y3: real] :
% 5.44/5.64 ( ( ord_less_real @ X2 @ Y3 )
% 5.44/5.64 | ( X2 = Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less
% 5.44/5.64 thf(fact_3155_order__le__less,axiom,
% 5.44/5.64 ( ord_less_eq_set_real
% 5.44/5.64 = ( ^ [X2: set_real,Y3: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ X2 @ Y3 )
% 5.44/5.64 | ( X2 = Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less
% 5.44/5.64 thf(fact_3156_order__le__less,axiom,
% 5.44/5.64 ( ord_less_eq_set_nat
% 5.44/5.64 = ( ^ [X2: set_nat,Y3: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ X2 @ Y3 )
% 5.44/5.64 | ( X2 = Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less
% 5.44/5.64 thf(fact_3157_order__le__less,axiom,
% 5.44/5.64 ( ord_less_eq_num
% 5.44/5.64 = ( ^ [X2: num,Y3: num] :
% 5.44/5.64 ( ( ord_less_num @ X2 @ Y3 )
% 5.44/5.64 | ( X2 = Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less
% 5.44/5.64 thf(fact_3158_order__le__less,axiom,
% 5.44/5.64 ( ord_less_eq_nat
% 5.44/5.64 = ( ^ [X2: nat,Y3: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X2 @ Y3 )
% 5.44/5.64 | ( X2 = Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less
% 5.44/5.64 thf(fact_3159_order__le__less,axiom,
% 5.44/5.64 ( ord_less_eq_int
% 5.44/5.64 = ( ^ [X2: int,Y3: int] :
% 5.44/5.64 ( ( ord_less_int @ X2 @ Y3 )
% 5.44/5.64 | ( X2 = Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less
% 5.44/5.64 thf(fact_3160_order__less__le,axiom,
% 5.44/5.64 ( ord_le72135733267957522d_enat
% 5.44/5.64 = ( ^ [X2: extended_enat,Y3: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ X2 @ Y3 )
% 5.44/5.64 & ( X2 != Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le
% 5.44/5.64 thf(fact_3161_order__less__le,axiom,
% 5.44/5.64 ( ord_less_real
% 5.44/5.64 = ( ^ [X2: real,Y3: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ X2 @ Y3 )
% 5.44/5.64 & ( X2 != Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le
% 5.44/5.64 thf(fact_3162_order__less__le,axiom,
% 5.44/5.64 ( ord_less_set_real
% 5.44/5.64 = ( ^ [X2: set_real,Y3: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X2 @ Y3 )
% 5.44/5.64 & ( X2 != Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le
% 5.44/5.64 thf(fact_3163_order__less__le,axiom,
% 5.44/5.64 ( ord_less_set_nat
% 5.44/5.64 = ( ^ [X2: set_nat,Y3: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 5.44/5.64 & ( X2 != Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le
% 5.44/5.64 thf(fact_3164_order__less__le,axiom,
% 5.44/5.64 ( ord_less_num
% 5.44/5.64 = ( ^ [X2: num,Y3: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X2 @ Y3 )
% 5.44/5.64 & ( X2 != Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le
% 5.44/5.64 thf(fact_3165_order__less__le,axiom,
% 5.44/5.64 ( ord_less_nat
% 5.44/5.64 = ( ^ [X2: nat,Y3: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 5.44/5.64 & ( X2 != Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le
% 5.44/5.64 thf(fact_3166_order__less__le,axiom,
% 5.44/5.64 ( ord_less_int
% 5.44/5.64 = ( ^ [X2: int,Y3: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X2 @ Y3 )
% 5.44/5.64 & ( X2 != Y3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le
% 5.44/5.64 thf(fact_3167_linorder__not__le,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ~ ( ord_le2932123472753598470d_enat @ X @ Y ) )
% 5.44/5.64 = ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_le
% 5.44/5.64 thf(fact_3168_linorder__not__le,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 5.44/5.64 = ( ord_less_real @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_le
% 5.44/5.64 thf(fact_3169_linorder__not__le,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 5.44/5.64 = ( ord_less_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_le
% 5.44/5.64 thf(fact_3170_linorder__not__le,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 5.44/5.64 = ( ord_less_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_le
% 5.44/5.64 thf(fact_3171_linorder__not__le,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 5.44/5.64 = ( ord_less_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_le
% 5.44/5.64 thf(fact_3172_linorder__not__less,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ~ ( ord_le72135733267957522d_enat @ X @ Y ) )
% 5.44/5.64 = ( ord_le2932123472753598470d_enat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_less
% 5.44/5.64 thf(fact_3173_linorder__not__less,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.44/5.64 = ( ord_less_eq_real @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_less
% 5.44/5.64 thf(fact_3174_linorder__not__less,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.44/5.64 = ( ord_less_eq_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_less
% 5.44/5.64 thf(fact_3175_linorder__not__less,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.44/5.64 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_less
% 5.44/5.64 thf(fact_3176_linorder__not__less,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.44/5.64 = ( ord_less_eq_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_not_less
% 5.44/5.64 thf(fact_3177_order__less__imp__le,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( ord_le2932123472753598470d_enat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_le
% 5.44/5.64 thf(fact_3178_order__less__imp__le,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_le
% 5.44/5.64 thf(fact_3179_order__less__imp__le,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_set_real @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_le
% 5.44/5.64 thf(fact_3180_order__less__imp__le,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_le
% 5.44/5.64 thf(fact_3181_order__less__imp__le,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_le
% 5.44/5.64 thf(fact_3182_order__less__imp__le,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_le
% 5.44/5.64 thf(fact_3183_order__less__imp__le,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_imp_le
% 5.44/5.64 thf(fact_3184_order__le__neq__trans,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.64 => ( ( A != B )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_neq_trans
% 5.44/5.64 thf(fact_3185_order__le__neq__trans,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.64 => ( ( A != B )
% 5.44/5.64 => ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_neq_trans
% 5.44/5.64 thf(fact_3186_order__le__neq__trans,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( ( A != B )
% 5.44/5.64 => ( ord_less_set_real @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_neq_trans
% 5.44/5.64 thf(fact_3187_order__le__neq__trans,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 => ( ( A != B )
% 5.44/5.64 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_neq_trans
% 5.44/5.64 thf(fact_3188_order__le__neq__trans,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( A != B )
% 5.44/5.64 => ( ord_less_num @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_neq_trans
% 5.44/5.64 thf(fact_3189_order__le__neq__trans,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( A != B )
% 5.44/5.64 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_neq_trans
% 5.44/5.64 thf(fact_3190_order__le__neq__trans,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ( A != B )
% 5.44/5.64 => ( ord_less_int @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_neq_trans
% 5.44/5.64 thf(fact_3191_order__neq__le__trans,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.64 ( ( A != B )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_neq_le_trans
% 5.44/5.64 thf(fact_3192_order__neq__le__trans,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( A != B )
% 5.44/5.64 => ( ( ord_less_eq_real @ A @ B )
% 5.44/5.64 => ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_neq_le_trans
% 5.44/5.64 thf(fact_3193_order__neq__le__trans,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real] :
% 5.44/5.64 ( ( A != B )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 => ( ord_less_set_real @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_neq_le_trans
% 5.44/5.64 thf(fact_3194_order__neq__le__trans,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat] :
% 5.44/5.64 ( ( A != B )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_neq_le_trans
% 5.44/5.64 thf(fact_3195_order__neq__le__trans,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( A != B )
% 5.44/5.64 => ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ord_less_num @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_neq_le_trans
% 5.44/5.64 thf(fact_3196_order__neq__le__trans,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( A != B )
% 5.44/5.64 => ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_neq_le_trans
% 5.44/5.64 thf(fact_3197_order__neq__le__trans,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( A != B )
% 5.44/5.64 => ( ( ord_less_eq_int @ A @ B )
% 5.44/5.64 => ( ord_less_int @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_neq_le_trans
% 5.44/5.64 thf(fact_3198_order__le__less__trans,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ Y @ Z )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_trans
% 5.44/5.64 thf(fact_3199_order__le__less__trans,axiom,
% 5.44/5.64 ! [X: real,Y: real,Z: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_real @ Y @ Z )
% 5.44/5.64 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_trans
% 5.44/5.64 thf(fact_3200_order__le__less__trans,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real,Z: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_set_real @ Y @ Z )
% 5.44/5.64 => ( ord_less_set_real @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_trans
% 5.44/5.64 thf(fact_3201_order__le__less__trans,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_set_nat @ Y @ Z )
% 5.44/5.64 => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_trans
% 5.44/5.64 thf(fact_3202_order__le__less__trans,axiom,
% 5.44/5.64 ! [X: num,Y: num,Z: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 => ( ( ord_less_num @ Y @ Z )
% 5.44/5.64 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_trans
% 5.44/5.64 thf(fact_3203_order__le__less__trans,axiom,
% 5.44/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_nat @ Y @ Z )
% 5.44/5.64 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_trans
% 5.44/5.64 thf(fact_3204_order__le__less__trans,axiom,
% 5.44/5.64 ! [X: int,Y: int,Z: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 => ( ( ord_less_int @ Y @ Z )
% 5.44/5.64 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_trans
% 5.44/5.64 thf(fact_3205_order__less__le__trans,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ Y @ Z )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_trans
% 5.44/5.64 thf(fact_3206_order__less__le__trans,axiom,
% 5.44/5.64 ! [X: real,Y: real,Z: real] :
% 5.44/5.64 ( ( ord_less_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_real @ Y @ Z )
% 5.44/5.64 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_trans
% 5.44/5.64 thf(fact_3207_order__less__le__trans,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real,Z: set_real] :
% 5.44/5.64 ( ( ord_less_set_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_set_real @ Y @ Z )
% 5.44/5.64 => ( ord_less_set_real @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_trans
% 5.44/5.64 thf(fact_3208_order__less__le__trans,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_set_nat @ Y @ Z )
% 5.44/5.64 => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_trans
% 5.44/5.64 thf(fact_3209_order__less__le__trans,axiom,
% 5.44/5.64 ! [X: num,Y: num,Z: num] :
% 5.44/5.64 ( ( ord_less_num @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_num @ Y @ Z )
% 5.44/5.64 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_trans
% 5.44/5.64 thf(fact_3210_order__less__le__trans,axiom,
% 5.44/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.44/5.64 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_trans
% 5.44/5.64 thf(fact_3211_order__less__le__trans,axiom,
% 5.44/5.64 ! [X: int,Y: int,Z: int] :
% 5.44/5.64 ( ( ord_less_int @ X @ Y )
% 5.44/5.64 => ( ( ord_less_eq_int @ Y @ Z )
% 5.44/5.64 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_trans
% 5.44/5.64 thf(fact_3212_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: extended_enat > extended_enat,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3213_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: extended_enat > real,B: extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ B @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3214_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: real > extended_enat,B: real,C: real] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3215_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: real > real,B: real,C: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_real @ B @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3216_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: num > extended_enat,B: num,C: num] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3217_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: num > real,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3218_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: nat > extended_enat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3219_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3220_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: int > extended_enat,B: int,C: int] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3221_order__le__less__subst1,axiom,
% 5.44/5.64 ! [A: real,F: int > real,B: int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_int @ B @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst1
% 5.44/5.64 thf(fact_3222_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3223_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > real,C: real] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3224_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3225_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3226_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3227_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3228_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3229_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3230_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3231_order__le__less__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > int,C: int] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_less_subst2
% 5.44/5.64 thf(fact_3232_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: num > extended_enat,B: num,C: num] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3233_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: real,F: num > real,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3234_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: num,F: num > num,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3235_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3236_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: int,F: num > int,B: num,C: num] :
% 5.44/5.64 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_num @ B @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3237_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: extended_enat,F: nat > extended_enat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3238_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3239_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3240_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3241_order__less__le__subst1,axiom,
% 5.44/5.64 ! [A: int,F: nat > int,B: nat,C: nat] :
% 5.44/5.64 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.44/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst1
% 5.44/5.64 thf(fact_3242_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3243_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,F: extended_enat > real,C: real] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: extended_enat,Y5: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3244_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3245_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: real,B: real,F: real > real,C: real] :
% 5.44/5.64 ( ( ord_less_real @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: real,Y5: real] :
% 5.44/5.64 ( ( ord_less_real @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3246_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3247_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: num,B: num,F: num > real,C: real] :
% 5.44/5.64 ( ( ord_less_num @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: num,Y5: num] :
% 5.44/5.64 ( ( ord_less_num @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3248_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3249_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.44/5.64 ( ( ord_less_nat @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: nat,Y5: nat] :
% 5.44/5.64 ( ( ord_less_nat @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3250_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: int,B: int,F: int > extended_enat,C: extended_enat] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ( ( ord_le2932123472753598470d_enat @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_le72135733267957522d_enat @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3251_order__less__le__subst2,axiom,
% 5.44/5.64 ! [A: int,B: int,F: int > real,C: real] :
% 5.44/5.64 ( ( ord_less_int @ A @ B )
% 5.44/5.64 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.44/5.64 => ( ! [X5: int,Y5: int] :
% 5.44/5.64 ( ( ord_less_int @ X5 @ Y5 )
% 5.44/5.64 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 5.44/5.64 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_less_le_subst2
% 5.44/5.64 thf(fact_3252_linorder__le__less__linear,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 5.44/5.64 | ( ord_le72135733267957522d_enat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_le_less_linear
% 5.44/5.64 thf(fact_3253_linorder__le__less__linear,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.64 | ( ord_less_real @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_le_less_linear
% 5.44/5.64 thf(fact_3254_linorder__le__less__linear,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 | ( ord_less_num @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_le_less_linear
% 5.44/5.64 thf(fact_3255_linorder__le__less__linear,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 | ( ord_less_nat @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_le_less_linear
% 5.44/5.64 thf(fact_3256_linorder__le__less__linear,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 | ( ord_less_int @ Y @ X ) ) ).
% 5.44/5.64
% 5.44/5.64 % linorder_le_less_linear
% 5.44/5.64 thf(fact_3257_order__le__imp__less__or__eq,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 5.44/5.64 => ( ( ord_le72135733267957522d_enat @ X @ Y )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_imp_less_or_eq
% 5.44/5.64 thf(fact_3258_order__le__imp__less__or__eq,axiom,
% 5.44/5.64 ! [X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_real @ X @ Y )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_imp_less_or_eq
% 5.44/5.64 thf(fact_3259_order__le__imp__less__or__eq,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.64 => ( ( ord_less_set_real @ X @ Y )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_imp_less_or_eq
% 5.44/5.64 thf(fact_3260_order__le__imp__less__or__eq,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_set_nat @ X @ Y )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_imp_less_or_eq
% 5.44/5.64 thf(fact_3261_order__le__imp__less__or__eq,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 => ( ( ord_less_num @ X @ Y )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_imp_less_or_eq
% 5.44/5.64 thf(fact_3262_order__le__imp__less__or__eq,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_less_nat @ X @ Y )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_imp_less_or_eq
% 5.44/5.64 thf(fact_3263_order__le__imp__less__or__eq,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 => ( ( ord_less_int @ X @ Y )
% 5.44/5.64 | ( X = Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % order_le_imp_less_or_eq
% 5.44/5.64 thf(fact_3264_bot_Oextremum__uniqueI,axiom,
% 5.44/5.64 ! [A: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.44/5.64 => ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_uniqueI
% 5.44/5.64 thf(fact_3265_bot_Oextremum__uniqueI,axiom,
% 5.44/5.64 ! [A: set_int] :
% 5.44/5.64 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.44/5.64 => ( A = bot_bot_set_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_uniqueI
% 5.44/5.64 thf(fact_3266_bot_Oextremum__uniqueI,axiom,
% 5.44/5.64 ! [A: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.44/5.64 => ( A = bot_bot_set_real ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_uniqueI
% 5.44/5.64 thf(fact_3267_bot_Oextremum__uniqueI,axiom,
% 5.44/5.64 ! [A: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.44/5.64 => ( A = bot_bot_set_nat ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_uniqueI
% 5.44/5.64 thf(fact_3268_bot_Oextremum__uniqueI,axiom,
% 5.44/5.64 ! [A: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.44/5.64 => ( A = bot_bot_nat ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_uniqueI
% 5.44/5.64 thf(fact_3269_bot_Oextremum__unique,axiom,
% 5.44/5.64 ! [A: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.44/5.64 = ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_unique
% 5.44/5.64 thf(fact_3270_bot_Oextremum__unique,axiom,
% 5.44/5.64 ! [A: set_int] :
% 5.44/5.64 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.44/5.64 = ( A = bot_bot_set_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_unique
% 5.44/5.64 thf(fact_3271_bot_Oextremum__unique,axiom,
% 5.44/5.64 ! [A: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.44/5.64 = ( A = bot_bot_set_real ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_unique
% 5.44/5.64 thf(fact_3272_bot_Oextremum__unique,axiom,
% 5.44/5.64 ! [A: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.44/5.64 = ( A = bot_bot_set_nat ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_unique
% 5.44/5.64 thf(fact_3273_bot_Oextremum__unique,axiom,
% 5.44/5.64 ! [A: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.44/5.64 = ( A = bot_bot_nat ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_unique
% 5.44/5.64 thf(fact_3274_bot_Oextremum,axiom,
% 5.44/5.64 ! [A: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum
% 5.44/5.64 thf(fact_3275_bot_Oextremum,axiom,
% 5.44/5.64 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum
% 5.44/5.64 thf(fact_3276_bot_Oextremum,axiom,
% 5.44/5.64 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum
% 5.44/5.64 thf(fact_3277_bot_Oextremum,axiom,
% 5.44/5.64 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum
% 5.44/5.64 thf(fact_3278_bot_Oextremum,axiom,
% 5.44/5.64 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum
% 5.44/5.64 thf(fact_3279_bot_Oextremum__strict,axiom,
% 5.44/5.64 ! [A: set_nat] :
% 5.44/5.64 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_strict
% 5.44/5.64 thf(fact_3280_bot_Oextremum__strict,axiom,
% 5.44/5.64 ! [A: set_int] :
% 5.44/5.64 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_strict
% 5.44/5.64 thf(fact_3281_bot_Oextremum__strict,axiom,
% 5.44/5.64 ! [A: set_real] :
% 5.44/5.64 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_strict
% 5.44/5.64 thf(fact_3282_bot_Oextremum__strict,axiom,
% 5.44/5.64 ! [A: extended_enat] :
% 5.44/5.64 ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_strict
% 5.44/5.64 thf(fact_3283_bot_Oextremum__strict,axiom,
% 5.44/5.64 ! [A: nat] :
% 5.44/5.64 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.44/5.64
% 5.44/5.64 % bot.extremum_strict
% 5.44/5.64 thf(fact_3284_bot_Onot__eq__extremum,axiom,
% 5.44/5.64 ! [A: set_nat] :
% 5.44/5.64 ( ( A != bot_bot_set_nat )
% 5.44/5.64 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.not_eq_extremum
% 5.44/5.64 thf(fact_3285_bot_Onot__eq__extremum,axiom,
% 5.44/5.64 ! [A: set_int] :
% 5.44/5.64 ( ( A != bot_bot_set_int )
% 5.44/5.64 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.not_eq_extremum
% 5.44/5.64 thf(fact_3286_bot_Onot__eq__extremum,axiom,
% 5.44/5.64 ! [A: set_real] :
% 5.44/5.64 ( ( A != bot_bot_set_real )
% 5.44/5.64 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.not_eq_extremum
% 5.44/5.64 thf(fact_3287_bot_Onot__eq__extremum,axiom,
% 5.44/5.64 ! [A: extended_enat] :
% 5.44/5.64 ( ( A != bot_bo4199563552545308370d_enat )
% 5.44/5.64 = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.not_eq_extremum
% 5.44/5.64 thf(fact_3288_bot_Onot__eq__extremum,axiom,
% 5.44/5.64 ! [A: nat] :
% 5.44/5.64 ( ( A != bot_bot_nat )
% 5.44/5.64 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.44/5.64
% 5.44/5.64 % bot.not_eq_extremum
% 5.44/5.64 thf(fact_3289_max__absorb2,axiom,
% 5.44/5.64 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 5.44/5.64 => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 5.44/5.64 = Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb2
% 5.44/5.64 thf(fact_3290_max__absorb2,axiom,
% 5.44/5.64 ! [X: code_integer,Y: code_integer] :
% 5.44/5.64 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 5.44/5.64 => ( ( ord_max_Code_integer @ X @ Y )
% 5.44/5.64 = Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb2
% 5.44/5.64 thf(fact_3291_max__absorb2,axiom,
% 5.44/5.64 ! [X: set_real,Y: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.64 => ( ( ord_max_set_real @ X @ Y )
% 5.44/5.64 = Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb2
% 5.44/5.64 thf(fact_3292_max__absorb2,axiom,
% 5.44/5.64 ! [X: set_nat,Y: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_max_set_nat @ X @ Y )
% 5.44/5.64 = Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb2
% 5.44/5.64 thf(fact_3293_max__absorb2,axiom,
% 5.44/5.64 ! [X: num,Y: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ X @ Y )
% 5.44/5.64 => ( ( ord_max_num @ X @ Y )
% 5.44/5.64 = Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb2
% 5.44/5.64 thf(fact_3294_max__absorb2,axiom,
% 5.44/5.64 ! [X: nat,Y: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ X @ Y )
% 5.44/5.64 => ( ( ord_max_nat @ X @ Y )
% 5.44/5.64 = Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb2
% 5.44/5.64 thf(fact_3295_max__absorb2,axiom,
% 5.44/5.64 ! [X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.64 => ( ( ord_max_int @ X @ Y )
% 5.44/5.64 = Y ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb2
% 5.44/5.64 thf(fact_3296_max__absorb1,axiom,
% 5.44/5.64 ! [Y: extended_enat,X: extended_enat] :
% 5.44/5.64 ( ( ord_le2932123472753598470d_enat @ Y @ X )
% 5.44/5.64 => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 5.44/5.64 = X ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb1
% 5.44/5.64 thf(fact_3297_max__absorb1,axiom,
% 5.44/5.64 ! [Y: code_integer,X: code_integer] :
% 5.44/5.64 ( ( ord_le3102999989581377725nteger @ Y @ X )
% 5.44/5.64 => ( ( ord_max_Code_integer @ X @ Y )
% 5.44/5.64 = X ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb1
% 5.44/5.64 thf(fact_3298_max__absorb1,axiom,
% 5.44/5.64 ! [Y: set_real,X: set_real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ Y @ X )
% 5.44/5.64 => ( ( ord_max_set_real @ X @ Y )
% 5.44/5.64 = X ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb1
% 5.44/5.64 thf(fact_3299_max__absorb1,axiom,
% 5.44/5.64 ! [Y: set_nat,X: set_nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.44/5.64 => ( ( ord_max_set_nat @ X @ Y )
% 5.44/5.64 = X ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb1
% 5.44/5.64 thf(fact_3300_max__absorb1,axiom,
% 5.44/5.64 ! [Y: num,X: num] :
% 5.44/5.64 ( ( ord_less_eq_num @ Y @ X )
% 5.44/5.64 => ( ( ord_max_num @ X @ Y )
% 5.44/5.64 = X ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb1
% 5.44/5.64 thf(fact_3301_max__absorb1,axiom,
% 5.44/5.64 ! [Y: nat,X: nat] :
% 5.44/5.64 ( ( ord_less_eq_nat @ Y @ X )
% 5.44/5.64 => ( ( ord_max_nat @ X @ Y )
% 5.44/5.64 = X ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb1
% 5.44/5.64 thf(fact_3302_max__absorb1,axiom,
% 5.44/5.64 ! [Y: int,X: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ Y @ X )
% 5.44/5.64 => ( ( ord_max_int @ X @ Y )
% 5.44/5.64 = X ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_absorb1
% 5.44/5.64 thf(fact_3303_max__def,axiom,
% 5.44/5.64 ( ord_ma741700101516333627d_enat
% 5.44/5.64 = ( ^ [A4: extended_enat,B4: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_def
% 5.44/5.64 thf(fact_3304_max__def,axiom,
% 5.44/5.64 ( ord_max_Code_integer
% 5.44/5.64 = ( ^ [A4: code_integer,B4: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_def
% 5.44/5.64 thf(fact_3305_max__def,axiom,
% 5.44/5.64 ( ord_max_set_real
% 5.44/5.64 = ( ^ [A4: set_real,B4: set_real] : ( if_set_real @ ( ord_less_eq_set_real @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_def
% 5.44/5.64 thf(fact_3306_max__def,axiom,
% 5.44/5.64 ( ord_max_set_nat
% 5.44/5.64 = ( ^ [A4: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_def
% 5.44/5.64 thf(fact_3307_max__def,axiom,
% 5.44/5.64 ( ord_max_num
% 5.44/5.64 = ( ^ [A4: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_def
% 5.44/5.64 thf(fact_3308_max__def,axiom,
% 5.44/5.64 ( ord_max_nat
% 5.44/5.64 = ( ^ [A4: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_def
% 5.44/5.64 thf(fact_3309_max__def,axiom,
% 5.44/5.64 ( ord_max_int
% 5.44/5.64 = ( ^ [A4: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % max_def
% 5.44/5.64 thf(fact_3310_vebt__pred_Opelims,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.44/5.64 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.44/5.64 = Y )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [Uu2: $o,Uv2: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.64 => ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => ( ( Y = none_nat )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.44/5.64 => ( ! [A3: $o,Uw2: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.44/5.64 => ( ( Xa2
% 5.44/5.64 = ( suc @ zero_zero_nat ) )
% 5.44/5.64 => ( ( ( A3
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.64 & ( ~ A3
% 5.44/5.64 => ( Y = none_nat ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ! [Va2: nat] :
% 5.44/5.64 ( ( Xa2
% 5.44/5.64 = ( suc @ ( suc @ Va2 ) ) )
% 5.44/5.64 => ( ( ( B3
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.64 & ( ~ B3
% 5.44/5.64 => ( ( A3
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.64 & ( ~ A3
% 5.44/5.64 => ( Y = none_nat ) ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 5.44/5.64 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.44/5.64 => ( ( Y = none_nat )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.44/5.64 => ( ( Y = none_nat )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.44/5.64 => ( ( Y = none_nat )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 5.44/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( some_nat @ Ma2 ) ) )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 @ ( if_option_nat
% 5.44/5.64 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 != none_nat )
% 5.44/5.64 & ( 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 @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.64 @ ( 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 @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.64 @ ( if_option_nat
% 5.44/5.64 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.64 = none_nat )
% 5.44/5.64 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.44/5.64 @ ( 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 @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.64 @ none_nat ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_pred.pelims
% 5.44/5.64 thf(fact_3311_vebt__delete_Opelims,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.44/5.64 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 5.44/5.64 = Y )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Leaf @ $false @ B3 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( Xa2
% 5.44/5.64 = ( suc @ zero_zero_nat ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ $false ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ! [N4: nat] :
% 5.44/5.64 ( ( Xa2
% 5.44/5.64 = ( suc @ ( suc @ N4 ) ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N4 ) ) ) ) ) ) )
% 5.44/5.64 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ Xa2 ) ) ) )
% 5.44/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.44/5.64 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.44/5.64 => ( ( ( ( Xa2 = Mi2 )
% 5.44/5.64 & ( Xa2 = Ma2 ) )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.44/5.64 & ( ~ ( ( Xa2 = Mi2 )
% 5.44/5.64 & ( Xa2 = Ma2 ) )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 @ ( vEBT_Node
% 5.44/5.64 @ ( some_P7363390416028606310at_nat
% 5.44/5.64 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.44/5.64 @ ( if_nat
% 5.44/5.64 @ ( ( ( Xa2 = Mi2 )
% 5.44/5.64 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.44/5.64 = Ma2 ) )
% 5.44/5.64 & ( ( Xa2 != Mi2 )
% 5.44/5.64 => ( Xa2 = Ma2 ) ) )
% 5.44/5.64 @ ( if_nat
% 5.44/5.64 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 = none_nat )
% 5.44/5.64 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.44/5.64 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.64 @ Ma2 ) ) )
% 5.44/5.64 @ ( suc @ ( suc @ Va2 ) )
% 5.44/5.64 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 @ ( vEBT_Node
% 5.44/5.64 @ ( some_P7363390416028606310at_nat
% 5.44/5.64 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.44/5.64 @ ( if_nat
% 5.44/5.64 @ ( ( ( Xa2 = Mi2 )
% 5.44/5.64 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.44/5.64 = Ma2 ) )
% 5.44/5.64 & ( ( Xa2 != Mi2 )
% 5.44/5.64 => ( Xa2 = Ma2 ) ) )
% 5.44/5.64 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.44/5.64 @ Ma2 ) ) )
% 5.44/5.64 @ ( suc @ ( suc @ Va2 ) )
% 5.44/5.64 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 @ Summary2 ) )
% 5.44/5.64 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_delete.pelims
% 5.44/5.64 thf(fact_3312_vebt__insert_Opelims,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.44/5.64 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.44/5.64 = Y )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 5.44/5.64 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.64 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.44/5.64 & ( ( Xa2 != one_one_nat )
% 5.44/5.64 => ( Y
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( if_VEBT_VEBT
% 5.44/5.64 @ ( ( 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 @ TreeList3 ) )
% 5.44/5.64 & ~ ( ( Xa2 = Mi2 )
% 5.44/5.64 | ( Xa2 = Ma2 ) ) )
% 5.44/5.64 @ ( 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 @ TreeList3 @ ( 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 @ TreeList3 @ ( 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 @ TreeList3 @ ( 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 ) )
% 5.44/5.64 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_insert.pelims
% 5.44/5.64 thf(fact_3313_vebt__member_Opelims_I1_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.44/5.64 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.44/5.64 = Y )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => A3 )
% 5.44/5.64 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.64 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.64 => B3 )
% 5.44/5.64 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.64 => ( ~ Y
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.44/5.64 => ( ~ Y
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.44/5.64 => ( ~ Y
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( ( Xa2 != Mi2 )
% 5.44/5.64 => ( ( Xa2 != Ma2 )
% 5.44/5.64 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.64 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_member.pelims(1)
% 5.44/5.64 thf(fact_3314_vebt__member_Opelims_I3_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.64 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.44/5.64 => ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => A3 )
% 5.44/5.64 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.64 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.64 => B3 )
% 5.44/5.64 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.44/5.64 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.44/5.64 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.44/5.64 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.44/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.44/5.64 => ( ( Xa2 != Mi2 )
% 5.44/5.64 => ( ( Xa2 != Ma2 )
% 5.44/5.64 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.64 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_member.pelims(3)
% 5.44/5.64 thf(fact_3315_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.64 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.44/5.64 => ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => A3 )
% 5.44/5.64 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.64 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.64 => B3 )
% 5.44/5.64 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.44/5.64 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.44/5.64 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) )
% 5.44/5.64 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % VEBT_internal.naive_member.pelims(3)
% 5.44/5.64 thf(fact_3316_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.64 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.44/5.64 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => A3 )
% 5.44/5.64 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.64 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.64 => B3 )
% 5.44/5.64 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.44/5.64 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) )
% 5.44/5.64 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % VEBT_internal.naive_member.pelims(2)
% 5.44/5.64 thf(fact_3317_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.44/5.64 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.44/5.64 = Y )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => A3 )
% 5.44/5.64 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.64 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.64 => B3 )
% 5.44/5.64 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.44/5.64 => ( ~ Y
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % VEBT_internal.naive_member.pelims(1)
% 5.44/5.64 thf(fact_3318_max__enat__simps_I3_J,axiom,
% 5.44/5.64 ! [Q2: extended_enat] :
% 5.44/5.64 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.44/5.64 = Q2 ) ).
% 5.44/5.64
% 5.44/5.64 % max_enat_simps(3)
% 5.44/5.64 thf(fact_3319_max__enat__simps_I2_J,axiom,
% 5.44/5.64 ! [Q2: extended_enat] :
% 5.44/5.64 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.44/5.64 = Q2 ) ).
% 5.44/5.64
% 5.44/5.64 % max_enat_simps(2)
% 5.44/5.64 thf(fact_3320_set__bit__nonnegative__int__iff,axiom,
% 5.44/5.64 ! [N2: nat,K: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) )
% 5.44/5.64 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.44/5.64
% 5.44/5.64 % set_bit_nonnegative_int_iff
% 5.44/5.64 thf(fact_3321_set__bit__negative__int__iff,axiom,
% 5.44/5.64 ! [N2: nat,K: int] :
% 5.44/5.64 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 5.44/5.64 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % set_bit_negative_int_iff
% 5.44/5.64 thf(fact_3322_imult__is__0,axiom,
% 5.44/5.64 ! [M: extended_enat,N2: extended_enat] :
% 5.44/5.64 ( ( ( times_7803423173614009249d_enat @ M @ N2 )
% 5.44/5.64 = zero_z5237406670263579293d_enat )
% 5.44/5.64 = ( ( M = zero_z5237406670263579293d_enat )
% 5.44/5.64 | ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % imult_is_0
% 5.44/5.64 thf(fact_3323_zero__one__enat__neq_I1_J,axiom,
% 5.44/5.64 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.44/5.64
% 5.44/5.64 % zero_one_enat_neq(1)
% 5.44/5.64 thf(fact_3324_bot__enat__def,axiom,
% 5.44/5.64 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.44/5.64
% 5.44/5.64 % bot_enat_def
% 5.44/5.64 thf(fact_3325_set__bit__greater__eq,axiom,
% 5.44/5.64 ! [K: int,N2: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N2 @ K ) ) ).
% 5.44/5.64
% 5.44/5.64 % set_bit_greater_eq
% 5.44/5.64 thf(fact_3326_vebt__member_Opelims_I2_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.64 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [A3: $o,B3: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 5.44/5.64 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.64 => A3 )
% 5.44/5.64 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.64 => ( ( ( Xa2 = one_one_nat )
% 5.44/5.64 => B3 )
% 5.44/5.64 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.44/5.64 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.44/5.64 => ~ ( ( Xa2 != Mi2 )
% 5.44/5.64 => ( ( Xa2 != Ma2 )
% 5.44/5.64 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.44/5.64 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.64 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.44/5.64 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % vebt_member.pelims(2)
% 5.44/5.64 thf(fact_3327_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.44/5.64 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.44/5.64 = Y )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [Uu2: $o,Uv2: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.64 => ( ~ Y
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.44/5.64 => ( ~ Y
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( ( Xa2 = Mi2 )
% 5.44/5.64 | ( Xa2 = Ma2 ) ) )
% 5.44/5.64 => ~ ( 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 ) ) ) )
% 5.44/5.64 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( ( Xa2 = Mi2 )
% 5.44/5.64 | ( Xa2 = Ma2 )
% 5.44/5.64 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 5.44/5.64 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.44/5.64 => ( ( Y
% 5.44/5.64 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % VEBT_internal.membermima.pelims(1)
% 5.44/5.64 thf(fact_3328_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.64 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [Uu2: $o,Uv2: $o] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.44/5.64 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.44/5.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.44/5.64 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.44/5.64 => ( ( 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 ) )
% 5.44/5.64 => ( ( Xa2 = Mi2 )
% 5.44/5.64 | ( Xa2 = Ma2 ) ) ) )
% 5.44/5.64 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.44/5.64 => ( ( Xa2 = Mi2 )
% 5.44/5.64 | ( Xa2 = Ma2 )
% 5.44/5.64 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.44/5.64 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.44/5.64 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % VEBT_internal.membermima.pelims(3)
% 5.44/5.64 thf(fact_3329_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.44/5.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.64 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.64 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.44/5.64 => ( ( 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 ) )
% 5.44/5.64 => ~ ( ( Xa2 = Mi2 )
% 5.44/5.64 | ( Xa2 = Ma2 ) ) ) )
% 5.44/5.64 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.44/5.64 => ~ ( ( Xa2 = Mi2 )
% 5.44/5.64 | ( Xa2 = Ma2 )
% 5.44/5.64 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.44/5.64 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.44/5.64 ( ( X
% 5.44/5.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.44/5.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.44/5.64 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.44/5.64 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.64 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % VEBT_internal.membermima.pelims(2)
% 5.44/5.64 thf(fact_3330_atLeastatMost__empty,axiom,
% 5.44/5.64 ! [B: extended_enat,A: extended_enat] :
% 5.44/5.64 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.44/5.64 => ( ( set_or5403411693681687835d_enat @ A @ B )
% 5.44/5.64 = bot_bo7653980558646680370d_enat ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty
% 5.44/5.64 thf(fact_3331_atLeastatMost__empty,axiom,
% 5.44/5.64 ! [B: num,A: num] :
% 5.44/5.64 ( ( ord_less_num @ B @ A )
% 5.44/5.64 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.44/5.64 = bot_bot_set_num ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty
% 5.44/5.64 thf(fact_3332_atLeastatMost__empty,axiom,
% 5.44/5.64 ! [B: nat,A: nat] :
% 5.44/5.64 ( ( ord_less_nat @ B @ A )
% 5.44/5.64 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.44/5.64 = bot_bot_set_nat ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty
% 5.44/5.64 thf(fact_3333_atLeastatMost__empty,axiom,
% 5.44/5.64 ! [B: int,A: int] :
% 5.44/5.64 ( ( ord_less_int @ B @ A )
% 5.44/5.64 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.44/5.64 = bot_bot_set_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty
% 5.44/5.64 thf(fact_3334_atLeastatMost__empty,axiom,
% 5.44/5.64 ! [B: real,A: real] :
% 5.44/5.64 ( ( ord_less_real @ B @ A )
% 5.44/5.64 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.44/5.64 = bot_bot_set_real ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty
% 5.44/5.64 thf(fact_3335_atLeastatMost__subset__iff,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,C: set_real,D: set_real] :
% 5.44/5.64 ( ( ord_le3558479182127378552t_real @ ( set_or7743017856606604397t_real @ A @ B ) @ ( set_or7743017856606604397t_real @ C @ D ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_set_real @ C @ A )
% 5.44/5.64 & ( ord_less_eq_set_real @ B @ D ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_subset_iff
% 5.44/5.64 thf(fact_3336_atLeastatMost__subset__iff,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.44/5.64 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.44/5.64 & ( ord_less_eq_set_nat @ B @ D ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_subset_iff
% 5.44/5.64 thf(fact_3337_atLeastatMost__subset__iff,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num,D: num] :
% 5.44/5.64 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_num @ C @ A )
% 5.44/5.64 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_subset_iff
% 5.44/5.64 thf(fact_3338_atLeastatMost__subset__iff,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.64 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_nat @ C @ A )
% 5.44/5.64 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_subset_iff
% 5.44/5.64 thf(fact_3339_atLeastatMost__subset__iff,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.64 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_int @ C @ A )
% 5.44/5.64 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_subset_iff
% 5.44/5.64 thf(fact_3340_atLeastatMost__subset__iff,axiom,
% 5.44/5.64 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.64 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_real @ C @ A )
% 5.44/5.64 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_subset_iff
% 5.44/5.64 thf(fact_3341_atLeastatMost__empty__iff,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real] :
% 5.44/5.64 ( ( ( set_or7743017856606604397t_real @ A @ B )
% 5.44/5.64 = bot_bot_set_set_real )
% 5.44/5.64 = ( ~ ( ord_less_eq_set_real @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff
% 5.44/5.64 thf(fact_3342_atLeastatMost__empty__iff,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat] :
% 5.44/5.64 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 5.44/5.64 = bot_bot_set_set_nat )
% 5.44/5.64 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff
% 5.44/5.64 thf(fact_3343_atLeastatMost__empty__iff,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.44/5.64 = bot_bot_set_num )
% 5.44/5.64 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff
% 5.44/5.64 thf(fact_3344_atLeastatMost__empty__iff,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.44/5.64 = bot_bot_set_nat )
% 5.44/5.64 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff
% 5.44/5.64 thf(fact_3345_atLeastatMost__empty__iff,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.44/5.64 = bot_bot_set_int )
% 5.44/5.64 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff
% 5.44/5.64 thf(fact_3346_atLeastatMost__empty__iff,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.44/5.64 = bot_bot_set_real )
% 5.44/5.64 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff
% 5.44/5.64 thf(fact_3347_atLeastatMost__empty__iff2,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real] :
% 5.44/5.64 ( ( bot_bot_set_set_real
% 5.44/5.64 = ( set_or7743017856606604397t_real @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_set_real @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff2
% 5.44/5.64 thf(fact_3348_atLeastatMost__empty__iff2,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat] :
% 5.44/5.64 ( ( bot_bot_set_set_nat
% 5.44/5.64 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff2
% 5.44/5.64 thf(fact_3349_atLeastatMost__empty__iff2,axiom,
% 5.44/5.64 ! [A: num,B: num] :
% 5.44/5.64 ( ( bot_bot_set_num
% 5.44/5.64 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff2
% 5.44/5.64 thf(fact_3350_atLeastatMost__empty__iff2,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( bot_bot_set_nat
% 5.44/5.64 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff2
% 5.44/5.64 thf(fact_3351_atLeastatMost__empty__iff2,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( bot_bot_set_int
% 5.44/5.64 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff2
% 5.44/5.64 thf(fact_3352_atLeastatMost__empty__iff2,axiom,
% 5.44/5.64 ! [A: real,B: real] :
% 5.44/5.64 ( ( bot_bot_set_real
% 5.44/5.64 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.44/5.64 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_empty_iff2
% 5.44/5.64 thf(fact_3353_Icc__eq__Icc,axiom,
% 5.44/5.64 ! [L2: set_real,H2: set_real,L3: set_real,H3: set_real] :
% 5.44/5.64 ( ( ( set_or7743017856606604397t_real @ L2 @ H2 )
% 5.44/5.64 = ( set_or7743017856606604397t_real @ L3 @ H3 ) )
% 5.44/5.64 = ( ( ( L2 = L3 )
% 5.44/5.64 & ( H2 = H3 ) )
% 5.44/5.64 | ( ~ ( ord_less_eq_set_real @ L2 @ H2 )
% 5.44/5.64 & ~ ( ord_less_eq_set_real @ L3 @ H3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Icc_eq_Icc
% 5.44/5.64 thf(fact_3354_Icc__eq__Icc,axiom,
% 5.44/5.64 ! [L2: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 5.44/5.64 ( ( ( set_or4548717258645045905et_nat @ L2 @ H2 )
% 5.44/5.64 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 5.44/5.64 = ( ( ( L2 = L3 )
% 5.44/5.64 & ( H2 = H3 ) )
% 5.44/5.64 | ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 5.44/5.64 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Icc_eq_Icc
% 5.44/5.64 thf(fact_3355_Icc__eq__Icc,axiom,
% 5.44/5.64 ! [L2: num,H2: num,L3: num,H3: num] :
% 5.44/5.64 ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 5.44/5.64 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.44/5.64 = ( ( ( L2 = L3 )
% 5.44/5.64 & ( H2 = H3 ) )
% 5.44/5.64 | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.44/5.64 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Icc_eq_Icc
% 5.44/5.64 thf(fact_3356_Icc__eq__Icc,axiom,
% 5.44/5.64 ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 5.44/5.64 ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 5.44/5.64 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.44/5.64 = ( ( ( L2 = L3 )
% 5.44/5.64 & ( H2 = H3 ) )
% 5.44/5.64 | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.44/5.64 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Icc_eq_Icc
% 5.44/5.64 thf(fact_3357_Icc__eq__Icc,axiom,
% 5.44/5.64 ! [L2: int,H2: int,L3: int,H3: int] :
% 5.44/5.64 ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 5.44/5.64 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.44/5.64 = ( ( ( L2 = L3 )
% 5.44/5.64 & ( H2 = H3 ) )
% 5.44/5.64 | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.44/5.64 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Icc_eq_Icc
% 5.44/5.64 thf(fact_3358_Icc__eq__Icc,axiom,
% 5.44/5.64 ! [L2: real,H2: real,L3: real,H3: real] :
% 5.44/5.64 ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 5.44/5.64 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.44/5.64 = ( ( ( L2 = L3 )
% 5.44/5.64 & ( H2 = H3 ) )
% 5.44/5.64 | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.44/5.64 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Icc_eq_Icc
% 5.44/5.64 thf(fact_3359_atLeastAtMost__iff,axiom,
% 5.44/5.64 ! [I2: set_real,L2: set_real,U: set_real] :
% 5.44/5.64 ( ( member_set_real @ I2 @ ( set_or7743017856606604397t_real @ L2 @ U ) )
% 5.44/5.64 = ( ( ord_less_eq_set_real @ L2 @ I2 )
% 5.44/5.64 & ( ord_less_eq_set_real @ I2 @ U ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastAtMost_iff
% 5.44/5.64 thf(fact_3360_atLeastAtMost__iff,axiom,
% 5.44/5.64 ! [I2: set_nat,L2: set_nat,U: set_nat] :
% 5.44/5.64 ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 5.44/5.64 = ( ( ord_less_eq_set_nat @ L2 @ I2 )
% 5.44/5.64 & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastAtMost_iff
% 5.44/5.64 thf(fact_3361_atLeastAtMost__iff,axiom,
% 5.44/5.64 ! [I2: num,L2: num,U: num] :
% 5.44/5.64 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 5.44/5.64 = ( ( ord_less_eq_num @ L2 @ I2 )
% 5.44/5.64 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastAtMost_iff
% 5.44/5.64 thf(fact_3362_atLeastAtMost__iff,axiom,
% 5.44/5.64 ! [I2: nat,L2: nat,U: nat] :
% 5.44/5.64 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.44/5.64 = ( ( ord_less_eq_nat @ L2 @ I2 )
% 5.44/5.64 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastAtMost_iff
% 5.44/5.64 thf(fact_3363_atLeastAtMost__iff,axiom,
% 5.44/5.64 ! [I2: int,L2: int,U: int] :
% 5.44/5.64 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.44/5.64 = ( ( ord_less_eq_int @ L2 @ I2 )
% 5.44/5.64 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastAtMost_iff
% 5.44/5.64 thf(fact_3364_atLeastAtMost__iff,axiom,
% 5.44/5.64 ! [I2: real,L2: real,U: real] :
% 5.44/5.64 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 5.44/5.64 = ( ( ord_less_eq_real @ L2 @ I2 )
% 5.44/5.64 & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastAtMost_iff
% 5.44/5.64 thf(fact_3365_bounded__Max__nat,axiom,
% 5.44/5.64 ! [P: nat > $o,X: nat,M7: nat] :
% 5.44/5.64 ( ( P @ X )
% 5.44/5.64 => ( ! [X5: nat] :
% 5.44/5.64 ( ( P @ X5 )
% 5.44/5.64 => ( ord_less_eq_nat @ X5 @ M7 ) )
% 5.44/5.64 => ~ ! [M5: nat] :
% 5.44/5.64 ( ( P @ M5 )
% 5.44/5.64 => ~ ! [X3: nat] :
% 5.44/5.64 ( ( P @ X3 )
% 5.44/5.64 => ( ord_less_eq_nat @ X3 @ M5 ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % bounded_Max_nat
% 5.44/5.64 thf(fact_3366_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.44/5.64 ! [X: produc3368934014287244435at_num] :
% 5.44/5.64 ~ ! [F2: nat > num > num,A3: nat,B3: nat,Acc: num] :
% 5.44/5.64 ( X
% 5.44/5.64 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A3 @ ( product_Pair_nat_num @ B3 @ Acc ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % fold_atLeastAtMost_nat.cases
% 5.44/5.64 thf(fact_3367_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.44/5.64 ! [X: produc4471711990508489141at_nat] :
% 5.44/5.64 ~ ! [F2: nat > nat > nat,A3: nat,B3: nat,Acc: nat] :
% 5.44/5.64 ( X
% 5.44/5.64 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ Acc ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % fold_atLeastAtMost_nat.cases
% 5.44/5.64 thf(fact_3368_atLeastatMost__psubset__iff,axiom,
% 5.44/5.64 ! [A: extended_enat,B: extended_enat,C: extended_enat,D: extended_enat] :
% 5.44/5.64 ( ( ord_le2529575680413868914d_enat @ ( set_or5403411693681687835d_enat @ A @ B ) @ ( set_or5403411693681687835d_enat @ C @ D ) )
% 5.44/5.64 = ( ( ~ ( ord_le2932123472753598470d_enat @ A @ B )
% 5.44/5.64 | ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.44/5.64 & ( ord_le2932123472753598470d_enat @ B @ D )
% 5.44/5.64 & ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.44/5.64 | ( ord_le72135733267957522d_enat @ B @ D ) ) ) )
% 5.44/5.64 & ( ord_le2932123472753598470d_enat @ C @ D ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_psubset_iff
% 5.44/5.64 thf(fact_3369_atLeastatMost__psubset__iff,axiom,
% 5.44/5.64 ! [A: set_real,B: set_real,C: set_real,D: set_real] :
% 5.44/5.64 ( ( ord_le7926960851185191020t_real @ ( set_or7743017856606604397t_real @ A @ B ) @ ( set_or7743017856606604397t_real @ C @ D ) )
% 5.44/5.64 = ( ( ~ ( ord_less_eq_set_real @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_set_real @ C @ A )
% 5.44/5.64 & ( ord_less_eq_set_real @ B @ D )
% 5.44/5.64 & ( ( ord_less_set_real @ C @ A )
% 5.44/5.64 | ( ord_less_set_real @ B @ D ) ) ) )
% 5.44/5.64 & ( ord_less_eq_set_real @ C @ D ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_psubset_iff
% 5.44/5.64 thf(fact_3370_atLeastatMost__psubset__iff,axiom,
% 5.44/5.64 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.44/5.64 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.44/5.64 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.44/5.64 & ( ord_less_eq_set_nat @ B @ D )
% 5.44/5.64 & ( ( ord_less_set_nat @ C @ A )
% 5.44/5.64 | ( ord_less_set_nat @ B @ D ) ) ) )
% 5.44/5.64 & ( ord_less_eq_set_nat @ C @ D ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_psubset_iff
% 5.44/5.64 thf(fact_3371_atLeastatMost__psubset__iff,axiom,
% 5.44/5.64 ! [A: num,B: num,C: num,D: num] :
% 5.44/5.64 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.44/5.64 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_num @ C @ A )
% 5.44/5.64 & ( ord_less_eq_num @ B @ D )
% 5.44/5.64 & ( ( ord_less_num @ C @ A )
% 5.44/5.64 | ( ord_less_num @ B @ D ) ) ) )
% 5.44/5.64 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_psubset_iff
% 5.44/5.64 thf(fact_3372_atLeastatMost__psubset__iff,axiom,
% 5.44/5.64 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.64 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.44/5.64 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_nat @ C @ A )
% 5.44/5.64 & ( ord_less_eq_nat @ B @ D )
% 5.44/5.64 & ( ( ord_less_nat @ C @ A )
% 5.44/5.64 | ( ord_less_nat @ B @ D ) ) ) )
% 5.44/5.64 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_psubset_iff
% 5.44/5.64 thf(fact_3373_atLeastatMost__psubset__iff,axiom,
% 5.44/5.64 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.64 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.44/5.64 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_int @ C @ A )
% 5.44/5.64 & ( ord_less_eq_int @ B @ D )
% 5.44/5.64 & ( ( ord_less_int @ C @ A )
% 5.44/5.64 | ( ord_less_int @ B @ D ) ) ) )
% 5.44/5.64 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_psubset_iff
% 5.44/5.64 thf(fact_3374_atLeastatMost__psubset__iff,axiom,
% 5.44/5.64 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.64 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.44/5.64 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.44/5.64 | ( ( ord_less_eq_real @ C @ A )
% 5.44/5.64 & ( ord_less_eq_real @ B @ D )
% 5.44/5.64 & ( ( ord_less_real @ C @ A )
% 5.44/5.64 | ( ord_less_real @ B @ D ) ) ) )
% 5.44/5.64 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % atLeastatMost_psubset_iff
% 5.44/5.64 thf(fact_3375_double__eq__0__iff,axiom,
% 5.44/5.64 ! [A: real] :
% 5.44/5.64 ( ( ( plus_plus_real @ A @ A )
% 5.44/5.64 = zero_zero_real )
% 5.44/5.64 = ( A = zero_zero_real ) ) ).
% 5.44/5.64
% 5.44/5.64 % double_eq_0_iff
% 5.44/5.64 thf(fact_3376_double__eq__0__iff,axiom,
% 5.44/5.64 ! [A: int] :
% 5.44/5.64 ( ( ( plus_plus_int @ A @ A )
% 5.44/5.64 = zero_zero_int )
% 5.44/5.64 = ( A = zero_zero_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % double_eq_0_iff
% 5.44/5.64 thf(fact_3377_unset__bit__0,axiom,
% 5.44/5.64 ! [A: code_integer] :
% 5.44/5.64 ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 5.44/5.64 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % unset_bit_0
% 5.44/5.64 thf(fact_3378_unset__bit__0,axiom,
% 5.44/5.64 ! [A: int] :
% 5.44/5.64 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.44/5.64 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % unset_bit_0
% 5.44/5.64 thf(fact_3379_unset__bit__0,axiom,
% 5.44/5.64 ! [A: nat] :
% 5.44/5.64 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.44/5.64 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % unset_bit_0
% 5.44/5.64 thf(fact_3380_Bolzano,axiom,
% 5.44/5.64 ! [A: real,B: real,P: real > real > $o] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.64 => ( ! [A3: real,B3: real,C3: real] :
% 5.44/5.64 ( ( P @ A3 @ B3 )
% 5.44/5.64 => ( ( P @ B3 @ C3 )
% 5.44/5.64 => ( ( ord_less_eq_real @ A3 @ B3 )
% 5.44/5.64 => ( ( ord_less_eq_real @ B3 @ C3 )
% 5.44/5.64 => ( P @ A3 @ C3 ) ) ) ) )
% 5.44/5.64 => ( ! [X5: real] :
% 5.44/5.64 ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.64 => ( ( ord_less_eq_real @ X5 @ B )
% 5.44/5.64 => ? [D5: real] :
% 5.44/5.64 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.44/5.64 & ! [A3: real,B3: real] :
% 5.44/5.64 ( ( ( ord_less_eq_real @ A3 @ X5 )
% 5.44/5.64 & ( ord_less_eq_real @ X5 @ B3 )
% 5.44/5.64 & ( ord_less_real @ ( minus_minus_real @ B3 @ A3 ) @ D5 ) )
% 5.44/5.64 => ( P @ A3 @ B3 ) ) ) ) )
% 5.44/5.64 => ( P @ A @ B ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % Bolzano
% 5.44/5.64 thf(fact_3381_mult__le__cancel__iff1,axiom,
% 5.44/5.64 ! [Z: real,X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.44/5.64 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.44/5.64 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % mult_le_cancel_iff1
% 5.44/5.64 thf(fact_3382_mult__le__cancel__iff1,axiom,
% 5.44/5.64 ! [Z: int,X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.44/5.64 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.44/5.64 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % mult_le_cancel_iff1
% 5.44/5.64 thf(fact_3383_mult__le__cancel__iff2,axiom,
% 5.44/5.64 ! [Z: real,X: real,Y: real] :
% 5.44/5.64 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.44/5.64 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 5.44/5.64 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % mult_le_cancel_iff2
% 5.44/5.64 thf(fact_3384_mult__le__cancel__iff2,axiom,
% 5.44/5.64 ! [Z: int,X: int,Y: int] :
% 5.44/5.64 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.44/5.64 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 5.44/5.64 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % mult_le_cancel_iff2
% 5.44/5.64 thf(fact_3385_divides__aux__eq,axiom,
% 5.44/5.64 ! [Q2: nat,R: nat] :
% 5.44/5.64 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.44/5.64 = ( R = zero_zero_nat ) ) ).
% 5.44/5.64
% 5.44/5.64 % divides_aux_eq
% 5.44/5.64 thf(fact_3386_divides__aux__eq,axiom,
% 5.44/5.64 ! [Q2: int,R: int] :
% 5.44/5.64 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.44/5.64 = ( R = zero_zero_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % divides_aux_eq
% 5.44/5.64 thf(fact_3387_low__def,axiom,
% 5.44/5.64 ( vEBT_VEBT_low
% 5.44/5.64 = ( ^ [X2: nat,N: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.64
% 5.44/5.64 % low_def
% 5.44/5.64 thf(fact_3388_mod__mod__trivial,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.44/5.64 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % mod_mod_trivial
% 5.44/5.64 thf(fact_3389_mod__mod__trivial,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.44/5.64 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % mod_mod_trivial
% 5.44/5.64 thf(fact_3390_bits__mod__0,axiom,
% 5.44/5.64 ! [A: nat] :
% 5.44/5.64 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.44/5.64 = zero_zero_nat ) ).
% 5.44/5.64
% 5.44/5.64 % bits_mod_0
% 5.44/5.64 thf(fact_3391_bits__mod__0,axiom,
% 5.44/5.64 ! [A: int] :
% 5.44/5.64 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.44/5.64 = zero_zero_int ) ).
% 5.44/5.64
% 5.44/5.64 % bits_mod_0
% 5.44/5.64 thf(fact_3392_mod__add__self2,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.44/5.64 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % mod_add_self2
% 5.44/5.64 thf(fact_3393_mod__add__self2,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.44/5.64 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % mod_add_self2
% 5.44/5.64 thf(fact_3394_mod__add__self1,axiom,
% 5.44/5.64 ! [B: nat,A: nat] :
% 5.44/5.64 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.44/5.64 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % mod_add_self1
% 5.44/5.64 thf(fact_3395_mod__add__self1,axiom,
% 5.44/5.64 ! [B: int,A: int] :
% 5.44/5.64 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.44/5.64 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % mod_add_self1
% 5.44/5.64 thf(fact_3396_minus__mod__self2,axiom,
% 5.44/5.64 ! [A: int,B: int] :
% 5.44/5.64 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.44/5.64 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.64
% 5.44/5.64 % minus_mod_self2
% 5.44/5.64 thf(fact_3397_unset__bit__nonnegative__int__iff,axiom,
% 5.44/5.64 ! [N2: nat,K: int] :
% 5.44/5.64 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) )
% 5.44/5.64 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.44/5.64
% 5.44/5.64 % unset_bit_nonnegative_int_iff
% 5.44/5.64 thf(fact_3398_unset__bit__negative__int__iff,axiom,
% 5.44/5.64 ! [N2: nat,K: int] :
% 5.44/5.64 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 5.44/5.64 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.44/5.64
% 5.44/5.64 % unset_bit_negative_int_iff
% 5.44/5.64 thf(fact_3399_mod__less,axiom,
% 5.44/5.64 ! [M: nat,N2: nat] :
% 5.44/5.64 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.64 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.44/5.64 = M ) ) ).
% 5.44/5.64
% 5.44/5.64 % mod_less
% 5.44/5.64 thf(fact_3400_mod__mult__self1__is__0,axiom,
% 5.44/5.64 ! [B: nat,A: nat] :
% 5.44/5.64 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.44/5.64 = zero_zero_nat ) ).
% 5.44/5.64
% 5.44/5.64 % mod_mult_self1_is_0
% 5.44/5.64 thf(fact_3401_mod__mult__self1__is__0,axiom,
% 5.44/5.64 ! [B: int,A: int] :
% 5.44/5.64 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.44/5.64 = zero_zero_int ) ).
% 5.44/5.64
% 5.44/5.64 % mod_mult_self1_is_0
% 5.44/5.64 thf(fact_3402_mod__mult__self2__is__0,axiom,
% 5.44/5.64 ! [A: nat,B: nat] :
% 5.44/5.64 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.44/5.64 = zero_zero_nat ) ).
% 5.44/5.64
% 5.44/5.64 % mod_mult_self2_is_0
% 5.44/5.65 thf(fact_3403_mod__mult__self2__is__0,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.44/5.65 = zero_zero_int ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self2_is_0
% 5.44/5.65 thf(fact_3404_mod__by__1,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.44/5.65 = zero_zero_nat ) ).
% 5.44/5.65
% 5.44/5.65 % mod_by_1
% 5.44/5.65 thf(fact_3405_mod__by__1,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.44/5.65 = zero_zero_int ) ).
% 5.44/5.65
% 5.44/5.65 % mod_by_1
% 5.44/5.65 thf(fact_3406_bits__mod__by__1,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.44/5.65 = zero_zero_nat ) ).
% 5.44/5.65
% 5.44/5.65 % bits_mod_by_1
% 5.44/5.65 thf(fact_3407_bits__mod__by__1,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.44/5.65 = zero_zero_int ) ).
% 5.44/5.65
% 5.44/5.65 % bits_mod_by_1
% 5.44/5.65 thf(fact_3408_bits__mod__div__trivial,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.44/5.65 = zero_z3403309356797280102nteger ) ).
% 5.44/5.65
% 5.44/5.65 % bits_mod_div_trivial
% 5.44/5.65 thf(fact_3409_bits__mod__div__trivial,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.44/5.65 = zero_zero_nat ) ).
% 5.44/5.65
% 5.44/5.65 % bits_mod_div_trivial
% 5.44/5.65 thf(fact_3410_bits__mod__div__trivial,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.44/5.65 = zero_zero_int ) ).
% 5.44/5.65
% 5.44/5.65 % bits_mod_div_trivial
% 5.44/5.65 thf(fact_3411_mod__div__trivial,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.44/5.65 = zero_z3403309356797280102nteger ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_trivial
% 5.44/5.65 thf(fact_3412_mod__div__trivial,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.44/5.65 = zero_zero_nat ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_trivial
% 5.44/5.65 thf(fact_3413_mod__div__trivial,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.44/5.65 = zero_zero_int ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_trivial
% 5.44/5.65 thf(fact_3414_mod__mult__self4,axiom,
% 5.44/5.65 ! [B: nat,C: nat,A: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self4
% 5.44/5.65 thf(fact_3415_mod__mult__self4,axiom,
% 5.44/5.65 ! [B: int,C: int,A: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.44/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self4
% 5.44/5.65 thf(fact_3416_mod__mult__self3,axiom,
% 5.44/5.65 ! [C: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self3
% 5.44/5.65 thf(fact_3417_mod__mult__self3,axiom,
% 5.44/5.65 ! [C: int,B: int,A: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.44/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self3
% 5.44/5.65 thf(fact_3418_mod__mult__self2,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self2
% 5.44/5.65 thf(fact_3419_mod__mult__self2,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.44/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self2
% 5.44/5.65 thf(fact_3420_mod__mult__self1,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self1
% 5.44/5.65 thf(fact_3421_mod__mult__self1,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.44/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_self1
% 5.44/5.65 thf(fact_3422_mod__by__Suc__0,axiom,
% 5.44/5.65 ! [M: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.44/5.65 = zero_zero_nat ) ).
% 5.44/5.65
% 5.44/5.65 % mod_by_Suc_0
% 5.44/5.65 thf(fact_3423_Suc__mod__mult__self4,axiom,
% 5.44/5.65 ! [N2: nat,K: nat,M: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % Suc_mod_mult_self4
% 5.44/5.65 thf(fact_3424_Suc__mod__mult__self3,axiom,
% 5.44/5.65 ! [K: nat,N2: nat,M: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % Suc_mod_mult_self3
% 5.44/5.65 thf(fact_3425_Suc__mod__mult__self2,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,K: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % Suc_mod_mult_self2
% 5.44/5.65 thf(fact_3426_Suc__mod__mult__self1,axiom,
% 5.44/5.65 ! [M: nat,K: nat,N2: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % Suc_mod_mult_self1
% 5.44/5.65 thf(fact_3427_bits__one__mod__two__eq__one,axiom,
% 5.44/5.65 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_nat ) ).
% 5.44/5.65
% 5.44/5.65 % bits_one_mod_two_eq_one
% 5.44/5.65 thf(fact_3428_bits__one__mod__two__eq__one,axiom,
% 5.44/5.65 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_int ) ).
% 5.44/5.65
% 5.44/5.65 % bits_one_mod_two_eq_one
% 5.44/5.65 thf(fact_3429_one__mod__two__eq__one,axiom,
% 5.44/5.65 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_nat ) ).
% 5.44/5.65
% 5.44/5.65 % one_mod_two_eq_one
% 5.44/5.65 thf(fact_3430_one__mod__two__eq__one,axiom,
% 5.44/5.65 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_int ) ).
% 5.44/5.65
% 5.44/5.65 % one_mod_two_eq_one
% 5.44/5.65 thf(fact_3431_mod2__Suc__Suc,axiom,
% 5.44/5.65 ! [M: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod2_Suc_Suc
% 5.44/5.65 thf(fact_3432_Suc__times__numeral__mod__eq,axiom,
% 5.44/5.65 ! [K: num,N2: nat] :
% 5.44/5.65 ( ( ( numeral_numeral_nat @ K )
% 5.44/5.65 != one_one_nat )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 5.44/5.65 = one_one_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % Suc_times_numeral_mod_eq
% 5.44/5.65 thf(fact_3433_not__mod__2__eq__1__eq__0,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 != one_one_nat )
% 5.44/5.65 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % not_mod_2_eq_1_eq_0
% 5.44/5.65 thf(fact_3434_not__mod__2__eq__1__eq__0,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 != one_one_int )
% 5.44/5.65 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % not_mod_2_eq_1_eq_0
% 5.44/5.65 thf(fact_3435_not__mod__2__eq__0__eq__1,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 != zero_zero_nat )
% 5.44/5.65 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % not_mod_2_eq_0_eq_1
% 5.44/5.65 thf(fact_3436_not__mod__2__eq__0__eq__1,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 != zero_zero_int )
% 5.44/5.65 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % not_mod_2_eq_0_eq_1
% 5.44/5.65 thf(fact_3437_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 != ( suc @ zero_zero_nat ) )
% 5.44/5.65 = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % not_mod2_eq_Suc_0_eq_0
% 5.44/5.65 thf(fact_3438_add__self__mod__2,axiom,
% 5.44/5.65 ! [M: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_zero_nat ) ).
% 5.44/5.65
% 5.44/5.65 % add_self_mod_2
% 5.44/5.65 thf(fact_3439_mod2__gr__0,axiom,
% 5.44/5.65 ! [M: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod2_gr_0
% 5.44/5.65 thf(fact_3440_mod__mult__right__eq,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_right_eq
% 5.44/5.65 thf(fact_3441_mod__mult__right__eq,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_right_eq
% 5.44/5.65 thf(fact_3442_mod__mult__left__eq,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_left_eq
% 5.44/5.65 thf(fact_3443_mod__mult__left__eq,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_left_eq
% 5.44/5.65 thf(fact_3444_mult__mod__right,axiom,
% 5.44/5.65 ! [C: nat,A: nat,B: nat] :
% 5.44/5.65 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.44/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_mod_right
% 5.44/5.65 thf(fact_3445_mult__mod__right,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.44/5.65 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_mod_right
% 5.44/5.65 thf(fact_3446_mod__mult__mult2,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.44/5.65 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_mult2
% 5.44/5.65 thf(fact_3447_mod__mult__mult2,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.44/5.65 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_mult2
% 5.44/5.65 thf(fact_3448_mod__mult__cong,axiom,
% 5.44/5.65 ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ A @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ A6 @ C ) )
% 5.44/5.65 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ B6 @ C ) )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_cong
% 5.44/5.65 thf(fact_3449_mod__mult__cong,axiom,
% 5.44/5.65 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.44/5.65 = ( modulo_modulo_int @ A6 @ C ) )
% 5.44/5.65 => ( ( ( modulo_modulo_int @ B @ C )
% 5.44/5.65 = ( modulo_modulo_int @ B6 @ C ) )
% 5.44/5.65 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( times_times_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_cong
% 5.44/5.65 thf(fact_3450_mod__mult__eq,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_eq
% 5.44/5.65 thf(fact_3451_mod__mult__eq,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_eq
% 5.44/5.65 thf(fact_3452_mod__add__right__eq,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_add_right_eq
% 5.44/5.65 thf(fact_3453_mod__add__right__eq,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_add_right_eq
% 5.44/5.65 thf(fact_3454_mod__add__left__eq,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_add_left_eq
% 5.44/5.65 thf(fact_3455_mod__add__left__eq,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_add_left_eq
% 5.44/5.65 thf(fact_3456_mod__add__cong,axiom,
% 5.44/5.65 ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ A @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ A6 @ C ) )
% 5.44/5.65 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ B6 @ C ) )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ ( plus_plus_nat @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_add_cong
% 5.44/5.65 thf(fact_3457_mod__add__cong,axiom,
% 5.44/5.65 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.44/5.65 = ( modulo_modulo_int @ A6 @ C ) )
% 5.44/5.65 => ( ( ( modulo_modulo_int @ B @ C )
% 5.44/5.65 = ( modulo_modulo_int @ B6 @ C ) )
% 5.44/5.65 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( plus_plus_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_add_cong
% 5.44/5.65 thf(fact_3458_mod__add__eq,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_add_eq
% 5.44/5.65 thf(fact_3459_mod__add__eq,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_add_eq
% 5.44/5.65 thf(fact_3460_mod__diff__right__eq,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_diff_right_eq
% 5.44/5.65 thf(fact_3461_mod__diff__left__eq,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_diff_left_eq
% 5.44/5.65 thf(fact_3462_mod__diff__cong,axiom,
% 5.44/5.65 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.44/5.65 = ( modulo_modulo_int @ A6 @ C ) )
% 5.44/5.65 => ( ( ( modulo_modulo_int @ B @ C )
% 5.44/5.65 = ( modulo_modulo_int @ B6 @ C ) )
% 5.44/5.65 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( minus_minus_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_diff_cong
% 5.44/5.65 thf(fact_3463_mod__diff__eq,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_diff_eq
% 5.44/5.65 thf(fact_3464_power__mod,axiom,
% 5.44/5.65 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
% 5.44/5.65 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_mod
% 5.44/5.65 thf(fact_3465_power__mod,axiom,
% 5.44/5.65 ! [A: int,B: int,N2: nat] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N2 ) @ B )
% 5.44/5.65 = ( modulo_modulo_int @ ( power_power_int @ A @ N2 ) @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_mod
% 5.44/5.65 thf(fact_3466_mod__Suc__Suc__eq,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_Suc_Suc_eq
% 5.44/5.65 thf(fact_3467_mod__Suc__eq,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_Suc_eq
% 5.44/5.65 thf(fact_3468_mod__less__eq__dividend,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 5.44/5.65
% 5.44/5.65 % mod_less_eq_dividend
% 5.44/5.65 thf(fact_3469_unset__bit__less__eq,axiom,
% 5.44/5.65 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ K ) ).
% 5.44/5.65
% 5.44/5.65 % unset_bit_less_eq
% 5.44/5.65 thf(fact_3470_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.65 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.44/5.65 thf(fact_3471_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.65 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.44/5.65 thf(fact_3472_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.65 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.44/5.65 thf(fact_3473_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.65 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.44/5.65 thf(fact_3474_cong__exp__iff__simps_I9_J,axiom,
% 5.44/5.65 ! [M: num,Q2: num,N2: num] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.65 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.44/5.65 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.44/5.65 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(9)
% 5.44/5.65 thf(fact_3475_cong__exp__iff__simps_I9_J,axiom,
% 5.44/5.65 ! [M: num,Q2: num,N2: num] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.65 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.44/5.65 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.44/5.65 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(9)
% 5.44/5.65 thf(fact_3476_mod__eq__self__iff__div__eq__0,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.44/5.65 = A )
% 5.44/5.65 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.44/5.65 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_self_iff_div_eq_0
% 5.44/5.65 thf(fact_3477_mod__eq__self__iff__div__eq__0,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ A @ B )
% 5.44/5.65 = A )
% 5.44/5.65 = ( ( divide_divide_nat @ A @ B )
% 5.44/5.65 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_self_iff_div_eq_0
% 5.44/5.65 thf(fact_3478_mod__eq__self__iff__div__eq__0,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ A @ B )
% 5.44/5.65 = A )
% 5.44/5.65 = ( ( divide_divide_int @ A @ B )
% 5.44/5.65 = zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_self_iff_div_eq_0
% 5.44/5.65 thf(fact_3479_cong__exp__iff__simps_I4_J,axiom,
% 5.44/5.65 ! [M: num,N2: num] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.44/5.65 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(4)
% 5.44/5.65 thf(fact_3480_cong__exp__iff__simps_I4_J,axiom,
% 5.44/5.65 ! [M: num,N2: num] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.44/5.65 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(4)
% 5.44/5.65 thf(fact_3481_mod__eqE,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.44/5.65 = ( modulo_modulo_int @ B @ C ) )
% 5.44/5.65 => ~ ! [D3: int] :
% 5.44/5.65 ( B
% 5.44/5.65 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eqE
% 5.44/5.65 thf(fact_3482_div__add1__eq,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_add1_eq
% 5.44/5.65 thf(fact_3483_div__add1__eq,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.65 = ( 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 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_add1_eq
% 5.44/5.65 thf(fact_3484_div__add1__eq,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.65 = ( 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 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_add1_eq
% 5.44/5.65 thf(fact_3485_mod__Suc,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.44/5.65 = N2 )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 5.44/5.65 = zero_zero_nat ) )
% 5.44/5.65 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.44/5.65 != N2 )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 5.44/5.65 = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_Suc
% 5.44/5.65 thf(fact_3486_mod__induct,axiom,
% 5.44/5.65 ! [P: nat > $o,N2: nat,P5: nat,M: nat] :
% 5.44/5.65 ( ( P @ N2 )
% 5.44/5.65 => ( ( ord_less_nat @ N2 @ P5 )
% 5.44/5.65 => ( ( ord_less_nat @ M @ P5 )
% 5.44/5.65 => ( ! [N4: nat] :
% 5.44/5.65 ( ( ord_less_nat @ N4 @ P5 )
% 5.44/5.65 => ( ( P @ N4 )
% 5.44/5.65 => ( P @ ( modulo_modulo_nat @ ( suc @ N4 ) @ P5 ) ) ) )
% 5.44/5.65 => ( P @ M ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_induct
% 5.44/5.65 thf(fact_3487_mod__less__divisor,axiom,
% 5.44/5.65 ! [N2: nat,M: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_less_divisor
% 5.44/5.65 thf(fact_3488_mod__Suc__le__divisor,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 5.44/5.65
% 5.44/5.65 % mod_Suc_le_divisor
% 5.44/5.65 thf(fact_3489_mod__eq__0D,axiom,
% 5.44/5.65 ! [M: nat,D: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ M @ D )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 => ? [Q3: nat] :
% 5.44/5.65 ( M
% 5.44/5.65 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_0D
% 5.44/5.65 thf(fact_3490_mod__if,axiom,
% 5.44/5.65 ( modulo_modulo_nat
% 5.44/5.65 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_if
% 5.44/5.65 thf(fact_3491_mod__geq,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ~ ( ord_less_nat @ M @ N2 )
% 5.44/5.65 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_geq
% 5.44/5.65 thf(fact_3492_nat__mod__eq__iff,axiom,
% 5.44/5.65 ! [X: nat,N2: nat,Y: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ X @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.44/5.65 = ( ? [Q1: nat,Q22: nat] :
% 5.44/5.65 ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
% 5.44/5.65 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % nat_mod_eq_iff
% 5.44/5.65 thf(fact_3493_le__mod__geq,axiom,
% 5.44/5.65 ! [N2: nat,M: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % le_mod_geq
% 5.44/5.65 thf(fact_3494_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.65 => ( ( ord_less_nat @ A @ B )
% 5.44/5.65 => ( ( modulo_modulo_nat @ A @ B )
% 5.44/5.65 = A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.mod_less
% 5.44/5.65 thf(fact_3495_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.65 => ( ( ord_less_int @ A @ B )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ B )
% 5.44/5.65 = A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.mod_less
% 5.44/5.65 thf(fact_3496_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.65 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.44/5.65 thf(fact_3497_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.44/5.65 thf(fact_3498_cong__exp__iff__simps_I2_J,axiom,
% 5.44/5.65 ! [N2: num,Q2: num] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.44/5.65 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(2)
% 5.44/5.65 thf(fact_3499_cong__exp__iff__simps_I2_J,axiom,
% 5.44/5.65 ! [N2: num,Q2: num] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.65 = zero_zero_int )
% 5.44/5.65 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 5.44/5.65 = zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(2)
% 5.44/5.65 thf(fact_3500_cong__exp__iff__simps_I1_J,axiom,
% 5.44/5.65 ! [N2: num] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 5.44/5.65 = zero_zero_nat ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(1)
% 5.44/5.65 thf(fact_3501_cong__exp__iff__simps_I1_J,axiom,
% 5.44/5.65 ! [N2: num] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 5.44/5.65 = zero_zero_int ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(1)
% 5.44/5.65 thf(fact_3502_cong__exp__iff__simps_I6_J,axiom,
% 5.44/5.65 ! [Q2: num,N2: num] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.65 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(6)
% 5.44/5.65 thf(fact_3503_cong__exp__iff__simps_I6_J,axiom,
% 5.44/5.65 ! [Q2: num,N2: num] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.65 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(6)
% 5.44/5.65 thf(fact_3504_cong__exp__iff__simps_I8_J,axiom,
% 5.44/5.65 ! [M: num,Q2: num] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.65 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(8)
% 5.44/5.65 thf(fact_3505_cong__exp__iff__simps_I8_J,axiom,
% 5.44/5.65 ! [M: num,Q2: num] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.65 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % cong_exp_iff_simps(8)
% 5.44/5.65 thf(fact_3506_mult__div__mod__eq,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mult_div_mod_eq
% 5.44/5.65 thf(fact_3507_mult__div__mod__eq,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mult_div_mod_eq
% 5.44/5.65 thf(fact_3508_mult__div__mod__eq,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mult_div_mod_eq
% 5.44/5.65 thf(fact_3509_mod__mult__div__eq,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_div_eq
% 5.44/5.65 thf(fact_3510_mod__mult__div__eq,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_div_eq
% 5.44/5.65 thf(fact_3511_mod__mult__div__eq,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult_div_eq
% 5.44/5.65 thf(fact_3512_mod__div__mult__eq,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_mult_eq
% 5.44/5.65 thf(fact_3513_mod__div__mult__eq,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_mult_eq
% 5.44/5.65 thf(fact_3514_mod__div__mult__eq,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_mult_eq
% 5.44/5.65 thf(fact_3515_div__mult__mod__eq,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_mod_eq
% 5.44/5.65 thf(fact_3516_div__mult__mod__eq,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_mod_eq
% 5.44/5.65 thf(fact_3517_div__mult__mod__eq,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_mod_eq
% 5.44/5.65 thf(fact_3518_mod__div__decomp,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( A
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_decomp
% 5.44/5.65 thf(fact_3519_mod__div__decomp,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( A
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_decomp
% 5.44/5.65 thf(fact_3520_mod__div__decomp,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( A
% 5.44/5.65 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_div_decomp
% 5.44/5.65 thf(fact_3521_cancel__div__mod__rules_I1_J,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % cancel_div_mod_rules(1)
% 5.44/5.65 thf(fact_3522_cancel__div__mod__rules_I1_J,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.44/5.65 = ( plus_plus_nat @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % cancel_div_mod_rules(1)
% 5.44/5.65 thf(fact_3523_cancel__div__mod__rules_I1_J,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.44/5.65 = ( plus_plus_int @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % cancel_div_mod_rules(1)
% 5.44/5.65 thf(fact_3524_cancel__div__mod__rules_I2_J,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % cancel_div_mod_rules(2)
% 5.44/5.65 thf(fact_3525_cancel__div__mod__rules_I2_J,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.44/5.65 = ( plus_plus_nat @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % cancel_div_mod_rules(2)
% 5.44/5.65 thf(fact_3526_cancel__div__mod__rules_I2_J,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.44/5.65 = ( plus_plus_int @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % cancel_div_mod_rules(2)
% 5.44/5.65 thf(fact_3527_div__mult1__eq,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult1_eq
% 5.44/5.65 thf(fact_3528_div__mult1__eq,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.44/5.65 = ( 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 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult1_eq
% 5.44/5.65 thf(fact_3529_div__mult1__eq,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.44/5.65 = ( 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 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult1_eq
% 5.44/5.65 thf(fact_3530_minus__mult__div__eq__mod,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.44/5.65 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mult_div_eq_mod
% 5.44/5.65 thf(fact_3531_minus__mult__div__eq__mod,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mult_div_eq_mod
% 5.44/5.65 thf(fact_3532_minus__mult__div__eq__mod,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.44/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mult_div_eq_mod
% 5.44/5.65 thf(fact_3533_minus__mod__eq__mult__div,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.44/5.65 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mod_eq_mult_div
% 5.44/5.65 thf(fact_3534_minus__mod__eq__mult__div,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.44/5.65 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mod_eq_mult_div
% 5.44/5.65 thf(fact_3535_minus__mod__eq__mult__div,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.44/5.65 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mod_eq_mult_div
% 5.44/5.65 thf(fact_3536_minus__mod__eq__div__mult,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.44/5.65 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mod_eq_div_mult
% 5.44/5.65 thf(fact_3537_minus__mod__eq__div__mult,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.44/5.65 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mod_eq_div_mult
% 5.44/5.65 thf(fact_3538_minus__mod__eq__div__mult,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.44/5.65 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_mod_eq_div_mult
% 5.44/5.65 thf(fact_3539_minus__div__mult__eq__mod,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.44/5.65 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_div_mult_eq_mod
% 5.44/5.65 thf(fact_3540_minus__div__mult__eq__mod,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_div_mult_eq_mod
% 5.44/5.65 thf(fact_3541_minus__div__mult__eq__mod,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.44/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % minus_div_mult_eq_mod
% 5.44/5.65 thf(fact_3542_mod__le__divisor,axiom,
% 5.44/5.65 ! [N2: nat,M: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_le_divisor
% 5.44/5.65 thf(fact_3543_nat__mod__eq__lemma,axiom,
% 5.44/5.65 ! [X: nat,N2: nat,Y: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ X @ N2 )
% 5.44/5.65 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.44/5.65 => ( ( ord_less_eq_nat @ Y @ X )
% 5.44/5.65 => ? [Q3: nat] :
% 5.44/5.65 ( X
% 5.44/5.65 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q3 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % nat_mod_eq_lemma
% 5.44/5.65 thf(fact_3544_mod__eq__nat2E,axiom,
% 5.44/5.65 ! [M: nat,Q2: nat,N2: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.44/5.65 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 5.44/5.65 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ~ ! [S2: nat] :
% 5.44/5.65 ( N2
% 5.44/5.65 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_nat2E
% 5.44/5.65 thf(fact_3545_mod__eq__nat1E,axiom,
% 5.44/5.65 ! [M: nat,Q2: nat,N2: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.44/5.65 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 5.44/5.65 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ~ ! [S2: nat] :
% 5.44/5.65 ( M
% 5.44/5.65 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_nat1E
% 5.44/5.65 thf(fact_3546_mod__mult2__eq,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mult2_eq
% 5.44/5.65 thf(fact_3547_modulo__nat__def,axiom,
% 5.44/5.65 ( modulo_modulo_nat
% 5.44/5.65 = ( ^ [M6: nat,N: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N ) @ N ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % modulo_nat_def
% 5.44/5.65 thf(fact_3548_split__mod,axiom,
% 5.44/5.65 ! [P: nat > $o,M: nat,N2: nat] :
% 5.44/5.65 ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.44/5.65 = ( ( ( N2 = zero_zero_nat )
% 5.44/5.65 => ( P @ M ) )
% 5.44/5.65 & ( ( N2 != zero_zero_nat )
% 5.44/5.65 => ! [I5: nat,J3: nat] :
% 5.44/5.65 ( ( ord_less_nat @ J3 @ N2 )
% 5.44/5.65 => ( ( M
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 5.44/5.65 => ( P @ J3 ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % split_mod
% 5.44/5.65 thf(fact_3549_unset__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: code_integer] :
% 5.44/5.65 ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unset_bit_Suc
% 5.44/5.65 thf(fact_3550_unset__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: int] :
% 5.44/5.65 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unset_bit_Suc
% 5.44/5.65 thf(fact_3551_unset__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: nat] :
% 5.44/5.65 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unset_bit_Suc
% 5.44/5.65 thf(fact_3552_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.44/5.65 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.44/5.65 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.44/5.65 thf(fact_3553_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.44/5.65 ! [C: nat,A: nat,B: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.44/5.65 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.44/5.65 thf(fact_3554_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.65 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.44/5.65 thf(fact_3555_Suc__times__mod__eq,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 5.44/5.65 = one_one_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % Suc_times_mod_eq
% 5.44/5.65 thf(fact_3556_divmod__digit__0_I2_J,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.65 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.44/5.65 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_0(2)
% 5.44/5.65 thf(fact_3557_divmod__digit__0_I2_J,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.65 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.44/5.65 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_0(2)
% 5.44/5.65 thf(fact_3558_bits__stable__imp__add__self,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = A )
% 5.44/5.65 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.65
% 5.44/5.65 % bits_stable_imp_add_self
% 5.44/5.65 thf(fact_3559_bits__stable__imp__add__self,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = A )
% 5.44/5.65 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % bits_stable_imp_add_self
% 5.44/5.65 thf(fact_3560_bits__stable__imp__add__self,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = A )
% 5.44/5.65 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % bits_stable_imp_add_self
% 5.44/5.65 thf(fact_3561_div__exp__mod__exp__eq,axiom,
% 5.44/5.65 ! [A: code_integer,N2: nat,M: nat] :
% 5.44/5.65 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_exp_mod_exp_eq
% 5.44/5.65 thf(fact_3562_div__exp__mod__exp__eq,axiom,
% 5.44/5.65 ! [A: nat,N2: nat,M: nat] :
% 5.44/5.65 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.65 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_exp_mod_exp_eq
% 5.44/5.65 thf(fact_3563_div__exp__mod__exp__eq,axiom,
% 5.44/5.65 ! [A: int,N2: nat,M: nat] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.65 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_exp_mod_exp_eq
% 5.44/5.65 thf(fact_3564_divmod__digit__0_I1_J,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.44/5.65 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_0(1)
% 5.44/5.65 thf(fact_3565_divmod__digit__0_I1_J,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.65 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.44/5.65 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.44/5.65 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_0(1)
% 5.44/5.65 thf(fact_3566_divmod__digit__0_I1_J,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.65 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.44/5.65 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.44/5.65 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_0(1)
% 5.44/5.65 thf(fact_3567_mult__exp__mod__exp__eq,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,A: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.65 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_exp_mod_exp_eq
% 5.44/5.65 thf(fact_3568_mult__exp__mod__exp__eq,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,A: int] :
% 5.44/5.65 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.65 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_exp_mod_exp_eq
% 5.44/5.65 thf(fact_3569_mod__double__modulus,axiom,
% 5.44/5.65 ! [M: nat,X: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.44/5.65 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.65 = ( modulo_modulo_nat @ X @ M ) )
% 5.44/5.65 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.65 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_double_modulus
% 5.44/5.65 thf(fact_3570_mod__double__modulus,axiom,
% 5.44/5.65 ! [M: int,X: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ M )
% 5.44/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.65 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.65 = ( modulo_modulo_int @ X @ M ) )
% 5.44/5.65 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.44/5.65 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_double_modulus
% 5.44/5.65 thf(fact_3571_divmod__digit__1_I2_J,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.65 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.44/5.65 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_1(2)
% 5.44/5.65 thf(fact_3572_divmod__digit__1_I2_J,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.65 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.44/5.65 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.44/5.65 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_1(2)
% 5.44/5.65 thf(fact_3573_set__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: code_integer] :
% 5.44/5.65 ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % set_bit_Suc
% 5.44/5.65 thf(fact_3574_set__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: int] :
% 5.44/5.65 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % set_bit_Suc
% 5.44/5.65 thf(fact_3575_set__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: nat] :
% 5.44/5.65 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % set_bit_Suc
% 5.44/5.65 thf(fact_3576_divmod__digit__1_I1_J,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.44/5.65 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.44/5.65 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.44/5.65 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.44/5.65 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_1(1)
% 5.44/5.65 thf(fact_3577_divmod__digit__1_I1_J,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.44/5.65 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.44/5.65 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 5.44/5.65 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_1(1)
% 5.44/5.65 thf(fact_3578_divmod__digit__1_I1_J,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.44/5.65 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.44/5.65 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 5.44/5.65 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % divmod_digit_1(1)
% 5.44/5.65 thf(fact_3579_mult__less__iff1,axiom,
% 5.44/5.65 ! [Z: real,X: real,Y: real] :
% 5.44/5.65 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.44/5.65 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.44/5.65 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_less_iff1
% 5.44/5.65 thf(fact_3580_mult__less__iff1,axiom,
% 5.44/5.65 ! [Z: int,X: int,Y: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.44/5.65 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.44/5.65 = ( ord_less_int @ X @ Y ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_less_iff1
% 5.44/5.65 thf(fact_3581_verit__le__mono__div,axiom,
% 5.44/5.65 ! [A2: nat,B2: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_nat @ A2 @ B2 )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ord_less_eq_nat
% 5.44/5.65 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 5.44/5.65 @ ( if_nat
% 5.44/5.65 @ ( ( modulo_modulo_nat @ B2 @ N2 )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 @ one_one_nat
% 5.44/5.65 @ zero_zero_nat ) )
% 5.44/5.65 @ ( divide_divide_nat @ B2 @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_le_mono_div
% 5.44/5.65 thf(fact_3582_div__mod__decomp,axiom,
% 5.44/5.65 ! [A2: nat,N2: nat] :
% 5.44/5.65 ( A2
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mod_decomp
% 5.44/5.65 thf(fact_3583_flip__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: code_integer] :
% 5.44/5.65 ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % flip_bit_Suc
% 5.44/5.65 thf(fact_3584_flip__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: int] :
% 5.44/5.65 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % flip_bit_Suc
% 5.44/5.65 thf(fact_3585_flip__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,A: nat] :
% 5.44/5.65 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 5.44/5.65 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % flip_bit_Suc
% 5.44/5.65 thf(fact_3586_div__less__mono,axiom,
% 5.44/5.65 ! [A2: nat,B2: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_nat @ A2 @ B2 )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 => ( ( ( modulo_modulo_nat @ B2 @ N2 )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B2 @ N2 ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_less_mono
% 5.44/5.65 thf(fact_3587_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_num,Ys: list_num] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3588_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_Code_integer,Ys: list_o] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3589_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3590_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3591_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3592_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3593_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3594_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_o,Ys: list_o] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3595_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_o,Ys: list_nat] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3596_product__nth,axiom,
% 5.44/5.65 ! [N2: nat,Xs2: list_o,Ys: list_int] :
% 5.44/5.65 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.44/5.65 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N2 )
% 5.44/5.65 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % product_nth
% 5.44/5.65 thf(fact_3597_obtain__set__succ,axiom,
% 5.44/5.65 ! [X: nat,Z: nat,A2: set_nat,B2: set_nat] :
% 5.44/5.65 ( ( ord_less_nat @ X @ Z )
% 5.44/5.65 => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 5.44/5.65 => ( ( finite_finite_nat @ B2 )
% 5.44/5.65 => ( ( A2 = B2 )
% 5.44/5.65 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_1 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % obtain_set_succ
% 5.44/5.65 thf(fact_3598_obtain__set__pred,axiom,
% 5.44/5.65 ! [Z: nat,X: nat,A2: set_nat] :
% 5.44/5.65 ( ( ord_less_nat @ Z @ X )
% 5.44/5.65 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 5.44/5.65 => ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % obtain_set_pred
% 5.44/5.65 thf(fact_3599_set__vebt__finite,axiom,
% 5.44/5.65 ! [T: vEBT_VEBT,N2: nat] :
% 5.44/5.65 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.44/5.65 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % set_vebt_finite
% 5.44/5.65 thf(fact_3600_pred__none__empty,axiom,
% 5.44/5.65 ! [Xs2: set_nat,A: nat] :
% 5.44/5.65 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 5.44/5.65 => ( ( finite_finite_nat @ Xs2 )
% 5.44/5.65 => ~ ? [X3: nat] :
% 5.44/5.65 ( ( member_nat @ X3 @ Xs2 )
% 5.44/5.65 & ( ord_less_nat @ X3 @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % pred_none_empty
% 5.44/5.65 thf(fact_3601_succ__none__empty,axiom,
% 5.44/5.65 ! [Xs2: set_nat,A: nat] :
% 5.44/5.65 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 5.44/5.65 => ( ( finite_finite_nat @ Xs2 )
% 5.44/5.65 => ~ ? [X3: nat] :
% 5.44/5.65 ( ( member_nat @ X3 @ Xs2 )
% 5.44/5.65 & ( ord_less_nat @ A @ X3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % succ_none_empty
% 5.44/5.65 thf(fact_3602_verit__eq__simplify_I8_J,axiom,
% 5.44/5.65 ! [X22: num,Y22: num] :
% 5.44/5.65 ( ( ( bit0 @ X22 )
% 5.44/5.65 = ( bit0 @ Y22 ) )
% 5.44/5.65 = ( X22 = Y22 ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_eq_simplify(8)
% 5.44/5.65 thf(fact_3603_old_Oprod_Oinject,axiom,
% 5.44/5.65 ! [A: code_integer,B: $o,A6: code_integer,B6: $o] :
% 5.44/5.65 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.44/5.65 = ( produc6677183202524767010eger_o @ A6 @ B6 ) )
% 5.44/5.65 = ( ( A = A6 )
% 5.44/5.65 & ( B = B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.inject
% 5.44/5.65 thf(fact_3604_old_Oprod_Oinject,axiom,
% 5.44/5.65 ! [A: num,B: num,A6: num,B6: num] :
% 5.44/5.65 ( ( ( product_Pair_num_num @ A @ B )
% 5.44/5.65 = ( product_Pair_num_num @ A6 @ B6 ) )
% 5.44/5.65 = ( ( A = A6 )
% 5.44/5.65 & ( B = B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.inject
% 5.44/5.65 thf(fact_3605_old_Oprod_Oinject,axiom,
% 5.44/5.65 ! [A: nat,B: num,A6: nat,B6: num] :
% 5.44/5.65 ( ( ( product_Pair_nat_num @ A @ B )
% 5.44/5.65 = ( product_Pair_nat_num @ A6 @ B6 ) )
% 5.44/5.65 = ( ( A = A6 )
% 5.44/5.65 & ( B = B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.inject
% 5.44/5.65 thf(fact_3606_old_Oprod_Oinject,axiom,
% 5.44/5.65 ! [A: nat,B: nat,A6: nat,B6: nat] :
% 5.44/5.65 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.44/5.65 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 5.44/5.65 = ( ( A = A6 )
% 5.44/5.65 & ( B = B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.inject
% 5.44/5.65 thf(fact_3607_old_Oprod_Oinject,axiom,
% 5.44/5.65 ! [A: int,B: int,A6: int,B6: int] :
% 5.44/5.65 ( ( ( product_Pair_int_int @ A @ B )
% 5.44/5.65 = ( product_Pair_int_int @ A6 @ B6 ) )
% 5.44/5.65 = ( ( A = A6 )
% 5.44/5.65 & ( B = B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.inject
% 5.44/5.65 thf(fact_3608_prod_Oinject,axiom,
% 5.44/5.65 ! [X1: code_integer,X22: $o,Y1: code_integer,Y22: $o] :
% 5.44/5.65 ( ( ( produc6677183202524767010eger_o @ X1 @ X22 )
% 5.44/5.65 = ( produc6677183202524767010eger_o @ Y1 @ Y22 ) )
% 5.44/5.65 = ( ( X1 = Y1 )
% 5.44/5.65 & ( X22 = Y22 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.inject
% 5.44/5.65 thf(fact_3609_prod_Oinject,axiom,
% 5.44/5.65 ! [X1: num,X22: num,Y1: num,Y22: num] :
% 5.44/5.65 ( ( ( product_Pair_num_num @ X1 @ X22 )
% 5.44/5.65 = ( product_Pair_num_num @ Y1 @ Y22 ) )
% 5.44/5.65 = ( ( X1 = Y1 )
% 5.44/5.65 & ( X22 = Y22 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.inject
% 5.44/5.65 thf(fact_3610_prod_Oinject,axiom,
% 5.44/5.65 ! [X1: nat,X22: num,Y1: nat,Y22: num] :
% 5.44/5.65 ( ( ( product_Pair_nat_num @ X1 @ X22 )
% 5.44/5.65 = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 5.44/5.65 = ( ( X1 = Y1 )
% 5.44/5.65 & ( X22 = Y22 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.inject
% 5.44/5.65 thf(fact_3611_prod_Oinject,axiom,
% 5.44/5.65 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 5.44/5.65 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 5.44/5.65 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 5.44/5.65 = ( ( X1 = Y1 )
% 5.44/5.65 & ( X22 = Y22 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.inject
% 5.44/5.65 thf(fact_3612_prod_Oinject,axiom,
% 5.44/5.65 ! [X1: int,X22: int,Y1: int,Y22: int] :
% 5.44/5.65 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 5.44/5.65 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 5.44/5.65 = ( ( X1 = Y1 )
% 5.44/5.65 & ( X22 = Y22 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.inject
% 5.44/5.65 thf(fact_3613_List_Ofinite__set,axiom,
% 5.44/5.65 ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % List.finite_set
% 5.44/5.65 thf(fact_3614_List_Ofinite__set,axiom,
% 5.44/5.65 ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % List.finite_set
% 5.44/5.65 thf(fact_3615_List_Ofinite__set,axiom,
% 5.44/5.65 ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % List.finite_set
% 5.44/5.65 thf(fact_3616_List_Ofinite__set,axiom,
% 5.44/5.65 ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % List.finite_set
% 5.44/5.65 thf(fact_3617_flip__bit__nonnegative__int__iff,axiom,
% 5.44/5.65 ! [N2: nat,K: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) )
% 5.44/5.65 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.44/5.65
% 5.44/5.65 % flip_bit_nonnegative_int_iff
% 5.44/5.65 thf(fact_3618_flip__bit__negative__int__iff,axiom,
% 5.44/5.65 ! [N2: nat,K: int] :
% 5.44/5.65 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 5.44/5.65 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % flip_bit_negative_int_iff
% 5.44/5.65 thf(fact_3619_infinite__Icc__iff,axiom,
% 5.44/5.65 ! [A: real,B: real] :
% 5.44/5.65 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.44/5.65 = ( ord_less_real @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_Icc_iff
% 5.44/5.65 thf(fact_3620_mod__pos__pos__trivial,axiom,
% 5.44/5.65 ! [K: int,L2: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.65 => ( ( ord_less_int @ K @ L2 )
% 5.44/5.65 => ( ( modulo_modulo_int @ K @ L2 )
% 5.44/5.65 = K ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_pos_pos_trivial
% 5.44/5.65 thf(fact_3621_mod__neg__neg__trivial,axiom,
% 5.44/5.65 ! [K: int,L2: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.44/5.65 => ( ( ord_less_int @ L2 @ K )
% 5.44/5.65 => ( ( modulo_modulo_int @ K @ L2 )
% 5.44/5.65 = K ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_neg_neg_trivial
% 5.44/5.65 thf(fact_3622_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.44/5.65 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3623_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.44/5.65 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3624_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.44/5.65 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3625_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.44/5.65 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3626_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.44/5.65 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3627_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_o,Ys: list_o] :
% 5.44/5.65 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3628_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_o,Ys: list_nat] :
% 5.44/5.65 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3629_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_o,Ys: list_int] :
% 5.44/5.65 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3630_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.44/5.65 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3631_length__product,axiom,
% 5.44/5.65 ! [Xs2: list_nat,Ys: list_o] :
% 5.44/5.65 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 5.44/5.65 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % length_product
% 5.44/5.65 thf(fact_3632_zmod__numeral__Bit0,axiom,
% 5.44/5.65 ! [V: num,W: num] :
% 5.44/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.44/5.65 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zmod_numeral_Bit0
% 5.44/5.65 thf(fact_3633_bounded__nat__set__is__finite,axiom,
% 5.44/5.65 ! [N3: set_nat,N2: nat] :
% 5.44/5.65 ( ! [X5: nat] :
% 5.44/5.65 ( ( member_nat @ X5 @ N3 )
% 5.44/5.65 => ( ord_less_nat @ X5 @ N2 ) )
% 5.44/5.65 => ( finite_finite_nat @ N3 ) ) ).
% 5.44/5.65
% 5.44/5.65 % bounded_nat_set_is_finite
% 5.44/5.65 thf(fact_3634_finite__nat__set__iff__bounded,axiom,
% 5.44/5.65 ( finite_finite_nat
% 5.44/5.65 = ( ^ [N6: set_nat] :
% 5.44/5.65 ? [M6: nat] :
% 5.44/5.65 ! [X2: nat] :
% 5.44/5.65 ( ( member_nat @ X2 @ N6 )
% 5.44/5.65 => ( ord_less_nat @ X2 @ M6 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_nat_set_iff_bounded
% 5.44/5.65 thf(fact_3635_finite__nat__set__iff__bounded__le,axiom,
% 5.44/5.65 ( finite_finite_nat
% 5.44/5.65 = ( ^ [N6: set_nat] :
% 5.44/5.65 ? [M6: nat] :
% 5.44/5.65 ! [X2: nat] :
% 5.44/5.65 ( ( member_nat @ X2 @ N6 )
% 5.44/5.65 => ( ord_less_eq_nat @ X2 @ M6 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_nat_set_iff_bounded_le
% 5.44/5.65 thf(fact_3636_finite__list,axiom,
% 5.44/5.65 ! [A2: set_VEBT_VEBT] :
% 5.44/5.65 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.44/5.65 => ? [Xs3: list_VEBT_VEBT] :
% 5.44/5.65 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.44/5.65 = A2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_list
% 5.44/5.65 thf(fact_3637_finite__list,axiom,
% 5.44/5.65 ! [A2: set_int] :
% 5.44/5.65 ( ( finite_finite_int @ A2 )
% 5.44/5.65 => ? [Xs3: list_int] :
% 5.44/5.65 ( ( set_int2 @ Xs3 )
% 5.44/5.65 = A2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_list
% 5.44/5.65 thf(fact_3638_finite__list,axiom,
% 5.44/5.65 ! [A2: set_nat] :
% 5.44/5.65 ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ? [Xs3: list_nat] :
% 5.44/5.65 ( ( set_nat2 @ Xs3 )
% 5.44/5.65 = A2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_list
% 5.44/5.65 thf(fact_3639_finite__list,axiom,
% 5.44/5.65 ! [A2: set_complex] :
% 5.44/5.65 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.65 => ? [Xs3: list_complex] :
% 5.44/5.65 ( ( set_complex2 @ Xs3 )
% 5.44/5.65 = A2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_list
% 5.44/5.65 thf(fact_3640_finite__M__bounded__by__nat,axiom,
% 5.44/5.65 ! [P: nat > $o,I2: nat] :
% 5.44/5.65 ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [K3: nat] :
% 5.44/5.65 ( ( P @ K3 )
% 5.44/5.65 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_M_bounded_by_nat
% 5.44/5.65 thf(fact_3641_finite__less__ub,axiom,
% 5.44/5.65 ! [F: nat > nat,U: nat] :
% 5.44/5.65 ( ! [N4: nat] : ( ord_less_eq_nat @ N4 @ ( F @ N4 ) )
% 5.44/5.65 => ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_less_ub
% 5.44/5.65 thf(fact_3642_finite__lists__length__eq,axiom,
% 5.44/5.65 ! [A2: set_complex,N2: nat] :
% 5.44/5.65 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.65 => ( finite8712137658972009173omplex
% 5.44/5.65 @ ( collect_list_complex
% 5.44/5.65 @ ^ [Xs: list_complex] :
% 5.44/5.65 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.44/5.65 = N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_eq
% 5.44/5.65 thf(fact_3643_finite__lists__length__eq,axiom,
% 5.44/5.65 ! [A2: set_VEBT_VEBT,N2: nat] :
% 5.44/5.65 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.44/5.65 => ( finite3004134309566078307T_VEBT
% 5.44/5.65 @ ( collec5608196760682091941T_VEBT
% 5.44/5.65 @ ^ [Xs: list_VEBT_VEBT] :
% 5.44/5.65 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.44/5.65 = N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_eq
% 5.44/5.65 thf(fact_3644_finite__lists__length__eq,axiom,
% 5.44/5.65 ! [A2: set_o,N2: nat] :
% 5.44/5.65 ( ( finite_finite_o @ A2 )
% 5.44/5.65 => ( finite_finite_list_o
% 5.44/5.65 @ ( collect_list_o
% 5.44/5.65 @ ^ [Xs: list_o] :
% 5.44/5.65 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ( size_size_list_o @ Xs )
% 5.44/5.65 = N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_eq
% 5.44/5.65 thf(fact_3645_finite__lists__length__eq,axiom,
% 5.44/5.65 ! [A2: set_int,N2: nat] :
% 5.44/5.65 ( ( finite_finite_int @ A2 )
% 5.44/5.65 => ( finite3922522038869484883st_int
% 5.44/5.65 @ ( collect_list_int
% 5.44/5.65 @ ^ [Xs: list_int] :
% 5.44/5.65 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ( size_size_list_int @ Xs )
% 5.44/5.65 = N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_eq
% 5.44/5.65 thf(fact_3646_finite__lists__length__eq,axiom,
% 5.44/5.65 ! [A2: set_real,N2: nat] :
% 5.44/5.65 ( ( finite_finite_real @ A2 )
% 5.44/5.65 => ( finite306553202115118035t_real
% 5.44/5.65 @ ( collect_list_real
% 5.44/5.65 @ ^ [Xs: list_real] :
% 5.44/5.65 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ( size_size_list_real @ Xs )
% 5.44/5.65 = N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_eq
% 5.44/5.65 thf(fact_3647_finite__lists__length__eq,axiom,
% 5.44/5.65 ! [A2: set_nat,N2: nat] :
% 5.44/5.65 ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ( finite8100373058378681591st_nat
% 5.44/5.65 @ ( collect_list_nat
% 5.44/5.65 @ ^ [Xs: list_nat] :
% 5.44/5.65 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ( size_size_list_nat @ Xs )
% 5.44/5.65 = N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_eq
% 5.44/5.65 thf(fact_3648_neg__mod__bound,axiom,
% 5.44/5.65 ! [L2: int,K: int] :
% 5.44/5.65 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.44/5.65 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % neg_mod_bound
% 5.44/5.65 thf(fact_3649_Euclidean__Division_Opos__mod__bound,axiom,
% 5.44/5.65 ! [L2: int,K: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.44/5.65 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % Euclidean_Division.pos_mod_bound
% 5.44/5.65 thf(fact_3650_infinite__Icc,axiom,
% 5.44/5.65 ! [A: real,B: real] :
% 5.44/5.65 ( ( ord_less_real @ A @ B )
% 5.44/5.65 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_Icc
% 5.44/5.65 thf(fact_3651_finite__lists__length__le,axiom,
% 5.44/5.65 ! [A2: set_complex,N2: nat] :
% 5.44/5.65 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.65 => ( finite8712137658972009173omplex
% 5.44/5.65 @ ( collect_list_complex
% 5.44/5.65 @ ^ [Xs: list_complex] :
% 5.44/5.65 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_le
% 5.44/5.65 thf(fact_3652_finite__lists__length__le,axiom,
% 5.44/5.65 ! [A2: set_VEBT_VEBT,N2: nat] :
% 5.44/5.65 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.44/5.65 => ( finite3004134309566078307T_VEBT
% 5.44/5.65 @ ( collec5608196760682091941T_VEBT
% 5.44/5.65 @ ^ [Xs: list_VEBT_VEBT] :
% 5.44/5.65 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_le
% 5.44/5.65 thf(fact_3653_finite__lists__length__le,axiom,
% 5.44/5.65 ! [A2: set_o,N2: nat] :
% 5.44/5.65 ( ( finite_finite_o @ A2 )
% 5.44/5.65 => ( finite_finite_list_o
% 5.44/5.65 @ ( collect_list_o
% 5.44/5.65 @ ^ [Xs: list_o] :
% 5.44/5.65 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_le
% 5.44/5.65 thf(fact_3654_finite__lists__length__le,axiom,
% 5.44/5.65 ! [A2: set_int,N2: nat] :
% 5.44/5.65 ( ( finite_finite_int @ A2 )
% 5.44/5.65 => ( finite3922522038869484883st_int
% 5.44/5.65 @ ( collect_list_int
% 5.44/5.65 @ ^ [Xs: list_int] :
% 5.44/5.65 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_le
% 5.44/5.65 thf(fact_3655_finite__lists__length__le,axiom,
% 5.44/5.65 ! [A2: set_real,N2: nat] :
% 5.44/5.65 ( ( finite_finite_real @ A2 )
% 5.44/5.65 => ( finite306553202115118035t_real
% 5.44/5.65 @ ( collect_list_real
% 5.44/5.65 @ ^ [Xs: list_real] :
% 5.44/5.65 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_le
% 5.44/5.65 thf(fact_3656_finite__lists__length__le,axiom,
% 5.44/5.65 ! [A2: set_nat,N2: nat] :
% 5.44/5.65 ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ( finite8100373058378681591st_nat
% 5.44/5.65 @ ( collect_list_nat
% 5.44/5.65 @ ^ [Xs: list_nat] :
% 5.44/5.65 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.44/5.65 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_lists_length_le
% 5.44/5.65 thf(fact_3657_Euclidean__Division_Opos__mod__sign,axiom,
% 5.44/5.65 ! [L2: int,K: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.44/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % Euclidean_Division.pos_mod_sign
% 5.44/5.65 thf(fact_3658_neg__mod__sign,axiom,
% 5.44/5.65 ! [L2: int,K: int] :
% 5.44/5.65 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.44/5.65 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % neg_mod_sign
% 5.44/5.65 thf(fact_3659_verit__la__disequality,axiom,
% 5.44/5.65 ! [A: num,B: num] :
% 5.44/5.65 ( ( A = B )
% 5.44/5.65 | ~ ( ord_less_eq_num @ A @ B )
% 5.44/5.65 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_la_disequality
% 5.44/5.65 thf(fact_3660_verit__la__disequality,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( A = B )
% 5.44/5.65 | ~ ( ord_less_eq_nat @ A @ B )
% 5.44/5.65 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_la_disequality
% 5.44/5.65 thf(fact_3661_verit__la__disequality,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( A = B )
% 5.44/5.65 | ~ ( ord_less_eq_int @ A @ B )
% 5.44/5.65 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_la_disequality
% 5.44/5.65 thf(fact_3662_verit__comp__simplify1_I2_J,axiom,
% 5.44/5.65 ! [A: set_real] : ( ord_less_eq_set_real @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(2)
% 5.44/5.65 thf(fact_3663_verit__comp__simplify1_I2_J,axiom,
% 5.44/5.65 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(2)
% 5.44/5.65 thf(fact_3664_verit__comp__simplify1_I2_J,axiom,
% 5.44/5.65 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(2)
% 5.44/5.65 thf(fact_3665_verit__comp__simplify1_I2_J,axiom,
% 5.44/5.65 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(2)
% 5.44/5.65 thf(fact_3666_verit__comp__simplify1_I2_J,axiom,
% 5.44/5.65 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(2)
% 5.44/5.65 thf(fact_3667_verit__comp__simplify1_I1_J,axiom,
% 5.44/5.65 ! [A: extended_enat] :
% 5.44/5.65 ~ ( ord_le72135733267957522d_enat @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(1)
% 5.44/5.65 thf(fact_3668_verit__comp__simplify1_I1_J,axiom,
% 5.44/5.65 ! [A: real] :
% 5.44/5.65 ~ ( ord_less_real @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(1)
% 5.44/5.65 thf(fact_3669_verit__comp__simplify1_I1_J,axiom,
% 5.44/5.65 ! [A: num] :
% 5.44/5.65 ~ ( ord_less_num @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(1)
% 5.44/5.65 thf(fact_3670_verit__comp__simplify1_I1_J,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ~ ( ord_less_nat @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(1)
% 5.44/5.65 thf(fact_3671_verit__comp__simplify1_I1_J,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ~ ( ord_less_int @ A @ A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(1)
% 5.44/5.65 thf(fact_3672_Pair__inject,axiom,
% 5.44/5.65 ! [A: code_integer,B: $o,A6: code_integer,B6: $o] :
% 5.44/5.65 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.44/5.65 = ( produc6677183202524767010eger_o @ A6 @ B6 ) )
% 5.44/5.65 => ~ ( ( A = A6 )
% 5.44/5.65 => ( B = ~ B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % Pair_inject
% 5.44/5.65 thf(fact_3673_Pair__inject,axiom,
% 5.44/5.65 ! [A: num,B: num,A6: num,B6: num] :
% 5.44/5.65 ( ( ( product_Pair_num_num @ A @ B )
% 5.44/5.65 = ( product_Pair_num_num @ A6 @ B6 ) )
% 5.44/5.65 => ~ ( ( A = A6 )
% 5.44/5.65 => ( B != B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % Pair_inject
% 5.44/5.65 thf(fact_3674_Pair__inject,axiom,
% 5.44/5.65 ! [A: nat,B: num,A6: nat,B6: num] :
% 5.44/5.65 ( ( ( product_Pair_nat_num @ A @ B )
% 5.44/5.65 = ( product_Pair_nat_num @ A6 @ B6 ) )
% 5.44/5.65 => ~ ( ( A = A6 )
% 5.44/5.65 => ( B != B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % Pair_inject
% 5.44/5.65 thf(fact_3675_Pair__inject,axiom,
% 5.44/5.65 ! [A: nat,B: nat,A6: nat,B6: nat] :
% 5.44/5.65 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.44/5.65 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 5.44/5.65 => ~ ( ( A = A6 )
% 5.44/5.65 => ( B != B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % Pair_inject
% 5.44/5.65 thf(fact_3676_Pair__inject,axiom,
% 5.44/5.65 ! [A: int,B: int,A6: int,B6: int] :
% 5.44/5.65 ( ( ( product_Pair_int_int @ A @ B )
% 5.44/5.65 = ( product_Pair_int_int @ A6 @ B6 ) )
% 5.44/5.65 => ~ ( ( A = A6 )
% 5.44/5.65 => ( B != B6 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % Pair_inject
% 5.44/5.65 thf(fact_3677_prod__cases,axiom,
% 5.44/5.65 ! [P: produc6271795597528267376eger_o > $o,P5: produc6271795597528267376eger_o] :
% 5.44/5.65 ( ! [A3: code_integer,B3: $o] : ( P @ ( produc6677183202524767010eger_o @ A3 @ B3 ) )
% 5.44/5.65 => ( P @ P5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod_cases
% 5.44/5.65 thf(fact_3678_prod__cases,axiom,
% 5.44/5.65 ! [P: product_prod_num_num > $o,P5: product_prod_num_num] :
% 5.44/5.65 ( ! [A3: num,B3: num] : ( P @ ( product_Pair_num_num @ A3 @ B3 ) )
% 5.44/5.65 => ( P @ P5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod_cases
% 5.44/5.65 thf(fact_3679_prod__cases,axiom,
% 5.44/5.65 ! [P: product_prod_nat_num > $o,P5: product_prod_nat_num] :
% 5.44/5.65 ( ! [A3: nat,B3: num] : ( P @ ( product_Pair_nat_num @ A3 @ B3 ) )
% 5.44/5.65 => ( P @ P5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod_cases
% 5.44/5.65 thf(fact_3680_prod__cases,axiom,
% 5.44/5.65 ! [P: product_prod_nat_nat > $o,P5: product_prod_nat_nat] :
% 5.44/5.65 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 5.44/5.65 => ( P @ P5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod_cases
% 5.44/5.65 thf(fact_3681_prod__cases,axiom,
% 5.44/5.65 ! [P: product_prod_int_int > $o,P5: product_prod_int_int] :
% 5.44/5.65 ( ! [A3: int,B3: int] : ( P @ ( product_Pair_int_int @ A3 @ B3 ) )
% 5.44/5.65 => ( P @ P5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod_cases
% 5.44/5.65 thf(fact_3682_surj__pair,axiom,
% 5.44/5.65 ! [P5: produc6271795597528267376eger_o] :
% 5.44/5.65 ? [X5: code_integer,Y5: $o] :
% 5.44/5.65 ( P5
% 5.44/5.65 = ( produc6677183202524767010eger_o @ X5 @ Y5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % surj_pair
% 5.44/5.65 thf(fact_3683_surj__pair,axiom,
% 5.44/5.65 ! [P5: product_prod_num_num] :
% 5.44/5.65 ? [X5: num,Y5: num] :
% 5.44/5.65 ( P5
% 5.44/5.65 = ( product_Pair_num_num @ X5 @ Y5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % surj_pair
% 5.44/5.65 thf(fact_3684_surj__pair,axiom,
% 5.44/5.65 ! [P5: product_prod_nat_num] :
% 5.44/5.65 ? [X5: nat,Y5: num] :
% 5.44/5.65 ( P5
% 5.44/5.65 = ( product_Pair_nat_num @ X5 @ Y5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % surj_pair
% 5.44/5.65 thf(fact_3685_surj__pair,axiom,
% 5.44/5.65 ! [P5: product_prod_nat_nat] :
% 5.44/5.65 ? [X5: nat,Y5: nat] :
% 5.44/5.65 ( P5
% 5.44/5.65 = ( product_Pair_nat_nat @ X5 @ Y5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % surj_pair
% 5.44/5.65 thf(fact_3686_surj__pair,axiom,
% 5.44/5.65 ! [P5: product_prod_int_int] :
% 5.44/5.65 ? [X5: int,Y5: int] :
% 5.44/5.65 ( P5
% 5.44/5.65 = ( product_Pair_int_int @ X5 @ Y5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % surj_pair
% 5.44/5.65 thf(fact_3687_old_Oprod_Oexhaust,axiom,
% 5.44/5.65 ! [Y: produc6271795597528267376eger_o] :
% 5.44/5.65 ~ ! [A3: code_integer,B3: $o] :
% 5.44/5.65 ( Y
% 5.44/5.65 != ( produc6677183202524767010eger_o @ A3 @ B3 ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.exhaust
% 5.44/5.65 thf(fact_3688_old_Oprod_Oexhaust,axiom,
% 5.44/5.65 ! [Y: product_prod_num_num] :
% 5.44/5.65 ~ ! [A3: num,B3: num] :
% 5.44/5.65 ( Y
% 5.44/5.65 != ( product_Pair_num_num @ A3 @ B3 ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.exhaust
% 5.44/5.65 thf(fact_3689_old_Oprod_Oexhaust,axiom,
% 5.44/5.65 ! [Y: product_prod_nat_num] :
% 5.44/5.65 ~ ! [A3: nat,B3: num] :
% 5.44/5.65 ( Y
% 5.44/5.65 != ( product_Pair_nat_num @ A3 @ B3 ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.exhaust
% 5.44/5.65 thf(fact_3690_old_Oprod_Oexhaust,axiom,
% 5.44/5.65 ! [Y: product_prod_nat_nat] :
% 5.44/5.65 ~ ! [A3: nat,B3: nat] :
% 5.44/5.65 ( Y
% 5.44/5.65 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.exhaust
% 5.44/5.65 thf(fact_3691_old_Oprod_Oexhaust,axiom,
% 5.44/5.65 ! [Y: product_prod_int_int] :
% 5.44/5.65 ~ ! [A3: int,B3: int] :
% 5.44/5.65 ( Y
% 5.44/5.65 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 5.44/5.65
% 5.44/5.65 % old.prod.exhaust
% 5.44/5.65 thf(fact_3692_mod__pos__neg__trivial,axiom,
% 5.44/5.65 ! [K: int,L2: int] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ K )
% 5.44/5.65 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.44/5.65 => ( ( modulo_modulo_int @ K @ L2 )
% 5.44/5.65 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_pos_neg_trivial
% 5.44/5.65 thf(fact_3693_zmod__zmult2__eq,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.65 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zmod_zmult2_eq
% 5.44/5.65 thf(fact_3694_verit__comp__simplify1_I3_J,axiom,
% 5.44/5.65 ! [B6: extended_enat,A6: extended_enat] :
% 5.44/5.65 ( ( ~ ( ord_le2932123472753598470d_enat @ B6 @ A6 ) )
% 5.44/5.65 = ( ord_le72135733267957522d_enat @ A6 @ B6 ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(3)
% 5.44/5.65 thf(fact_3695_verit__comp__simplify1_I3_J,axiom,
% 5.44/5.65 ! [B6: real,A6: real] :
% 5.44/5.65 ( ( ~ ( ord_less_eq_real @ B6 @ A6 ) )
% 5.44/5.65 = ( ord_less_real @ A6 @ B6 ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(3)
% 5.44/5.65 thf(fact_3696_verit__comp__simplify1_I3_J,axiom,
% 5.44/5.65 ! [B6: num,A6: num] :
% 5.44/5.65 ( ( ~ ( ord_less_eq_num @ B6 @ A6 ) )
% 5.44/5.65 = ( ord_less_num @ A6 @ B6 ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(3)
% 5.44/5.65 thf(fact_3697_verit__comp__simplify1_I3_J,axiom,
% 5.44/5.65 ! [B6: nat,A6: nat] :
% 5.44/5.65 ( ( ~ ( ord_less_eq_nat @ B6 @ A6 ) )
% 5.44/5.65 = ( ord_less_nat @ A6 @ B6 ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(3)
% 5.44/5.65 thf(fact_3698_verit__comp__simplify1_I3_J,axiom,
% 5.44/5.65 ! [B6: int,A6: int] :
% 5.44/5.65 ( ( ~ ( ord_less_eq_int @ B6 @ A6 ) )
% 5.44/5.65 = ( ord_less_int @ A6 @ B6 ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_comp_simplify1(3)
% 5.44/5.65 thf(fact_3699_verit__sum__simplify,axiom,
% 5.44/5.65 ! [A: complex] :
% 5.44/5.65 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_sum_simplify
% 5.44/5.65 thf(fact_3700_verit__sum__simplify,axiom,
% 5.44/5.65 ! [A: real] :
% 5.44/5.65 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_sum_simplify
% 5.44/5.65 thf(fact_3701_verit__sum__simplify,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_sum_simplify
% 5.44/5.65 thf(fact_3702_verit__sum__simplify,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.44/5.65 = A ) ).
% 5.44/5.65
% 5.44/5.65 % verit_sum_simplify
% 5.44/5.65 thf(fact_3703_verit__eq__simplify_I10_J,axiom,
% 5.44/5.65 ! [X22: num] :
% 5.44/5.65 ( one
% 5.44/5.65 != ( bit0 @ X22 ) ) ).
% 5.44/5.65
% 5.44/5.65 % verit_eq_simplify(10)
% 5.44/5.65 thf(fact_3704_pos__zmod__mult__2,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.65 => ( ( 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 ) )
% 5.44/5.65 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % pos_zmod_mult_2
% 5.44/5.65 thf(fact_3705_neg__zmod__mult__2,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.65 => ( ( 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 ) )
% 5.44/5.65 = ( 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 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % neg_zmod_mult_2
% 5.44/5.65 thf(fact_3706_max__def__raw,axiom,
% 5.44/5.65 ( ord_ma741700101516333627d_enat
% 5.44/5.65 = ( ^ [A4: extended_enat,B4: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % max_def_raw
% 5.44/5.65 thf(fact_3707_max__def__raw,axiom,
% 5.44/5.65 ( ord_max_Code_integer
% 5.44/5.65 = ( ^ [A4: code_integer,B4: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % max_def_raw
% 5.44/5.65 thf(fact_3708_max__def__raw,axiom,
% 5.44/5.65 ( ord_max_set_real
% 5.44/5.65 = ( ^ [A4: set_real,B4: set_real] : ( if_set_real @ ( ord_less_eq_set_real @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % max_def_raw
% 5.44/5.65 thf(fact_3709_max__def__raw,axiom,
% 5.44/5.65 ( ord_max_set_nat
% 5.44/5.65 = ( ^ [A4: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % max_def_raw
% 5.44/5.65 thf(fact_3710_max__def__raw,axiom,
% 5.44/5.65 ( ord_max_num
% 5.44/5.65 = ( ^ [A4: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % max_def_raw
% 5.44/5.65 thf(fact_3711_max__def__raw,axiom,
% 5.44/5.65 ( ord_max_nat
% 5.44/5.65 = ( ^ [A4: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % max_def_raw
% 5.44/5.65 thf(fact_3712_max__def__raw,axiom,
% 5.44/5.65 ( ord_max_int
% 5.44/5.65 = ( ^ [A4: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % max_def_raw
% 5.44/5.65 thf(fact_3713_finite__Collect__le__nat,axiom,
% 5.44/5.65 ! [K: nat] :
% 5.44/5.65 ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_Collect_le_nat
% 5.44/5.65 thf(fact_3714_finite__Collect__less__nat,axiom,
% 5.44/5.65 ! [K: nat] :
% 5.44/5.65 ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_Collect_less_nat
% 5.44/5.65 thf(fact_3715_finite__Collect__subsets,axiom,
% 5.44/5.65 ! [A2: set_complex] :
% 5.44/5.65 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.65 => ( finite6551019134538273531omplex
% 5.44/5.65 @ ( collect_set_complex
% 5.44/5.65 @ ^ [B5: set_complex] : ( ord_le211207098394363844omplex @ B5 @ A2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_Collect_subsets
% 5.44/5.65 thf(fact_3716_finite__Collect__subsets,axiom,
% 5.44/5.65 ! [A2: set_real] :
% 5.44/5.65 ( ( finite_finite_real @ A2 )
% 5.44/5.65 => ( finite9007344921179782393t_real
% 5.44/5.65 @ ( collect_set_real
% 5.44/5.65 @ ^ [B5: set_real] : ( ord_less_eq_set_real @ B5 @ A2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_Collect_subsets
% 5.44/5.65 thf(fact_3717_finite__Collect__subsets,axiom,
% 5.44/5.65 ! [A2: set_nat] :
% 5.44/5.65 ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ( finite1152437895449049373et_nat
% 5.44/5.65 @ ( collect_set_nat
% 5.44/5.65 @ ^ [B5: set_nat] : ( ord_less_eq_set_nat @ B5 @ A2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_Collect_subsets
% 5.44/5.65 thf(fact_3718_finite__roots__unity,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.65 => ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [Z5: real] :
% 5.44/5.65 ( ( power_power_real @ Z5 @ N2 )
% 5.44/5.65 = one_one_real ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_roots_unity
% 5.44/5.65 thf(fact_3719_finite__roots__unity,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.65 => ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [Z5: complex] :
% 5.44/5.65 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.65 = one_one_complex ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_roots_unity
% 5.44/5.65 thf(fact_3720_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_int,X: int > extended_enat,Y: int > extended_enat] :
% 5.44/5.65 ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.65 => ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.65 => ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( times_7803423173614009249d_enat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3721_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_real,X: real > extended_enat,Y: real > extended_enat] :
% 5.44/5.65 ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.65 => ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.65 => ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( times_7803423173614009249d_enat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3722_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_nat,X: nat > extended_enat,Y: nat > extended_enat] :
% 5.44/5.65 ( ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.65 => ( ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.65 => ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( times_7803423173614009249d_enat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3723_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_complex,X: complex > extended_enat,Y: complex > extended_enat] :
% 5.44/5.65 ( ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.65 => ( ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.65 => ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( times_7803423173614009249d_enat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_on7984719198319812577d_enat ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3724_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_int,X: int > complex,Y: int > complex] :
% 5.44/5.65 ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_one_complex ) ) ) )
% 5.44/5.65 => ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_one_complex ) ) ) )
% 5.44/5.65 => ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_one_complex ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3725_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_real,X: real > complex,Y: real > complex] :
% 5.44/5.65 ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_one_complex ) ) ) )
% 5.44/5.65 => ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_one_complex ) ) ) )
% 5.44/5.65 => ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_one_complex ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3726_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 5.44/5.65 ( ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_one_complex ) ) ) )
% 5.44/5.65 => ( ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_one_complex ) ) ) )
% 5.44/5.65 => ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_one_complex ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3727_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 5.44/5.65 ( ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_one_complex ) ) ) )
% 5.44/5.65 => ( ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_one_complex ) ) ) )
% 5.44/5.65 => ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_one_complex ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3728_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_int,X: int > real,Y: int > real] :
% 5.44/5.65 ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_one_real ) ) ) )
% 5.44/5.65 => ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_one_real ) ) ) )
% 5.44/5.65 => ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_one_real ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3729_prod_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_real,X: real > real,Y: real > real] :
% 5.44/5.65 ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != one_one_real ) ) ) )
% 5.44/5.65 => ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != one_one_real ) ) ) )
% 5.44/5.65 => ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != one_one_real ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod.finite_Collect_op
% 5.44/5.65 thf(fact_3730_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_int,X: int > extended_enat,Y: int > extended_enat] :
% 5.44/5.65 ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) )
% 5.44/5.65 => ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) )
% 5.44/5.65 => ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_p3455044024723400733d_enat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3731_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_real,X: real > extended_enat,Y: real > extended_enat] :
% 5.44/5.65 ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) )
% 5.44/5.65 => ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) )
% 5.44/5.65 => ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_p3455044024723400733d_enat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3732_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_nat,X: nat > extended_enat,Y: nat > extended_enat] :
% 5.44/5.65 ( ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) )
% 5.44/5.65 => ( ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) )
% 5.44/5.65 => ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_p3455044024723400733d_enat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3733_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_complex,X: complex > extended_enat,Y: complex > extended_enat] :
% 5.44/5.65 ( ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) )
% 5.44/5.65 => ( ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) )
% 5.44/5.65 => ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_p3455044024723400733d_enat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3734_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_int,X: int > complex,Y: int > complex] :
% 5.44/5.65 ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_zero_complex ) ) ) )
% 5.44/5.65 => ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_zero_complex ) ) ) )
% 5.44/5.65 => ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_zero_complex ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3735_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_real,X: real > complex,Y: real > complex] :
% 5.44/5.65 ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_zero_complex ) ) ) )
% 5.44/5.65 => ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_zero_complex ) ) ) )
% 5.44/5.65 => ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_zero_complex ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3736_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 5.44/5.65 ( ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_zero_complex ) ) ) )
% 5.44/5.65 => ( ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_zero_complex ) ) ) )
% 5.44/5.65 => ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [I5: nat] :
% 5.44/5.65 ( ( member_nat @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_zero_complex ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3737_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 5.44/5.65 ( ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_zero_complex ) ) ) )
% 5.44/5.65 => ( ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_zero_complex ) ) ) )
% 5.44/5.65 => ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [I5: complex] :
% 5.44/5.65 ( ( member_complex @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_zero_complex ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3738_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_int,X: int > real,Y: int > real] :
% 5.44/5.65 ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_zero_real ) ) ) )
% 5.44/5.65 => ( ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_zero_real ) ) ) )
% 5.44/5.65 => ( finite_finite_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [I5: int] :
% 5.44/5.65 ( ( member_int @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3739_sum_Ofinite__Collect__op,axiom,
% 5.44/5.65 ! [I6: set_real,X: real > real,Y: real > real] :
% 5.44/5.65 ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( X @ I5 )
% 5.44/5.65 != zero_zero_real ) ) ) )
% 5.44/5.65 => ( ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( Y @ I5 )
% 5.44/5.65 != zero_zero_real ) ) ) )
% 5.44/5.65 => ( finite_finite_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [I5: real] :
% 5.44/5.65 ( ( member_real @ I5 @ I6 )
% 5.44/5.65 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.44/5.65 != zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % sum.finite_Collect_op
% 5.44/5.65 thf(fact_3740_neg__eucl__rel__int__mult__2,axiom,
% 5.44/5.65 ! [B: int,A: int,Q2: int,R: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.44/5.65 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.44/5.65 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % neg_eucl_rel_int_mult_2
% 5.44/5.65 thf(fact_3741_finite__maxlen,axiom,
% 5.44/5.65 ! [M7: set_list_VEBT_VEBT] :
% 5.44/5.65 ( ( finite3004134309566078307T_VEBT @ M7 )
% 5.44/5.65 => ? [N4: nat] :
% 5.44/5.65 ! [X3: list_VEBT_VEBT] :
% 5.44/5.65 ( ( member2936631157270082147T_VEBT @ X3 @ M7 )
% 5.44/5.65 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X3 ) @ N4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_maxlen
% 5.44/5.65 thf(fact_3742_finite__maxlen,axiom,
% 5.44/5.65 ! [M7: set_list_o] :
% 5.44/5.65 ( ( finite_finite_list_o @ M7 )
% 5.44/5.65 => ? [N4: nat] :
% 5.44/5.65 ! [X3: list_o] :
% 5.44/5.65 ( ( member_list_o @ X3 @ M7 )
% 5.44/5.65 => ( ord_less_nat @ ( size_size_list_o @ X3 ) @ N4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_maxlen
% 5.44/5.65 thf(fact_3743_finite__maxlen,axiom,
% 5.44/5.65 ! [M7: set_list_nat] :
% 5.44/5.65 ( ( finite8100373058378681591st_nat @ M7 )
% 5.44/5.65 => ? [N4: nat] :
% 5.44/5.65 ! [X3: list_nat] :
% 5.44/5.65 ( ( member_list_nat @ X3 @ M7 )
% 5.44/5.65 => ( ord_less_nat @ ( size_size_list_nat @ X3 ) @ N4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_maxlen
% 5.44/5.65 thf(fact_3744_finite__maxlen,axiom,
% 5.44/5.65 ! [M7: set_list_int] :
% 5.44/5.65 ( ( finite3922522038869484883st_int @ M7 )
% 5.44/5.65 => ? [N4: nat] :
% 5.44/5.65 ! [X3: list_int] :
% 5.44/5.65 ( ( member_list_int @ X3 @ M7 )
% 5.44/5.65 => ( ord_less_nat @ ( size_size_list_int @ X3 ) @ N4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_maxlen
% 5.44/5.65 thf(fact_3745_finite__has__maximal2,axiom,
% 5.44/5.65 ! [A2: set_real,A: real] :
% 5.44/5.65 ( ( finite_finite_real @ A2 )
% 5.44/5.65 => ( ( member_real @ A @ A2 )
% 5.44/5.65 => ? [X5: real] :
% 5.44/5.65 ( ( member_real @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_real @ A @ X5 )
% 5.44/5.65 & ! [Xa: real] :
% 5.44/5.65 ( ( member_real @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_real @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal2
% 5.44/5.65 thf(fact_3746_finite__has__maximal2,axiom,
% 5.44/5.65 ! [A2: set_set_real,A: set_real] :
% 5.44/5.65 ( ( finite9007344921179782393t_real @ A2 )
% 5.44/5.65 => ( ( member_set_real @ A @ A2 )
% 5.44/5.65 => ? [X5: set_real] :
% 5.44/5.65 ( ( member_set_real @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_set_real @ A @ X5 )
% 5.44/5.65 & ! [Xa: set_real] :
% 5.44/5.65 ( ( member_set_real @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_set_real @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal2
% 5.44/5.65 thf(fact_3747_finite__has__maximal2,axiom,
% 5.44/5.65 ! [A2: set_set_nat,A: set_nat] :
% 5.44/5.65 ( ( finite1152437895449049373et_nat @ A2 )
% 5.44/5.65 => ( ( member_set_nat @ A @ A2 )
% 5.44/5.65 => ? [X5: set_nat] :
% 5.44/5.65 ( ( member_set_nat @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_set_nat @ A @ X5 )
% 5.44/5.65 & ! [Xa: set_nat] :
% 5.44/5.65 ( ( member_set_nat @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_set_nat @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal2
% 5.44/5.65 thf(fact_3748_finite__has__maximal2,axiom,
% 5.44/5.65 ! [A2: set_num,A: num] :
% 5.44/5.65 ( ( finite_finite_num @ A2 )
% 5.44/5.65 => ( ( member_num @ A @ A2 )
% 5.44/5.65 => ? [X5: num] :
% 5.44/5.65 ( ( member_num @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_num @ A @ X5 )
% 5.44/5.65 & ! [Xa: num] :
% 5.44/5.65 ( ( member_num @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_num @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal2
% 5.44/5.65 thf(fact_3749_finite__has__maximal2,axiom,
% 5.44/5.65 ! [A2: set_nat,A: nat] :
% 5.44/5.65 ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ( ( member_nat @ A @ A2 )
% 5.44/5.65 => ? [X5: nat] :
% 5.44/5.65 ( ( member_nat @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_nat @ A @ X5 )
% 5.44/5.65 & ! [Xa: nat] :
% 5.44/5.65 ( ( member_nat @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_nat @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal2
% 5.44/5.65 thf(fact_3750_finite__has__maximal2,axiom,
% 5.44/5.65 ! [A2: set_int,A: int] :
% 5.44/5.65 ( ( finite_finite_int @ A2 )
% 5.44/5.65 => ( ( member_int @ A @ A2 )
% 5.44/5.65 => ? [X5: int] :
% 5.44/5.65 ( ( member_int @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_int @ A @ X5 )
% 5.44/5.65 & ! [Xa: int] :
% 5.44/5.65 ( ( member_int @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_int @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal2
% 5.44/5.65 thf(fact_3751_finite__has__minimal2,axiom,
% 5.44/5.65 ! [A2: set_real,A: real] :
% 5.44/5.65 ( ( finite_finite_real @ A2 )
% 5.44/5.65 => ( ( member_real @ A @ A2 )
% 5.44/5.65 => ? [X5: real] :
% 5.44/5.65 ( ( member_real @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_real @ X5 @ A )
% 5.44/5.65 & ! [Xa: real] :
% 5.44/5.65 ( ( member_real @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_real @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal2
% 5.44/5.65 thf(fact_3752_finite__has__minimal2,axiom,
% 5.44/5.65 ! [A2: set_set_real,A: set_real] :
% 5.44/5.65 ( ( finite9007344921179782393t_real @ A2 )
% 5.44/5.65 => ( ( member_set_real @ A @ A2 )
% 5.44/5.65 => ? [X5: set_real] :
% 5.44/5.65 ( ( member_set_real @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_set_real @ X5 @ A )
% 5.44/5.65 & ! [Xa: set_real] :
% 5.44/5.65 ( ( member_set_real @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_set_real @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal2
% 5.44/5.65 thf(fact_3753_finite__has__minimal2,axiom,
% 5.44/5.65 ! [A2: set_set_nat,A: set_nat] :
% 5.44/5.65 ( ( finite1152437895449049373et_nat @ A2 )
% 5.44/5.65 => ( ( member_set_nat @ A @ A2 )
% 5.44/5.65 => ? [X5: set_nat] :
% 5.44/5.65 ( ( member_set_nat @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_set_nat @ X5 @ A )
% 5.44/5.65 & ! [Xa: set_nat] :
% 5.44/5.65 ( ( member_set_nat @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_set_nat @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal2
% 5.44/5.65 thf(fact_3754_finite__has__minimal2,axiom,
% 5.44/5.65 ! [A2: set_num,A: num] :
% 5.44/5.65 ( ( finite_finite_num @ A2 )
% 5.44/5.65 => ( ( member_num @ A @ A2 )
% 5.44/5.65 => ? [X5: num] :
% 5.44/5.65 ( ( member_num @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_num @ X5 @ A )
% 5.44/5.65 & ! [Xa: num] :
% 5.44/5.65 ( ( member_num @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_num @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal2
% 5.44/5.65 thf(fact_3755_finite__has__minimal2,axiom,
% 5.44/5.65 ! [A2: set_nat,A: nat] :
% 5.44/5.65 ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ( ( member_nat @ A @ A2 )
% 5.44/5.65 => ? [X5: nat] :
% 5.44/5.65 ( ( member_nat @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_nat @ X5 @ A )
% 5.44/5.65 & ! [Xa: nat] :
% 5.44/5.65 ( ( member_nat @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_nat @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal2
% 5.44/5.65 thf(fact_3756_finite__has__minimal2,axiom,
% 5.44/5.65 ! [A2: set_int,A: int] :
% 5.44/5.65 ( ( finite_finite_int @ A2 )
% 5.44/5.65 => ( ( member_int @ A @ A2 )
% 5.44/5.65 => ? [X5: int] :
% 5.44/5.65 ( ( member_int @ X5 @ A2 )
% 5.44/5.65 & ( ord_less_eq_int @ X5 @ A )
% 5.44/5.65 & ! [Xa: int] :
% 5.44/5.65 ( ( member_int @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_int @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal2
% 5.44/5.65 thf(fact_3757_finite__subset,axiom,
% 5.44/5.65 ! [A2: set_complex,B2: set_complex] :
% 5.44/5.65 ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.65 => ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.65 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_subset
% 5.44/5.65 thf(fact_3758_finite__subset,axiom,
% 5.44/5.65 ! [A2: set_real,B2: set_real] :
% 5.44/5.65 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.65 => ( ( finite_finite_real @ B2 )
% 5.44/5.65 => ( finite_finite_real @ A2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_subset
% 5.44/5.65 thf(fact_3759_finite__subset,axiom,
% 5.44/5.65 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.65 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.65 => ( ( finite_finite_nat @ B2 )
% 5.44/5.65 => ( finite_finite_nat @ A2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_subset
% 5.44/5.65 thf(fact_3760_infinite__super,axiom,
% 5.44/5.65 ! [S: set_complex,T3: set_complex] :
% 5.44/5.65 ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.65 => ( ~ ( finite3207457112153483333omplex @ S )
% 5.44/5.65 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_super
% 5.44/5.65 thf(fact_3761_infinite__super,axiom,
% 5.44/5.65 ! [S: set_real,T3: set_real] :
% 5.44/5.65 ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.65 => ( ~ ( finite_finite_real @ S )
% 5.44/5.65 => ~ ( finite_finite_real @ T3 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_super
% 5.44/5.65 thf(fact_3762_infinite__super,axiom,
% 5.44/5.65 ! [S: set_nat,T3: set_nat] :
% 5.44/5.65 ( ( ord_less_eq_set_nat @ S @ T3 )
% 5.44/5.65 => ( ~ ( finite_finite_nat @ S )
% 5.44/5.65 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_super
% 5.44/5.65 thf(fact_3763_rev__finite__subset,axiom,
% 5.44/5.65 ! [B2: set_complex,A2: set_complex] :
% 5.44/5.65 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.65 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.65 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % rev_finite_subset
% 5.44/5.65 thf(fact_3764_rev__finite__subset,axiom,
% 5.44/5.65 ! [B2: set_real,A2: set_real] :
% 5.44/5.65 ( ( finite_finite_real @ B2 )
% 5.44/5.65 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.65 => ( finite_finite_real @ A2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % rev_finite_subset
% 5.44/5.65 thf(fact_3765_rev__finite__subset,axiom,
% 5.44/5.65 ! [B2: set_nat,A2: set_nat] :
% 5.44/5.65 ( ( finite_finite_nat @ B2 )
% 5.44/5.65 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.65 => ( finite_finite_nat @ A2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % rev_finite_subset
% 5.44/5.65 thf(fact_3766_finite__has__maximal,axiom,
% 5.44/5.65 ! [A2: set_real] :
% 5.44/5.65 ( ( finite_finite_real @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_real )
% 5.44/5.65 => ? [X5: real] :
% 5.44/5.65 ( ( member_real @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: real] :
% 5.44/5.65 ( ( member_real @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_real @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal
% 5.44/5.65 thf(fact_3767_finite__has__maximal,axiom,
% 5.44/5.65 ! [A2: set_set_real] :
% 5.44/5.65 ( ( finite9007344921179782393t_real @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_set_real )
% 5.44/5.65 => ? [X5: set_real] :
% 5.44/5.65 ( ( member_set_real @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: set_real] :
% 5.44/5.65 ( ( member_set_real @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_set_real @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal
% 5.44/5.65 thf(fact_3768_finite__has__maximal,axiom,
% 5.44/5.65 ! [A2: set_set_nat] :
% 5.44/5.65 ( ( finite1152437895449049373et_nat @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_set_nat )
% 5.44/5.65 => ? [X5: set_nat] :
% 5.44/5.65 ( ( member_set_nat @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: set_nat] :
% 5.44/5.65 ( ( member_set_nat @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_set_nat @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal
% 5.44/5.65 thf(fact_3769_finite__has__maximal,axiom,
% 5.44/5.65 ! [A2: set_num] :
% 5.44/5.65 ( ( finite_finite_num @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_num )
% 5.44/5.65 => ? [X5: num] :
% 5.44/5.65 ( ( member_num @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: num] :
% 5.44/5.65 ( ( member_num @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_num @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal
% 5.44/5.65 thf(fact_3770_finite__has__maximal,axiom,
% 5.44/5.65 ! [A2: set_nat] :
% 5.44/5.65 ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_nat )
% 5.44/5.65 => ? [X5: nat] :
% 5.44/5.65 ( ( member_nat @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: nat] :
% 5.44/5.65 ( ( member_nat @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_nat @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal
% 5.44/5.65 thf(fact_3771_finite__has__maximal,axiom,
% 5.44/5.65 ! [A2: set_int] :
% 5.44/5.65 ( ( finite_finite_int @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_int )
% 5.44/5.65 => ? [X5: int] :
% 5.44/5.65 ( ( member_int @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: int] :
% 5.44/5.65 ( ( member_int @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_int @ X5 @ Xa )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_maximal
% 5.44/5.65 thf(fact_3772_finite__has__minimal,axiom,
% 5.44/5.65 ! [A2: set_real] :
% 5.44/5.65 ( ( finite_finite_real @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_real )
% 5.44/5.65 => ? [X5: real] :
% 5.44/5.65 ( ( member_real @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: real] :
% 5.44/5.65 ( ( member_real @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_real @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal
% 5.44/5.65 thf(fact_3773_finite__has__minimal,axiom,
% 5.44/5.65 ! [A2: set_set_real] :
% 5.44/5.65 ( ( finite9007344921179782393t_real @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_set_real )
% 5.44/5.65 => ? [X5: set_real] :
% 5.44/5.65 ( ( member_set_real @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: set_real] :
% 5.44/5.65 ( ( member_set_real @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_set_real @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal
% 5.44/5.65 thf(fact_3774_finite__has__minimal,axiom,
% 5.44/5.65 ! [A2: set_set_nat] :
% 5.44/5.65 ( ( finite1152437895449049373et_nat @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_set_nat )
% 5.44/5.65 => ? [X5: set_nat] :
% 5.44/5.65 ( ( member_set_nat @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: set_nat] :
% 5.44/5.65 ( ( member_set_nat @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_set_nat @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal
% 5.44/5.65 thf(fact_3775_finite__has__minimal,axiom,
% 5.44/5.65 ! [A2: set_num] :
% 5.44/5.65 ( ( finite_finite_num @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_num )
% 5.44/5.65 => ? [X5: num] :
% 5.44/5.65 ( ( member_num @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: num] :
% 5.44/5.65 ( ( member_num @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_num @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal
% 5.44/5.65 thf(fact_3776_finite__has__minimal,axiom,
% 5.44/5.65 ! [A2: set_nat] :
% 5.44/5.65 ( ( finite_finite_nat @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_nat )
% 5.44/5.65 => ? [X5: nat] :
% 5.44/5.65 ( ( member_nat @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: nat] :
% 5.44/5.65 ( ( member_nat @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_nat @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal
% 5.44/5.65 thf(fact_3777_finite__has__minimal,axiom,
% 5.44/5.65 ! [A2: set_int] :
% 5.44/5.65 ( ( finite_finite_int @ A2 )
% 5.44/5.65 => ( ( A2 != bot_bot_set_int )
% 5.44/5.65 => ? [X5: int] :
% 5.44/5.65 ( ( member_int @ X5 @ A2 )
% 5.44/5.65 & ! [Xa: int] :
% 5.44/5.65 ( ( member_int @ Xa @ A2 )
% 5.44/5.65 => ( ( ord_less_eq_int @ Xa @ X5 )
% 5.44/5.65 => ( X5 = Xa ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_has_minimal
% 5.44/5.65 thf(fact_3778_pos__eucl__rel__int__mult__2,axiom,
% 5.44/5.65 ! [B: int,A: int,Q2: int,R: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.65 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.44/5.65 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % pos_eucl_rel_int_mult_2
% 5.44/5.65 thf(fact_3779_arcosh__1,axiom,
% 5.44/5.65 ( ( arcosh_real @ one_one_real )
% 5.44/5.65 = zero_zero_real ) ).
% 5.44/5.65
% 5.44/5.65 % arcosh_1
% 5.44/5.65 thf(fact_3780_finite__nth__roots,axiom,
% 5.44/5.65 ! [N2: nat,C: complex] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( finite3207457112153483333omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [Z5: complex] :
% 5.44/5.65 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.65 = C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_nth_roots
% 5.44/5.65 thf(fact_3781_gcd__nat__induct,axiom,
% 5.44/5.65 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.44/5.65 ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 5.44/5.65 => ( ! [M5: nat,N4: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.44/5.65 => ( ( P @ N4 @ ( modulo_modulo_nat @ M5 @ N4 ) )
% 5.44/5.65 => ( P @ M5 @ N4 ) ) )
% 5.44/5.65 => ( P @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % gcd_nat_induct
% 5.44/5.65 thf(fact_3782_concat__bit__Suc,axiom,
% 5.44/5.65 ! [N2: nat,K: int,L2: int] :
% 5.44/5.65 ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L2 )
% 5.44/5.65 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % concat_bit_Suc
% 5.44/5.65 thf(fact_3783_dbl__simps_I3_J,axiom,
% 5.44/5.65 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.44/5.65 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(3)
% 5.44/5.65 thf(fact_3784_dbl__simps_I3_J,axiom,
% 5.44/5.65 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.44/5.65 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(3)
% 5.44/5.65 thf(fact_3785_dbl__simps_I3_J,axiom,
% 5.44/5.65 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.44/5.65 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(3)
% 5.44/5.65 thf(fact_3786_even__succ__mod__exp,axiom,
% 5.44/5.65 ! [A: code_integer,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_mod_exp
% 5.44/5.65 thf(fact_3787_even__succ__mod__exp,axiom,
% 5.44/5.65 ! [A: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.65 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_mod_exp
% 5.44/5.65 thf(fact_3788_even__succ__mod__exp,axiom,
% 5.44/5.65 ! [A: int,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.65 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_mod_exp
% 5.44/5.65 thf(fact_3789_nat__dvd__1__iff__1,axiom,
% 5.44/5.65 ! [M: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.44/5.65 = ( M = one_one_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % nat_dvd_1_iff_1
% 5.44/5.65 thf(fact_3790_dvd__add__triv__left__iff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_left_iff
% 5.44/5.65 thf(fact_3791_dvd__add__triv__left__iff,axiom,
% 5.44/5.65 ! [A: complex,B: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.44/5.65 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_left_iff
% 5.44/5.65 thf(fact_3792_dvd__add__triv__left__iff,axiom,
% 5.44/5.65 ! [A: real,B: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.44/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_left_iff
% 5.44/5.65 thf(fact_3793_dvd__add__triv__left__iff,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_left_iff
% 5.44/5.65 thf(fact_3794_dvd__add__triv__left__iff,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_left_iff
% 5.44/5.65 thf(fact_3795_dvd__add__triv__right__iff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_right_iff
% 5.44/5.65 thf(fact_3796_dvd__add__triv__right__iff,axiom,
% 5.44/5.65 ! [A: complex,B: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ A ) )
% 5.44/5.65 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_right_iff
% 5.44/5.65 thf(fact_3797_dvd__add__triv__right__iff,axiom,
% 5.44/5.65 ! [A: real,B: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.44/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_right_iff
% 5.44/5.65 thf(fact_3798_dvd__add__triv__right__iff,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_right_iff
% 5.44/5.65 thf(fact_3799_dvd__add__triv__right__iff,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_triv_right_iff
% 5.44/5.65 thf(fact_3800_dvd__1__iff__1,axiom,
% 5.44/5.65 ! [M: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.44/5.65 = ( M
% 5.44/5.65 = ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_1_iff_1
% 5.44/5.65 thf(fact_3801_dvd__1__left,axiom,
% 5.44/5.65 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_1_left
% 5.44/5.65 thf(fact_3802_div__dvd__div,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ C )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.44/5.65 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_dvd_div
% 5.44/5.65 thf(fact_3803_div__dvd__div,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ C )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.44/5.65 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_dvd_div
% 5.44/5.65 thf(fact_3804_div__dvd__div,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_dvd_div
% 5.44/5.65 thf(fact_3805_nat__mult__dvd__cancel__disj,axiom,
% 5.44/5.65 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.65 = ( ( K = zero_zero_nat )
% 5.44/5.65 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % nat_mult_dvd_cancel_disj
% 5.44/5.65 thf(fact_3806_concat__bit__0,axiom,
% 5.44/5.65 ! [K: int,L2: int] :
% 5.44/5.65 ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 5.44/5.65 = L2 ) ).
% 5.44/5.65
% 5.44/5.65 % concat_bit_0
% 5.44/5.65 thf(fact_3807_dbl__simps_I2_J,axiom,
% 5.44/5.65 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.44/5.65 = zero_zero_complex ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(2)
% 5.44/5.65 thf(fact_3808_dbl__simps_I2_J,axiom,
% 5.44/5.65 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.44/5.65 = zero_zero_real ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(2)
% 5.44/5.65 thf(fact_3809_dbl__simps_I2_J,axiom,
% 5.44/5.65 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.44/5.65 = zero_zero_int ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(2)
% 5.44/5.65 thf(fact_3810_dvd__mult__cancel__left,axiom,
% 5.44/5.65 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.44/5.65 = ( ( C = zero_z3403309356797280102nteger )
% 5.44/5.65 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel_left
% 5.44/5.65 thf(fact_3811_dvd__mult__cancel__left,axiom,
% 5.44/5.65 ! [C: complex,A: complex,B: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.44/5.65 = ( ( C = zero_zero_complex )
% 5.44/5.65 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel_left
% 5.44/5.65 thf(fact_3812_dvd__mult__cancel__left,axiom,
% 5.44/5.65 ! [C: real,A: real,B: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.44/5.65 = ( ( C = zero_zero_real )
% 5.44/5.65 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel_left
% 5.44/5.65 thf(fact_3813_dvd__mult__cancel__left,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.44/5.65 = ( ( C = zero_zero_int )
% 5.44/5.65 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel_left
% 5.44/5.65 thf(fact_3814_dvd__mult__cancel__right,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.44/5.65 = ( ( C = zero_z3403309356797280102nteger )
% 5.44/5.65 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel_right
% 5.44/5.65 thf(fact_3815_dvd__mult__cancel__right,axiom,
% 5.44/5.65 ! [A: complex,C: complex,B: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.44/5.65 = ( ( C = zero_zero_complex )
% 5.44/5.65 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel_right
% 5.44/5.65 thf(fact_3816_dvd__mult__cancel__right,axiom,
% 5.44/5.65 ! [A: real,C: real,B: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.44/5.65 = ( ( C = zero_zero_real )
% 5.44/5.65 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel_right
% 5.44/5.65 thf(fact_3817_dvd__mult__cancel__right,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.44/5.65 = ( ( C = zero_zero_int )
% 5.44/5.65 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel_right
% 5.44/5.65 thf(fact_3818_dvd__times__left__cancel__iff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_times_left_cancel_iff
% 5.44/5.65 thf(fact_3819_dvd__times__left__cancel__iff,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( A != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.44/5.65 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_times_left_cancel_iff
% 5.44/5.65 thf(fact_3820_dvd__times__left__cancel__iff,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( A != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.44/5.65 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_times_left_cancel_iff
% 5.44/5.65 thf(fact_3821_dvd__times__right__cancel__iff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_times_right_cancel_iff
% 5.44/5.65 thf(fact_3822_dvd__times__right__cancel__iff,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( A != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.44/5.65 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_times_right_cancel_iff
% 5.44/5.65 thf(fact_3823_dvd__times__right__cancel__iff,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( A != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.44/5.65 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_times_right_cancel_iff
% 5.44/5.65 thf(fact_3824_dvd__add__times__triv__left__iff,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_left_iff
% 5.44/5.65 thf(fact_3825_dvd__add__times__triv__left__iff,axiom,
% 5.44/5.65 ! [A: complex,C: complex,B: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 5.44/5.65 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_left_iff
% 5.44/5.65 thf(fact_3826_dvd__add__times__triv__left__iff,axiom,
% 5.44/5.65 ! [A: real,C: real,B: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.44/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_left_iff
% 5.44/5.65 thf(fact_3827_dvd__add__times__triv__left__iff,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_left_iff
% 5.44/5.65 thf(fact_3828_dvd__add__times__triv__left__iff,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_left_iff
% 5.44/5.65 thf(fact_3829_dvd__add__times__triv__right__iff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_right_iff
% 5.44/5.65 thf(fact_3830_dvd__add__times__triv__right__iff,axiom,
% 5.44/5.65 ! [A: complex,B: complex,C: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 5.44/5.65 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_right_iff
% 5.44/5.65 thf(fact_3831_dvd__add__times__triv__right__iff,axiom,
% 5.44/5.65 ! [A: real,B: real,C: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.44/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_right_iff
% 5.44/5.65 thf(fact_3832_dvd__add__times__triv__right__iff,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_right_iff
% 5.44/5.65 thf(fact_3833_dvd__add__times__triv__right__iff,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_times_triv_right_iff
% 5.44/5.65 thf(fact_3834_unit__prod,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_prod
% 5.44/5.65 thf(fact_3835_unit__prod,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_prod
% 5.44/5.65 thf(fact_3836_unit__prod,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_prod
% 5.44/5.65 thf(fact_3837_dvd__div__mult__self,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult_self
% 5.44/5.65 thf(fact_3838_dvd__div__mult__self,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult_self
% 5.44/5.65 thf(fact_3839_dvd__div__mult__self,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult_self
% 5.44/5.65 thf(fact_3840_dvd__mult__div__cancel,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_div_cancel
% 5.44/5.65 thf(fact_3841_dvd__mult__div__cancel,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_div_cancel
% 5.44/5.65 thf(fact_3842_dvd__mult__div__cancel,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_div_cancel
% 5.44/5.65 thf(fact_3843_div__add,axiom,
% 5.44/5.65 ! [C: nat,A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_add
% 5.44/5.65 thf(fact_3844_div__add,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_add
% 5.44/5.65 thf(fact_3845_div__add,axiom,
% 5.44/5.65 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_add
% 5.44/5.65 thf(fact_3846_unit__div,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div
% 5.44/5.65 thf(fact_3847_unit__div,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div
% 5.44/5.65 thf(fact_3848_unit__div,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div
% 5.44/5.65 thf(fact_3849_unit__div__1__unit,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_1_unit
% 5.44/5.65 thf(fact_3850_unit__div__1__unit,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_1_unit
% 5.44/5.65 thf(fact_3851_unit__div__1__unit,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_1_unit
% 5.44/5.65 thf(fact_3852_unit__div__1__div__1,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_1_div_1
% 5.44/5.65 thf(fact_3853_unit__div__1__div__1,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_1_div_1
% 5.44/5.65 thf(fact_3854_unit__div__1__div__1,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_1_div_1
% 5.44/5.65 thf(fact_3855_div__diff,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.44/5.65 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_diff
% 5.44/5.65 thf(fact_3856_div__diff,axiom,
% 5.44/5.65 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.44/5.65 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_diff
% 5.44/5.65 thf(fact_3857_concat__bit__nonnegative__iff,axiom,
% 5.44/5.65 ! [N2: nat,K: int,L2: int] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K @ L2 ) )
% 5.44/5.65 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % concat_bit_nonnegative_iff
% 5.44/5.65 thf(fact_3858_concat__bit__negative__iff,axiom,
% 5.44/5.65 ! [N2: nat,K: int,L2: int] :
% 5.44/5.65 ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K @ L2 ) @ zero_zero_int )
% 5.44/5.65 = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % concat_bit_negative_iff
% 5.44/5.65 thf(fact_3859_dbl__simps_I5_J,axiom,
% 5.44/5.65 ! [K: num] :
% 5.44/5.65 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.44/5.65 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(5)
% 5.44/5.65 thf(fact_3860_dbl__simps_I5_J,axiom,
% 5.44/5.65 ! [K: num] :
% 5.44/5.65 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.44/5.65 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(5)
% 5.44/5.65 thf(fact_3861_dbl__simps_I5_J,axiom,
% 5.44/5.65 ! [K: num] :
% 5.44/5.65 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.44/5.65 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_simps(5)
% 5.44/5.65 thf(fact_3862_even__Suc,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_Suc
% 5.44/5.65 thf(fact_3863_even__Suc__Suc__iff,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N2 ) ) )
% 5.44/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_Suc_Suc_iff
% 5.44/5.65 thf(fact_3864_unit__mult__div__div,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.44/5.65 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_div_div
% 5.44/5.65 thf(fact_3865_unit__mult__div__div,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.44/5.65 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_div_div
% 5.44/5.65 thf(fact_3866_unit__mult__div__div,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_div_div
% 5.44/5.65 thf(fact_3867_unit__div__mult__self,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_mult_self
% 5.44/5.65 thf(fact_3868_unit__div__mult__self,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_mult_self
% 5.44/5.65 thf(fact_3869_unit__div__mult__self,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.44/5.65 = B ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_mult_self
% 5.44/5.65 thf(fact_3870_pow__divides__pow__iff,axiom,
% 5.44/5.65 ! [N2: nat,A: nat,B: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % pow_divides_pow_iff
% 5.44/5.65 thf(fact_3871_pow__divides__pow__iff,axiom,
% 5.44/5.65 ! [N2: nat,A: int,B: int] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % pow_divides_pow_iff
% 5.44/5.65 thf(fact_3872_even__mult__iff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mult_iff
% 5.44/5.65 thf(fact_3873_even__mult__iff,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mult_iff
% 5.44/5.65 thf(fact_3874_even__mult__iff,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.44/5.65 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mult_iff
% 5.44/5.65 thf(fact_3875_odd__add,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.44/5.65 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.65 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_add
% 5.44/5.65 thf(fact_3876_odd__add,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.44/5.65 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.65 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_add
% 5.44/5.65 thf(fact_3877_odd__add,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.44/5.65 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.65 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_add
% 5.44/5.65 thf(fact_3878_even__add,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_add
% 5.44/5.65 thf(fact_3879_even__add,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_add
% 5.44/5.65 thf(fact_3880_even__add,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.44/5.65 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_add
% 5.44/5.65 thf(fact_3881_even__mod__2__iff,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mod_2_iff
% 5.44/5.65 thf(fact_3882_even__mod__2__iff,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mod_2_iff
% 5.44/5.65 thf(fact_3883_even__mod__2__iff,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mod_2_iff
% 5.44/5.65 thf(fact_3884_odd__Suc__div__two,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_Suc_div_two
% 5.44/5.65 thf(fact_3885_even__Suc__div__two,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_Suc_div_two
% 5.44/5.65 thf(fact_3886_zero__le__power__eq__numeral,axiom,
% 5.44/5.65 ! [A: real,W: num] :
% 5.44/5.65 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_le_power_eq_numeral
% 5.44/5.65 thf(fact_3887_zero__le__power__eq__numeral,axiom,
% 5.44/5.65 ! [A: int,W: num] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_le_power_eq_numeral
% 5.44/5.65 thf(fact_3888_power__less__zero__eq,axiom,
% 5.44/5.65 ! [A: real,N2: nat] :
% 5.44/5.65 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.44/5.65 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_less_zero_eq
% 5.44/5.65 thf(fact_3889_power__less__zero__eq,axiom,
% 5.44/5.65 ! [A: int,N2: nat] :
% 5.44/5.65 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.44/5.65 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_less_zero_eq
% 5.44/5.65 thf(fact_3890_power__less__zero__eq__numeral,axiom,
% 5.44/5.65 ! [A: real,W: num] :
% 5.44/5.65 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.44/5.65 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_less_zero_eq_numeral
% 5.44/5.65 thf(fact_3891_power__less__zero__eq__numeral,axiom,
% 5.44/5.65 ! [A: int,W: num] :
% 5.44/5.65 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.44/5.65 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_less_zero_eq_numeral
% 5.44/5.65 thf(fact_3892_even__plus__one__iff,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_plus_one_iff
% 5.44/5.65 thf(fact_3893_even__plus__one__iff,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_plus_one_iff
% 5.44/5.65 thf(fact_3894_even__plus__one__iff,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_plus_one_iff
% 5.44/5.65 thf(fact_3895_even__diff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_diff
% 5.44/5.65 thf(fact_3896_even__diff,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.44/5.65 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_diff
% 5.44/5.65 thf(fact_3897_odd__Suc__minus__one,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.44/5.65 = N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_Suc_minus_one
% 5.44/5.65 thf(fact_3898_even__diff__nat,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.65 = ( ( ord_less_nat @ M @ N2 )
% 5.44/5.65 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_diff_nat
% 5.44/5.65 thf(fact_3899_zero__less__power__eq__numeral,axiom,
% 5.44/5.65 ! [A: real,W: num] :
% 5.44/5.65 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.44/5.65 = ( ( ( numeral_numeral_nat @ W )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( A != zero_zero_real ) )
% 5.44/5.65 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_less_power_eq_numeral
% 5.44/5.65 thf(fact_3900_zero__less__power__eq__numeral,axiom,
% 5.44/5.65 ! [A: int,W: num] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.44/5.65 = ( ( ( numeral_numeral_nat @ W )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( A != zero_zero_int ) )
% 5.44/5.65 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_less_power_eq_numeral
% 5.44/5.65 thf(fact_3901_even__succ__div__2,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_2
% 5.44/5.65 thf(fact_3902_even__succ__div__2,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_2
% 5.44/5.65 thf(fact_3903_even__succ__div__2,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_2
% 5.44/5.65 thf(fact_3904_odd__succ__div__two,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_succ_div_two
% 5.44/5.65 thf(fact_3905_odd__succ__div__two,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_succ_div_two
% 5.44/5.65 thf(fact_3906_odd__succ__div__two,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_succ_div_two
% 5.44/5.65 thf(fact_3907_even__succ__div__two,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_two
% 5.44/5.65 thf(fact_3908_even__succ__div__two,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_two
% 5.44/5.65 thf(fact_3909_even__succ__div__two,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_two
% 5.44/5.65 thf(fact_3910_even__power,axiom,
% 5.44/5.65 ! [A: code_integer,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_power
% 5.44/5.65 thf(fact_3911_even__power,axiom,
% 5.44/5.65 ! [A: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_power
% 5.44/5.65 thf(fact_3912_even__power,axiom,
% 5.44/5.65 ! [A: int,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 5.44/5.65 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_power
% 5.44/5.65 thf(fact_3913_odd__two__times__div__two__nat,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_two_times_div_two_nat
% 5.44/5.65 thf(fact_3914_odd__two__times__div__two__succ,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_two_times_div_two_succ
% 5.44/5.65 thf(fact_3915_odd__two__times__div__two__succ,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_two_times_div_two_succ
% 5.44/5.65 thf(fact_3916_odd__two__times__div__two__succ,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_two_times_div_two_succ
% 5.44/5.65 thf(fact_3917_power__le__zero__eq__numeral,axiom,
% 5.44/5.65 ! [A: real,W: num] :
% 5.44/5.65 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.44/5.65 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.44/5.65 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_zero_eq_numeral
% 5.44/5.65 thf(fact_3918_power__le__zero__eq__numeral,axiom,
% 5.44/5.65 ! [A: int,W: num] :
% 5.44/5.65 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.44/5.65 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.44/5.65 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.65 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_zero_eq_numeral
% 5.44/5.65 thf(fact_3919_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 5.44/5.65 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % semiring_parity_class.even_mask_iff
% 5.44/5.65 thf(fact_3920_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 5.44/5.65 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % semiring_parity_class.even_mask_iff
% 5.44/5.65 thf(fact_3921_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.44/5.65 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % semiring_parity_class.even_mask_iff
% 5.44/5.65 thf(fact_3922_even__succ__div__exp,axiom,
% 5.44/5.65 ! [A: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.65 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_exp
% 5.44/5.65 thf(fact_3923_even__succ__div__exp,axiom,
% 5.44/5.65 ! [A: int,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.65 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_exp
% 5.44/5.65 thf(fact_3924_even__succ__div__exp,axiom,
% 5.44/5.65 ! [A: code_integer,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_succ_div_exp
% 5.44/5.65 thf(fact_3925_dvd__productE,axiom,
% 5.44/5.65 ! [P5: nat,A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ P5 @ ( times_times_nat @ A @ B ) )
% 5.44/5.65 => ~ ! [X5: nat,Y5: nat] :
% 5.44/5.65 ( ( P5
% 5.44/5.65 = ( times_times_nat @ X5 @ Y5 ) )
% 5.44/5.65 => ( ( dvd_dvd_nat @ X5 @ A )
% 5.44/5.65 => ~ ( dvd_dvd_nat @ Y5 @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_productE
% 5.44/5.65 thf(fact_3926_dvd__productE,axiom,
% 5.44/5.65 ! [P5: int,A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ P5 @ ( times_times_int @ A @ B ) )
% 5.44/5.65 => ~ ! [X5: int,Y5: int] :
% 5.44/5.65 ( ( P5
% 5.44/5.65 = ( times_times_int @ X5 @ Y5 ) )
% 5.44/5.65 => ( ( dvd_dvd_int @ X5 @ A )
% 5.44/5.65 => ~ ( dvd_dvd_int @ Y5 @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_productE
% 5.44/5.65 thf(fact_3927_division__decomp,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.44/5.65 => ? [B7: nat,C5: nat] :
% 5.44/5.65 ( ( A
% 5.44/5.65 = ( times_times_nat @ B7 @ C5 ) )
% 5.44/5.65 & ( dvd_dvd_nat @ B7 @ B )
% 5.44/5.65 & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % division_decomp
% 5.44/5.65 thf(fact_3928_division__decomp,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.65 => ? [B7: int,C5: int] :
% 5.44/5.65 ( ( A
% 5.44/5.65 = ( times_times_int @ B7 @ C5 ) )
% 5.44/5.65 & ( dvd_dvd_int @ B7 @ B )
% 5.44/5.65 & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % division_decomp
% 5.44/5.65 thf(fact_3929_dvdE,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.65 => ~ ! [K2: code_integer] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdE
% 5.44/5.65 thf(fact_3930_dvdE,axiom,
% 5.44/5.65 ! [B: complex,A: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ B @ A )
% 5.44/5.65 => ~ ! [K2: complex] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( times_times_complex @ B @ K2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdE
% 5.44/5.65 thf(fact_3931_dvdE,axiom,
% 5.44/5.65 ! [B: real,A: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ B @ A )
% 5.44/5.65 => ~ ! [K2: real] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( times_times_real @ B @ K2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdE
% 5.44/5.65 thf(fact_3932_dvdE,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ A )
% 5.44/5.65 => ~ ! [K2: nat] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdE
% 5.44/5.65 thf(fact_3933_dvdE,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ A )
% 5.44/5.65 => ~ ! [K2: int] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdE
% 5.44/5.65 thf(fact_3934_dvdI,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.44/5.65 ( ( A
% 5.44/5.65 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdI
% 5.44/5.65 thf(fact_3935_dvdI,axiom,
% 5.44/5.65 ! [A: complex,B: complex,K: complex] :
% 5.44/5.65 ( ( A
% 5.44/5.65 = ( times_times_complex @ B @ K ) )
% 5.44/5.65 => ( dvd_dvd_complex @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdI
% 5.44/5.65 thf(fact_3936_dvdI,axiom,
% 5.44/5.65 ! [A: real,B: real,K: real] :
% 5.44/5.65 ( ( A
% 5.44/5.65 = ( times_times_real @ B @ K ) )
% 5.44/5.65 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdI
% 5.44/5.65 thf(fact_3937_dvdI,axiom,
% 5.44/5.65 ! [A: nat,B: nat,K: nat] :
% 5.44/5.65 ( ( A
% 5.44/5.65 = ( times_times_nat @ B @ K ) )
% 5.44/5.65 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdI
% 5.44/5.65 thf(fact_3938_dvdI,axiom,
% 5.44/5.65 ! [A: int,B: int,K: int] :
% 5.44/5.65 ( ( A
% 5.44/5.65 = ( times_times_int @ B @ K ) )
% 5.44/5.65 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvdI
% 5.44/5.65 thf(fact_3939_dvd__def,axiom,
% 5.44/5.65 ( dvd_dvd_Code_integer
% 5.44/5.65 = ( ^ [B4: code_integer,A4: code_integer] :
% 5.44/5.65 ? [K3: code_integer] :
% 5.44/5.65 ( A4
% 5.44/5.65 = ( times_3573771949741848930nteger @ B4 @ K3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_def
% 5.44/5.65 thf(fact_3940_dvd__def,axiom,
% 5.44/5.65 ( dvd_dvd_complex
% 5.44/5.65 = ( ^ [B4: complex,A4: complex] :
% 5.44/5.65 ? [K3: complex] :
% 5.44/5.65 ( A4
% 5.44/5.65 = ( times_times_complex @ B4 @ K3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_def
% 5.44/5.65 thf(fact_3941_dvd__def,axiom,
% 5.44/5.65 ( dvd_dvd_real
% 5.44/5.65 = ( ^ [B4: real,A4: real] :
% 5.44/5.65 ? [K3: real] :
% 5.44/5.65 ( A4
% 5.44/5.65 = ( times_times_real @ B4 @ K3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_def
% 5.44/5.65 thf(fact_3942_dvd__def,axiom,
% 5.44/5.65 ( dvd_dvd_nat
% 5.44/5.65 = ( ^ [B4: nat,A4: nat] :
% 5.44/5.65 ? [K3: nat] :
% 5.44/5.65 ( A4
% 5.44/5.65 = ( times_times_nat @ B4 @ K3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_def
% 5.44/5.65 thf(fact_3943_dvd__def,axiom,
% 5.44/5.65 ( dvd_dvd_int
% 5.44/5.65 = ( ^ [B4: int,A4: int] :
% 5.44/5.65 ? [K3: int] :
% 5.44/5.65 ( A4
% 5.44/5.65 = ( times_times_int @ B4 @ K3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_def
% 5.44/5.65 thf(fact_3944_dvd__mult,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult
% 5.44/5.65 thf(fact_3945_dvd__mult,axiom,
% 5.44/5.65 ! [A: complex,C: complex,B: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ C )
% 5.44/5.65 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult
% 5.44/5.65 thf(fact_3946_dvd__mult,axiom,
% 5.44/5.65 ! [A: real,C: real,B: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ C )
% 5.44/5.65 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult
% 5.44/5.65 thf(fact_3947_dvd__mult,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ C )
% 5.44/5.65 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult
% 5.44/5.65 thf(fact_3948_dvd__mult,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ C )
% 5.44/5.65 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult
% 5.44/5.65 thf(fact_3949_dvd__mult2,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult2
% 5.44/5.65 thf(fact_3950_dvd__mult2,axiom,
% 5.44/5.65 ! [A: complex,B: complex,C: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ B )
% 5.44/5.65 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult2
% 5.44/5.65 thf(fact_3951_dvd__mult2,axiom,
% 5.44/5.65 ! [A: real,B: real,C: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ B )
% 5.44/5.65 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult2
% 5.44/5.65 thf(fact_3952_dvd__mult2,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult2
% 5.44/5.65 thf(fact_3953_dvd__mult2,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult2
% 5.44/5.65 thf(fact_3954_dvd__mult__left,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_left
% 5.44/5.65 thf(fact_3955_dvd__mult__left,axiom,
% 5.44/5.65 ! [A: complex,B: complex,C: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_complex @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_left
% 5.44/5.65 thf(fact_3956_dvd__mult__left,axiom,
% 5.44/5.65 ! [A: real,B: real,C: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_left
% 5.44/5.65 thf(fact_3957_dvd__mult__left,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_left
% 5.44/5.65 thf(fact_3958_dvd__mult__left,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_left
% 5.44/5.65 thf(fact_3959_dvd__triv__left,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_left
% 5.44/5.65 thf(fact_3960_dvd__triv__left,axiom,
% 5.44/5.65 ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_left
% 5.44/5.65 thf(fact_3961_dvd__triv__left,axiom,
% 5.44/5.65 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_left
% 5.44/5.65 thf(fact_3962_dvd__triv__left,axiom,
% 5.44/5.65 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_left
% 5.44/5.65 thf(fact_3963_dvd__triv__left,axiom,
% 5.44/5.65 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_left
% 5.44/5.65 thf(fact_3964_mult__dvd__mono,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_dvd_mono
% 5.44/5.65 thf(fact_3965_mult__dvd__mono,axiom,
% 5.44/5.65 ! [A: complex,B: complex,C: complex,D: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_complex @ C @ D )
% 5.44/5.65 => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_dvd_mono
% 5.44/5.65 thf(fact_3966_mult__dvd__mono,axiom,
% 5.44/5.65 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_real @ C @ D )
% 5.44/5.65 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_dvd_mono
% 5.44/5.65 thf(fact_3967_mult__dvd__mono,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ C @ D )
% 5.44/5.65 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_dvd_mono
% 5.44/5.65 thf(fact_3968_mult__dvd__mono,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ D )
% 5.44/5.65 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_dvd_mono
% 5.44/5.65 thf(fact_3969_dvd__mult__right,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_right
% 5.44/5.65 thf(fact_3970_dvd__mult__right,axiom,
% 5.44/5.65 ! [A: complex,B: complex,C: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_complex @ B @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_right
% 5.44/5.65 thf(fact_3971_dvd__mult__right,axiom,
% 5.44/5.65 ! [A: real,B: real,C: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_right
% 5.44/5.65 thf(fact_3972_dvd__mult__right,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_right
% 5.44/5.65 thf(fact_3973_dvd__mult__right,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.44/5.65 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_right
% 5.44/5.65 thf(fact_3974_dvd__triv__right,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_right
% 5.44/5.65 thf(fact_3975_dvd__triv__right,axiom,
% 5.44/5.65 ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_right
% 5.44/5.65 thf(fact_3976_dvd__triv__right,axiom,
% 5.44/5.65 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_right
% 5.44/5.65 thf(fact_3977_dvd__triv__right,axiom,
% 5.44/5.65 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_right
% 5.44/5.65 thf(fact_3978_dvd__triv__right,axiom,
% 5.44/5.65 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_triv_right
% 5.44/5.65 thf(fact_3979_dvd__add,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add
% 5.44/5.65 thf(fact_3980_dvd__add,axiom,
% 5.44/5.65 ! [A: complex,B: complex,C: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_complex @ A @ C )
% 5.44/5.65 => ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add
% 5.44/5.65 thf(fact_3981_dvd__add,axiom,
% 5.44/5.65 ! [A: real,B: real,C: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_real @ A @ C )
% 5.44/5.65 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add
% 5.44/5.65 thf(fact_3982_dvd__add,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ C )
% 5.44/5.65 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add
% 5.44/5.65 thf(fact_3983_dvd__add,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ C )
% 5.44/5.65 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add
% 5.44/5.65 thf(fact_3984_dvd__add__left__iff,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_left_iff
% 5.44/5.65 thf(fact_3985_dvd__add__left__iff,axiom,
% 5.44/5.65 ! [A: complex,C: complex,B: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ C )
% 5.44/5.65 => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_left_iff
% 5.44/5.65 thf(fact_3986_dvd__add__left__iff,axiom,
% 5.44/5.65 ! [A: real,C: real,B: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ C )
% 5.44/5.65 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_left_iff
% 5.44/5.65 thf(fact_3987_dvd__add__left__iff,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ C )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_left_iff
% 5.44/5.65 thf(fact_3988_dvd__add__left__iff,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ C )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_left_iff
% 5.44/5.65 thf(fact_3989_dvd__add__right__iff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_right_iff
% 5.44/5.65 thf(fact_3990_dvd__add__right__iff,axiom,
% 5.44/5.65 ! [A: complex,B: complex,C: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_complex @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_right_iff
% 5.44/5.65 thf(fact_3991_dvd__add__right__iff,axiom,
% 5.44/5.65 ! [A: real,B: real,C: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_right_iff
% 5.44/5.65 thf(fact_3992_dvd__add__right__iff,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_right_iff
% 5.44/5.65 thf(fact_3993_dvd__add__right__iff,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_add_right_iff
% 5.44/5.65 thf(fact_3994_dvd__unit__imp__unit,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_unit_imp_unit
% 5.44/5.65 thf(fact_3995_dvd__unit__imp__unit,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_unit_imp_unit
% 5.44/5.65 thf(fact_3996_dvd__unit__imp__unit,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_unit_imp_unit
% 5.44/5.65 thf(fact_3997_unit__imp__dvd,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_imp_dvd
% 5.44/5.65 thf(fact_3998_unit__imp__dvd,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_imp_dvd
% 5.44/5.65 thf(fact_3999_unit__imp__dvd,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_imp_dvd
% 5.44/5.65 thf(fact_4000_one__dvd,axiom,
% 5.44/5.65 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.44/5.65
% 5.44/5.65 % one_dvd
% 5.44/5.65 thf(fact_4001_one__dvd,axiom,
% 5.44/5.65 ! [A: extended_enat] : ( dvd_dv3785147216227455552d_enat @ one_on7984719198319812577d_enat @ A ) ).
% 5.44/5.65
% 5.44/5.65 % one_dvd
% 5.44/5.65 thf(fact_4002_one__dvd,axiom,
% 5.44/5.65 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.44/5.65
% 5.44/5.65 % one_dvd
% 5.44/5.65 thf(fact_4003_one__dvd,axiom,
% 5.44/5.65 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.44/5.65
% 5.44/5.65 % one_dvd
% 5.44/5.65 thf(fact_4004_one__dvd,axiom,
% 5.44/5.65 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.44/5.65
% 5.44/5.65 % one_dvd
% 5.44/5.65 thf(fact_4005_one__dvd,axiom,
% 5.44/5.65 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.44/5.65
% 5.44/5.65 % one_dvd
% 5.44/5.65 thf(fact_4006_dvd__diff__commute,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_diff_commute
% 5.44/5.65 thf(fact_4007_dvd__diff__commute,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_diff_commute
% 5.44/5.65 thf(fact_4008_dvd__div__eq__iff,axiom,
% 5.44/5.65 ! [C: nat,A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( ( ( divide_divide_nat @ A @ C )
% 5.44/5.65 = ( divide_divide_nat @ B @ C ) )
% 5.44/5.65 = ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_iff
% 5.44/5.65 thf(fact_4009_dvd__div__eq__iff,axiom,
% 5.44/5.65 ! [C: real,A: real,B: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_real @ C @ B )
% 5.44/5.65 => ( ( ( divide_divide_real @ A @ C )
% 5.44/5.65 = ( divide_divide_real @ B @ C ) )
% 5.44/5.65 = ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_iff
% 5.44/5.65 thf(fact_4010_dvd__div__eq__iff,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( ( divide_divide_int @ A @ C )
% 5.44/5.65 = ( divide_divide_int @ B @ C ) )
% 5.44/5.65 = ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_iff
% 5.44/5.65 thf(fact_4011_dvd__div__eq__iff,axiom,
% 5.44/5.65 ! [C: complex,A: complex,B: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_complex @ C @ B )
% 5.44/5.65 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.44/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.65 = ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_iff
% 5.44/5.65 thf(fact_4012_dvd__div__eq__iff,axiom,
% 5.44/5.65 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.44/5.65 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.44/5.65 = ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_iff
% 5.44/5.65 thf(fact_4013_dvd__div__eq__cancel,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( ( divide_divide_nat @ A @ C )
% 5.44/5.65 = ( divide_divide_nat @ B @ C ) )
% 5.44/5.65 => ( ( dvd_dvd_nat @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_cancel
% 5.44/5.65 thf(fact_4014_dvd__div__eq__cancel,axiom,
% 5.44/5.65 ! [A: real,C: real,B: real] :
% 5.44/5.65 ( ( ( divide_divide_real @ A @ C )
% 5.44/5.65 = ( divide_divide_real @ B @ C ) )
% 5.44/5.65 => ( ( dvd_dvd_real @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_real @ C @ B )
% 5.44/5.65 => ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_cancel
% 5.44/5.65 thf(fact_4015_dvd__div__eq__cancel,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( ( divide_divide_int @ A @ C )
% 5.44/5.65 = ( divide_divide_int @ B @ C ) )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_cancel
% 5.44/5.65 thf(fact_4016_dvd__div__eq__cancel,axiom,
% 5.44/5.65 ! [A: complex,C: complex,B: complex] :
% 5.44/5.65 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.44/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.65 => ( ( dvd_dvd_complex @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_complex @ C @ B )
% 5.44/5.65 => ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_cancel
% 5.44/5.65 thf(fact_4017_dvd__div__eq__cancel,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.44/5.65 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.44/5.65 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( A = B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_cancel
% 5.44/5.65 thf(fact_4018_div__div__div__same,axiom,
% 5.44/5.65 ! [D: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ D @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ A )
% 5.44/5.65 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.44/5.65 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_div_div_same
% 5.44/5.65 thf(fact_4019_div__div__div__same,axiom,
% 5.44/5.65 ! [D: int,B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ D @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ A )
% 5.44/5.65 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.44/5.65 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_div_div_same
% 5.44/5.65 thf(fact_4020_div__div__div__same,axiom,
% 5.44/5.65 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_div_div_same
% 5.44/5.65 thf(fact_4021_dvd__power__same,axiom,
% 5.44/5.65 ! [X: code_integer,Y: code_integer,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_same
% 5.44/5.65 thf(fact_4022_dvd__power__same,axiom,
% 5.44/5.65 ! [X: nat,Y: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ X @ Y )
% 5.44/5.65 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_same
% 5.44/5.65 thf(fact_4023_dvd__power__same,axiom,
% 5.44/5.65 ! [X: real,Y: real,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_real @ X @ Y )
% 5.44/5.65 => ( dvd_dvd_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_same
% 5.44/5.65 thf(fact_4024_dvd__power__same,axiom,
% 5.44/5.65 ! [X: int,Y: int,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ X @ Y )
% 5.44/5.65 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_same
% 5.44/5.65 thf(fact_4025_dvd__power__same,axiom,
% 5.44/5.65 ! [X: complex,Y: complex,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_complex @ X @ Y )
% 5.44/5.65 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_same
% 5.44/5.65 thf(fact_4026_dvd__mod,axiom,
% 5.44/5.65 ! [K: code_integer,M: code_integer,N2: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ K @ N2 )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mod
% 5.44/5.65 thf(fact_4027_dvd__mod,axiom,
% 5.44/5.65 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ K @ M )
% 5.44/5.65 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.44/5.65 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mod
% 5.44/5.65 thf(fact_4028_dvd__mod,axiom,
% 5.44/5.65 ! [K: int,M: int,N2: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ K @ M )
% 5.44/5.65 => ( ( dvd_dvd_int @ K @ N2 )
% 5.44/5.65 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mod
% 5.44/5.65 thf(fact_4029_mod__mod__cancel,axiom,
% 5.44/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.44/5.65 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mod_cancel
% 5.44/5.65 thf(fact_4030_mod__mod__cancel,axiom,
% 5.44/5.65 ! [C: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mod_cancel
% 5.44/5.65 thf(fact_4031_mod__mod__cancel,axiom,
% 5.44/5.65 ! [C: int,B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.44/5.65 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_mod_cancel
% 5.44/5.65 thf(fact_4032_dvd__diff__nat,axiom,
% 5.44/5.65 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ K @ M )
% 5.44/5.65 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.44/5.65 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_diff_nat
% 5.44/5.65 thf(fact_4033_dvd__pos__nat,axiom,
% 5.44/5.65 ! [N2: nat,M: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.44/5.65 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_pos_nat
% 5.44/5.65 thf(fact_4034_bezout__add__nat,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ? [D3: nat,X5: nat,Y5: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ D3 @ A )
% 5.44/5.65 & ( dvd_dvd_nat @ D3 @ B )
% 5.44/5.65 & ( ( ( times_times_nat @ A @ X5 )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D3 ) )
% 5.44/5.65 | ( ( times_times_nat @ B @ X5 )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % bezout_add_nat
% 5.44/5.65 thf(fact_4035_bezout__lemma__nat,axiom,
% 5.44/5.65 ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ D @ A )
% 5.44/5.65 => ( ( dvd_dvd_nat @ D @ B )
% 5.44/5.65 => ( ( ( ( times_times_nat @ A @ X )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.44/5.65 | ( ( times_times_nat @ B @ X )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.44/5.65 => ? [X5: nat,Y5: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ D @ A )
% 5.44/5.65 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.44/5.65 & ( ( ( times_times_nat @ A @ X5 )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y5 ) @ D ) )
% 5.44/5.65 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X5 )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % bezout_lemma_nat
% 5.44/5.65 thf(fact_4036_bezout1__nat,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ? [D3: nat,X5: nat,Y5: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ D3 @ A )
% 5.44/5.65 & ( dvd_dvd_nat @ D3 @ B )
% 5.44/5.65 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y5 ) )
% 5.44/5.65 = D3 )
% 5.44/5.65 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y5 ) )
% 5.44/5.65 = D3 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % bezout1_nat
% 5.44/5.65 thf(fact_4037_subset__divisors__dvd,axiom,
% 5.44/5.65 ! [A: complex,B: complex] :
% 5.44/5.65 ( ( ord_le211207098394363844omplex
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.44/5.65 @ ( collect_complex
% 5.44/5.65 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 5.44/5.65 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % subset_divisors_dvd
% 5.44/5.65 thf(fact_4038_subset__divisors__dvd,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( ord_less_eq_set_int
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.44/5.65 @ ( collect_int
% 5.44/5.65 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % subset_divisors_dvd
% 5.44/5.65 thf(fact_4039_subset__divisors__dvd,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( ord_le7084787975880047091nteger
% 5.44/5.65 @ ( collect_Code_integer
% 5.44/5.65 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.44/5.65 @ ( collect_Code_integer
% 5.44/5.65 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % subset_divisors_dvd
% 5.44/5.65 thf(fact_4040_subset__divisors__dvd,axiom,
% 5.44/5.65 ! [A: real,B: real] :
% 5.44/5.65 ( ( ord_less_eq_set_real
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 5.44/5.65 @ ( collect_real
% 5.44/5.65 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 5.44/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % subset_divisors_dvd
% 5.44/5.65 thf(fact_4041_subset__divisors__dvd,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( ord_less_eq_set_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.44/5.65
% 5.44/5.65 % subset_divisors_dvd
% 5.44/5.65 thf(fact_4042_concat__bit__assoc,axiom,
% 5.44/5.65 ! [N2: nat,K: int,M: nat,L2: int,R: int] :
% 5.44/5.65 ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
% 5.44/5.65 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L2 ) @ R ) ) ).
% 5.44/5.65
% 5.44/5.65 % concat_bit_assoc
% 5.44/5.65 thf(fact_4043_not__is__unit__0,axiom,
% 5.44/5.65 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.44/5.65
% 5.44/5.65 % not_is_unit_0
% 5.44/5.65 thf(fact_4044_not__is__unit__0,axiom,
% 5.44/5.65 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.44/5.65
% 5.44/5.65 % not_is_unit_0
% 5.44/5.65 thf(fact_4045_not__is__unit__0,axiom,
% 5.44/5.65 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.44/5.65
% 5.44/5.65 % not_is_unit_0
% 5.44/5.65 thf(fact_4046_dvd__div__eq__0__iff,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ A )
% 5.44/5.65 => ( ( ( divide_divide_nat @ A @ B )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 = ( A = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_0_iff
% 5.44/5.65 thf(fact_4047_dvd__div__eq__0__iff,axiom,
% 5.44/5.65 ! [B: real,A: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ B @ A )
% 5.44/5.65 => ( ( ( divide_divide_real @ A @ B )
% 5.44/5.65 = zero_zero_real )
% 5.44/5.65 = ( A = zero_zero_real ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_0_iff
% 5.44/5.65 thf(fact_4048_dvd__div__eq__0__iff,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ A )
% 5.44/5.65 => ( ( ( divide_divide_int @ A @ B )
% 5.44/5.65 = zero_zero_int )
% 5.44/5.65 = ( A = zero_zero_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_0_iff
% 5.44/5.65 thf(fact_4049_dvd__div__eq__0__iff,axiom,
% 5.44/5.65 ! [B: complex,A: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ B @ A )
% 5.44/5.65 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.44/5.65 = zero_zero_complex )
% 5.44/5.65 = ( A = zero_zero_complex ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_0_iff
% 5.44/5.65 thf(fact_4050_dvd__div__eq__0__iff,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.44/5.65 = zero_z3403309356797280102nteger )
% 5.44/5.65 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_0_iff
% 5.44/5.65 thf(fact_4051_is__unit__mult__iff,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_mult_iff
% 5.44/5.65 thf(fact_4052_is__unit__mult__iff,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.44/5.65 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_mult_iff
% 5.44/5.65 thf(fact_4053_is__unit__mult__iff,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.44/5.65 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_mult_iff
% 5.44/5.65 thf(fact_4054_dvd__mult__unit__iff,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_unit_iff
% 5.44/5.65 thf(fact_4055_dvd__mult__unit__iff,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_unit_iff
% 5.44/5.65 thf(fact_4056_dvd__mult__unit__iff,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_unit_iff
% 5.44/5.65 thf(fact_4057_mult__unit__dvd__iff,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_unit_dvd_iff
% 5.44/5.65 thf(fact_4058_mult__unit__dvd__iff,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_unit_dvd_iff
% 5.44/5.65 thf(fact_4059_mult__unit__dvd__iff,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_unit_dvd_iff
% 5.44/5.65 thf(fact_4060_dvd__mult__unit__iff_H,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_unit_iff'
% 5.44/5.65 thf(fact_4061_dvd__mult__unit__iff_H,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_unit_iff'
% 5.44/5.65 thf(fact_4062_dvd__mult__unit__iff_H,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_unit_iff'
% 5.44/5.65 thf(fact_4063_mult__unit__dvd__iff_H,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_unit_dvd_iff'
% 5.44/5.65 thf(fact_4064_mult__unit__dvd__iff_H,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_unit_dvd_iff'
% 5.44/5.65 thf(fact_4065_mult__unit__dvd__iff_H,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mult_unit_dvd_iff'
% 5.44/5.65 thf(fact_4066_unit__mult__left__cancel,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.44/5.65 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_left_cancel
% 5.44/5.65 thf(fact_4067_unit__mult__left__cancel,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( ( times_times_nat @ A @ B )
% 5.44/5.65 = ( times_times_nat @ A @ C ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_left_cancel
% 5.44/5.65 thf(fact_4068_unit__mult__left__cancel,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( ( times_times_int @ A @ B )
% 5.44/5.65 = ( times_times_int @ A @ C ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_left_cancel
% 5.44/5.65 thf(fact_4069_unit__mult__right__cancel,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.44/5.65 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_right_cancel
% 5.44/5.65 thf(fact_4070_unit__mult__right__cancel,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( ( times_times_nat @ B @ A )
% 5.44/5.65 = ( times_times_nat @ C @ A ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_right_cancel
% 5.44/5.65 thf(fact_4071_unit__mult__right__cancel,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( ( times_times_int @ B @ A )
% 5.44/5.65 = ( times_times_int @ C @ A ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_mult_right_cancel
% 5.44/5.65 thf(fact_4072_dvd__div__mult,axiom,
% 5.44/5.65 ! [C: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.44/5.65 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult
% 5.44/5.65 thf(fact_4073_dvd__div__mult,axiom,
% 5.44/5.65 ! [C: int,B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.44/5.65 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult
% 5.44/5.65 thf(fact_4074_dvd__div__mult,axiom,
% 5.44/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult
% 5.44/5.65 thf(fact_4075_div__mult__swap,axiom,
% 5.44/5.65 ! [C: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.44/5.65 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_swap
% 5.44/5.65 thf(fact_4076_div__mult__swap,axiom,
% 5.44/5.65 ! [C: int,B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.44/5.65 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_swap
% 5.44/5.65 thf(fact_4077_div__mult__swap,axiom,
% 5.44/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_swap
% 5.44/5.65 thf(fact_4078_div__div__eq__right,axiom,
% 5.44/5.65 ! [C: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ A )
% 5.44/5.65 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.44/5.65 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_div_eq_right
% 5.44/5.65 thf(fact_4079_div__div__eq__right,axiom,
% 5.44/5.65 ! [C: int,B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ A )
% 5.44/5.65 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.44/5.65 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_div_eq_right
% 5.44/5.65 thf(fact_4080_div__div__eq__right,axiom,
% 5.44/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.44/5.65 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_div_eq_right
% 5.44/5.65 thf(fact_4081_dvd__div__mult2__eq,axiom,
% 5.44/5.65 ! [B: nat,C: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.44/5.65 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.44/5.65 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult2_eq
% 5.44/5.65 thf(fact_4082_dvd__div__mult2__eq,axiom,
% 5.44/5.65 ! [B: int,C: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.44/5.65 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.65 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult2_eq
% 5.44/5.65 thf(fact_4083_dvd__div__mult2__eq,axiom,
% 5.44/5.65 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_mult2_eq
% 5.44/5.65 thf(fact_4084_dvd__mult__imp__div,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.44/5.65 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_imp_div
% 5.44/5.65 thf(fact_4085_dvd__mult__imp__div,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.44/5.65 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_imp_div
% 5.44/5.65 thf(fact_4086_dvd__mult__imp__div,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_imp_div
% 5.44/5.65 thf(fact_4087_div__mult__div__if__dvd,axiom,
% 5.44/5.65 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ A )
% 5.44/5.65 => ( ( dvd_dvd_nat @ D @ C )
% 5.44/5.65 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.44/5.65 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_div_if_dvd
% 5.44/5.65 thf(fact_4088_div__mult__div__if__dvd,axiom,
% 5.44/5.65 ! [B: int,A: int,D: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ A )
% 5.44/5.65 => ( ( dvd_dvd_int @ D @ C )
% 5.44/5.65 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.44/5.65 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_div_if_dvd
% 5.44/5.65 thf(fact_4089_div__mult__div__if__dvd,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_div_if_dvd
% 5.44/5.65 thf(fact_4090_div__plus__div__distrib__dvd__left,axiom,
% 5.44/5.65 ! [C: nat,A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ A )
% 5.44/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_plus_div_distrib_dvd_left
% 5.44/5.65 thf(fact_4091_div__plus__div__distrib__dvd__left,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ A )
% 5.44/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_plus_div_distrib_dvd_left
% 5.44/5.65 thf(fact_4092_div__plus__div__distrib__dvd__left,axiom,
% 5.44/5.65 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_plus_div_distrib_dvd_left
% 5.44/5.65 thf(fact_4093_div__plus__div__distrib__dvd__right,axiom,
% 5.44/5.65 ! [C: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.44/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_plus_div_distrib_dvd_right
% 5.44/5.65 thf(fact_4094_div__plus__div__distrib__dvd__right,axiom,
% 5.44/5.65 ! [C: int,B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.44/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_plus_div_distrib_dvd_right
% 5.44/5.65 thf(fact_4095_div__plus__div__distrib__dvd__right,axiom,
% 5.44/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_plus_div_distrib_dvd_right
% 5.44/5.65 thf(fact_4096_unit__div__cancel,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ( ( ( divide_divide_nat @ B @ A )
% 5.44/5.65 = ( divide_divide_nat @ C @ A ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_cancel
% 5.44/5.65 thf(fact_4097_unit__div__cancel,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ( ( ( divide_divide_int @ B @ A )
% 5.44/5.65 = ( divide_divide_int @ C @ A ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_cancel
% 5.44/5.65 thf(fact_4098_unit__div__cancel,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.44/5.65 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.44/5.65 = ( B = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_cancel
% 5.44/5.65 thf(fact_4099_div__unit__dvd__iff,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_unit_dvd_iff
% 5.44/5.65 thf(fact_4100_div__unit__dvd__iff,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_unit_dvd_iff
% 5.44/5.65 thf(fact_4101_div__unit__dvd__iff,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_unit_dvd_iff
% 5.44/5.65 thf(fact_4102_dvd__div__unit__iff,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_unit_iff
% 5.44/5.65 thf(fact_4103_dvd__div__unit__iff,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.44/5.65 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_unit_iff
% 5.44/5.65 thf(fact_4104_dvd__div__unit__iff,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_unit_iff
% 5.44/5.65 thf(fact_4105_div__power,axiom,
% 5.44/5.65 ! [B: nat,A: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ A )
% 5.44/5.65 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
% 5.44/5.65 = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_power
% 5.44/5.65 thf(fact_4106_div__power,axiom,
% 5.44/5.65 ! [B: int,A: int,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ A )
% 5.44/5.65 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N2 )
% 5.44/5.65 = ( divide_divide_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_power
% 5.44/5.65 thf(fact_4107_div__power,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.65 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N2 )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_power
% 5.44/5.65 thf(fact_4108_dvd__power__le,axiom,
% 5.44/5.65 ! [X: code_integer,Y: code_integer,N2: nat,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.44/5.65 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_le
% 5.44/5.65 thf(fact_4109_dvd__power__le,axiom,
% 5.44/5.65 ! [X: nat,Y: nat,N2: nat,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ X @ Y )
% 5.44/5.65 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_le
% 5.44/5.65 thf(fact_4110_dvd__power__le,axiom,
% 5.44/5.65 ! [X: real,Y: real,N2: nat,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_real @ X @ Y )
% 5.44/5.65 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( dvd_dvd_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_le
% 5.44/5.65 thf(fact_4111_dvd__power__le,axiom,
% 5.44/5.65 ! [X: int,Y: int,N2: nat,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ X @ Y )
% 5.44/5.65 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_le
% 5.44/5.65 thf(fact_4112_dvd__power__le,axiom,
% 5.44/5.65 ! [X: complex,Y: complex,N2: nat,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_complex @ X @ Y )
% 5.44/5.65 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_le
% 5.44/5.65 thf(fact_4113_power__le__dvd,axiom,
% 5.44/5.65 ! [A: code_integer,N2: nat,B: code_integer,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ B )
% 5.44/5.65 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_dvd
% 5.44/5.65 thf(fact_4114_power__le__dvd,axiom,
% 5.44/5.65 ! [A: nat,N2: nat,B: nat,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 5.44/5.65 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_dvd
% 5.44/5.65 thf(fact_4115_power__le__dvd,axiom,
% 5.44/5.65 ! [A: real,N2: nat,B: real,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 5.44/5.65 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_dvd
% 5.44/5.65 thf(fact_4116_power__le__dvd,axiom,
% 5.44/5.65 ! [A: int,N2: nat,B: int,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 5.44/5.65 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_dvd
% 5.44/5.65 thf(fact_4117_power__le__dvd,axiom,
% 5.44/5.65 ! [A: complex,N2: nat,B: complex,M: nat] :
% 5.44/5.65 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 5.44/5.65 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_dvd
% 5.44/5.65 thf(fact_4118_le__imp__power__dvd,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,A: code_integer] :
% 5.44/5.65 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % le_imp_power_dvd
% 5.44/5.65 thf(fact_4119_le__imp__power__dvd,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,A: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % le_imp_power_dvd
% 5.44/5.65 thf(fact_4120_le__imp__power__dvd,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,A: real] :
% 5.44/5.65 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % le_imp_power_dvd
% 5.44/5.65 thf(fact_4121_le__imp__power__dvd,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,A: int] :
% 5.44/5.65 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % le_imp_power_dvd
% 5.44/5.65 thf(fact_4122_le__imp__power__dvd,axiom,
% 5.44/5.65 ! [M: nat,N2: nat,A: complex] :
% 5.44/5.65 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % le_imp_power_dvd
% 5.44/5.65 thf(fact_4123_mod__eq__dvd__iff,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.44/5.65 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.44/5.65 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_dvd_iff
% 5.44/5.65 thf(fact_4124_mod__eq__dvd__iff,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int] :
% 5.44/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.44/5.65 = ( modulo_modulo_int @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_dvd_iff
% 5.44/5.65 thf(fact_4125_bezout__add__strong__nat,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( A != zero_zero_nat )
% 5.44/5.65 => ? [D3: nat,X5: nat,Y5: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ D3 @ A )
% 5.44/5.65 & ( dvd_dvd_nat @ D3 @ B )
% 5.44/5.65 & ( ( times_times_nat @ A @ X5 )
% 5.44/5.65 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % bezout_add_strong_nat
% 5.44/5.65 thf(fact_4126_nat__dvd__not__less,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.65 => ( ( ord_less_nat @ M @ N2 )
% 5.44/5.65 => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % nat_dvd_not_less
% 5.44/5.65 thf(fact_4127_dvd__minus__self,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 5.44/5.65 = ( ( ord_less_nat @ N2 @ M )
% 5.44/5.65 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_minus_self
% 5.44/5.65 thf(fact_4128_dvd__diffD,axiom,
% 5.44/5.65 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.65 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.44/5.65 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_diffD
% 5.44/5.65 thf(fact_4129_dvd__diffD1,axiom,
% 5.44/5.65 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.65 => ( ( dvd_dvd_nat @ K @ M )
% 5.44/5.65 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_diffD1
% 5.44/5.65 thf(fact_4130_less__eq__dvd__minus,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.44/5.65 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % less_eq_dvd_minus
% 5.44/5.65 thf(fact_4131_dbl__def,axiom,
% 5.44/5.65 ( neg_nu7009210354673126013omplex
% 5.44/5.65 = ( ^ [X2: complex] : ( plus_plus_complex @ X2 @ X2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_def
% 5.44/5.65 thf(fact_4132_dbl__def,axiom,
% 5.44/5.65 ( neg_numeral_dbl_real
% 5.44/5.65 = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_def
% 5.44/5.65 thf(fact_4133_dbl__def,axiom,
% 5.44/5.65 ( neg_numeral_dbl_int
% 5.44/5.65 = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dbl_def
% 5.44/5.65 thf(fact_4134_finite__divisors__nat,axiom,
% 5.44/5.65 ! [M: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.65 => ( finite_finite_nat
% 5.44/5.65 @ ( collect_nat
% 5.44/5.65 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % finite_divisors_nat
% 5.44/5.65 thf(fact_4135_div2__even__ext__nat,axiom,
% 5.44/5.65 ! [X: nat,Y: nat] :
% 5.44/5.65 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.65 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.44/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.44/5.65 => ( X = Y ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div2_even_ext_nat
% 5.44/5.65 thf(fact_4136_unit__dvdE,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.65 => ! [C3: code_integer] :
% 5.44/5.65 ( B
% 5.44/5.65 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_dvdE
% 5.44/5.65 thf(fact_4137_unit__dvdE,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ~ ( ( A != zero_zero_nat )
% 5.44/5.65 => ! [C3: nat] :
% 5.44/5.65 ( B
% 5.44/5.65 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_dvdE
% 5.44/5.65 thf(fact_4138_unit__dvdE,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ~ ( ( A != zero_zero_int )
% 5.44/5.65 => ! [C3: int] :
% 5.44/5.65 ( B
% 5.44/5.65 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_dvdE
% 5.44/5.65 thf(fact_4139_dvd__div__eq__mult,axiom,
% 5.44/5.65 ! [A: nat,B: nat,C: nat] :
% 5.44/5.65 ( ( A != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( ( divide_divide_nat @ B @ A )
% 5.44/5.65 = C )
% 5.44/5.65 = ( B
% 5.44/5.65 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_mult
% 5.44/5.65 thf(fact_4140_dvd__div__eq__mult,axiom,
% 5.44/5.65 ! [A: int,B: int,C: int] :
% 5.44/5.65 ( ( A != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( ( divide_divide_int @ B @ A )
% 5.44/5.65 = C )
% 5.44/5.65 = ( B
% 5.44/5.65 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_mult
% 5.44/5.65 thf(fact_4141_dvd__div__eq__mult,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.44/5.65 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.44/5.65 = C )
% 5.44/5.65 = ( B
% 5.44/5.65 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_eq_mult
% 5.44/5.65 thf(fact_4142_div__dvd__iff__mult,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( B != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ A )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_dvd_iff_mult
% 5.44/5.65 thf(fact_4143_div__dvd__iff__mult,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( B != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ A )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_dvd_iff_mult
% 5.44/5.65 thf(fact_4144_div__dvd__iff__mult,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( B != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_dvd_iff_mult
% 5.44/5.65 thf(fact_4145_dvd__div__iff__mult,axiom,
% 5.44/5.65 ! [C: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( C != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ C @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_iff_mult
% 5.44/5.65 thf(fact_4146_dvd__div__iff__mult,axiom,
% 5.44/5.65 ! [C: int,B: int,A: int] :
% 5.44/5.65 ( ( C != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_iff_mult
% 5.44/5.65 thf(fact_4147_dvd__div__iff__mult,axiom,
% 5.44/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( C != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_iff_mult
% 5.44/5.65 thf(fact_4148_dvd__div__div__eq__mult,axiom,
% 5.44/5.65 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.44/5.65 ( ( A != zero_zero_nat )
% 5.44/5.65 => ( ( C != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_nat @ C @ D )
% 5.44/5.65 => ( ( ( divide_divide_nat @ B @ A )
% 5.44/5.65 = ( divide_divide_nat @ D @ C ) )
% 5.44/5.65 = ( ( times_times_nat @ B @ C )
% 5.44/5.65 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_div_eq_mult
% 5.44/5.65 thf(fact_4149_dvd__div__div__eq__mult,axiom,
% 5.44/5.65 ! [A: int,C: int,B: int,D: int] :
% 5.44/5.65 ( ( A != zero_zero_int )
% 5.44/5.65 => ( ( C != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ D )
% 5.44/5.65 => ( ( ( divide_divide_int @ B @ A )
% 5.44/5.65 = ( divide_divide_int @ D @ C ) )
% 5.44/5.65 = ( ( times_times_int @ B @ C )
% 5.44/5.65 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_div_eq_mult
% 5.44/5.65 thf(fact_4150_dvd__div__div__eq__mult,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.44/5.65 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( C != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.44/5.65 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.44/5.65 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.44/5.65 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_div_div_eq_mult
% 5.44/5.65 thf(fact_4151_even__numeral,axiom,
% 5.44/5.65 ! [N2: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_numeral
% 5.44/5.65 thf(fact_4152_even__numeral,axiom,
% 5.44/5.65 ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_numeral
% 5.44/5.65 thf(fact_4153_even__numeral,axiom,
% 5.44/5.65 ! [N2: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_numeral
% 5.44/5.65 thf(fact_4154_unit__div__eq__0__iff,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( ( divide_divide_nat @ A @ B )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 = ( A = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_eq_0_iff
% 5.44/5.65 thf(fact_4155_unit__div__eq__0__iff,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( ( divide_divide_int @ A @ B )
% 5.44/5.65 = zero_zero_int )
% 5.44/5.65 = ( A = zero_zero_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_eq_0_iff
% 5.44/5.65 thf(fact_4156_unit__div__eq__0__iff,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.44/5.65 = zero_z3403309356797280102nteger )
% 5.44/5.65 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_eq_0_iff
% 5.44/5.65 thf(fact_4157_unit__eq__div1,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( ( divide_divide_nat @ A @ B )
% 5.44/5.65 = C )
% 5.44/5.65 = ( A
% 5.44/5.65 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_eq_div1
% 5.44/5.65 thf(fact_4158_unit__eq__div1,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( ( divide_divide_int @ A @ B )
% 5.44/5.65 = C )
% 5.44/5.65 = ( A
% 5.44/5.65 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_eq_div1
% 5.44/5.65 thf(fact_4159_unit__eq__div1,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.44/5.65 = C )
% 5.44/5.65 = ( A
% 5.44/5.65 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_eq_div1
% 5.44/5.65 thf(fact_4160_unit__eq__div2,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( A
% 5.44/5.65 = ( divide_divide_nat @ C @ B ) )
% 5.44/5.65 = ( ( times_times_nat @ A @ B )
% 5.44/5.65 = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_eq_div2
% 5.44/5.65 thf(fact_4161_unit__eq__div2,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( A
% 5.44/5.65 = ( divide_divide_int @ C @ B ) )
% 5.44/5.65 = ( ( times_times_int @ A @ B )
% 5.44/5.65 = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_eq_div2
% 5.44/5.65 thf(fact_4162_unit__eq__div2,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( A
% 5.44/5.65 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.44/5.65 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.44/5.65 = C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_eq_div2
% 5.44/5.65 thf(fact_4163_div__mult__unit2,axiom,
% 5.44/5.65 ! [C: nat,B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ A )
% 5.44/5.65 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.44/5.65 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_unit2
% 5.44/5.65 thf(fact_4164_div__mult__unit2,axiom,
% 5.44/5.65 ! [C: int,B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ A )
% 5.44/5.65 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.65 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_unit2
% 5.44/5.65 thf(fact_4165_div__mult__unit2,axiom,
% 5.44/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % div_mult_unit2
% 5.44/5.65 thf(fact_4166_unit__div__commute,axiom,
% 5.44/5.65 ! [B: nat,A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.44/5.65 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_commute
% 5.44/5.65 thf(fact_4167_unit__div__commute,axiom,
% 5.44/5.65 ! [B: int,A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.44/5.65 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_commute
% 5.44/5.65 thf(fact_4168_unit__div__commute,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_commute
% 5.44/5.65 thf(fact_4169_unit__div__mult__swap,axiom,
% 5.44/5.65 ! [C: nat,A: nat,B: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.44/5.65 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.44/5.65 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_mult_swap
% 5.44/5.65 thf(fact_4170_unit__div__mult__swap,axiom,
% 5.44/5.65 ! [C: int,A: int,B: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.44/5.65 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.44/5.65 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_mult_swap
% 5.44/5.65 thf(fact_4171_unit__div__mult__swap,axiom,
% 5.44/5.65 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_div_mult_swap
% 5.44/5.65 thf(fact_4172_is__unit__div__mult2__eq,axiom,
% 5.44/5.65 ! [B: nat,C: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.44/5.65 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.44/5.65 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult2_eq
% 5.44/5.65 thf(fact_4173_is__unit__div__mult2__eq,axiom,
% 5.44/5.65 ! [B: int,C: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.44/5.65 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.44/5.65 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult2_eq
% 5.44/5.65 thf(fact_4174_is__unit__div__mult2__eq,axiom,
% 5.44/5.65 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult2_eq
% 5.44/5.65 thf(fact_4175_is__unit__power__iff,axiom,
% 5.44/5.65 ! [A: code_integer,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_power_iff
% 5.44/5.65 thf(fact_4176_is__unit__power__iff,axiom,
% 5.44/5.65 ! [A: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 5.44/5.65 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_power_iff
% 5.44/5.65 thf(fact_4177_is__unit__power__iff,axiom,
% 5.44/5.65 ! [A: int,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 5.44/5.65 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_power_iff
% 5.44/5.65 thf(fact_4178_unit__imp__mod__eq__0,axiom,
% 5.44/5.65 ! [B: code_integer,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.44/5.65 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_imp_mod_eq_0
% 5.44/5.65 thf(fact_4179_unit__imp__mod__eq__0,axiom,
% 5.44/5.65 ! [B: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( modulo_modulo_nat @ A @ B )
% 5.44/5.65 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_imp_mod_eq_0
% 5.44/5.65 thf(fact_4180_unit__imp__mod__eq__0,axiom,
% 5.44/5.65 ! [B: int,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ B )
% 5.44/5.65 = zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % unit_imp_mod_eq_0
% 5.44/5.65 thf(fact_4181_dvd__imp__le,axiom,
% 5.44/5.65 ! [K: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ K @ N2 )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_imp_le
% 5.44/5.65 thf(fact_4182_dvd__mult__cancel,axiom,
% 5.44/5.65 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.65 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.65 => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel
% 5.44/5.65 thf(fact_4183_nat__mult__dvd__cancel1,axiom,
% 5.44/5.65 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.44/5.65 = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % nat_mult_dvd_cancel1
% 5.44/5.65 thf(fact_4184_mod__greater__zero__iff__not__dvd,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_greater_zero_iff_not_dvd
% 5.44/5.65 thf(fact_4185_mod__eq__dvd__iff__nat,axiom,
% 5.44/5.65 ! [N2: nat,M: nat,Q2: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.65 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.44/5.65 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 5.44/5.65 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_eq_dvd_iff_nat
% 5.44/5.65 thf(fact_4186_prod__decode__aux_Ocases,axiom,
% 5.44/5.65 ! [X: product_prod_nat_nat] :
% 5.44/5.65 ~ ! [K2: nat,M5: nat] :
% 5.44/5.65 ( X
% 5.44/5.65 != ( product_Pair_nat_nat @ K2 @ M5 ) ) ).
% 5.44/5.65
% 5.44/5.65 % prod_decode_aux.cases
% 5.44/5.65 thf(fact_4187_even__zero,axiom,
% 5.44/5.65 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.44/5.65
% 5.44/5.65 % even_zero
% 5.44/5.65 thf(fact_4188_even__zero,axiom,
% 5.44/5.65 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.44/5.65
% 5.44/5.65 % even_zero
% 5.44/5.65 thf(fact_4189_even__zero,axiom,
% 5.44/5.65 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.44/5.65
% 5.44/5.65 % even_zero
% 5.44/5.65 thf(fact_4190_evenE,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ~ ! [B3: code_integer] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % evenE
% 5.44/5.65 thf(fact_4191_evenE,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ~ ! [B3: nat] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % evenE
% 5.44/5.65 thf(fact_4192_evenE,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ~ ! [B3: int] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % evenE
% 5.44/5.65 thf(fact_4193_is__unitE,axiom,
% 5.44/5.65 ! [A: nat,C: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.44/5.65 => ~ ( ( A != zero_zero_nat )
% 5.44/5.65 => ! [B3: nat] :
% 5.44/5.65 ( ( B3 != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 5.44/5.65 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.44/5.65 = B3 )
% 5.44/5.65 => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 5.44/5.65 = A )
% 5.44/5.65 => ( ( ( times_times_nat @ A @ B3 )
% 5.44/5.65 = one_one_nat )
% 5.44/5.65 => ( ( divide_divide_nat @ C @ A )
% 5.44/5.65 != ( times_times_nat @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unitE
% 5.44/5.65 thf(fact_4194_is__unitE,axiom,
% 5.44/5.65 ! [A: int,C: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.44/5.65 => ~ ( ( A != zero_zero_int )
% 5.44/5.65 => ! [B3: int] :
% 5.44/5.65 ( ( B3 != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 5.44/5.65 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.44/5.65 = B3 )
% 5.44/5.65 => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 5.44/5.65 = A )
% 5.44/5.65 => ( ( ( times_times_int @ A @ B3 )
% 5.44/5.65 = one_one_int )
% 5.44/5.65 => ( ( divide_divide_int @ C @ A )
% 5.44/5.65 != ( times_times_int @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unitE
% 5.44/5.65 thf(fact_4195_is__unitE,axiom,
% 5.44/5.65 ! [A: code_integer,C: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.44/5.65 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.65 => ! [B3: code_integer] :
% 5.44/5.65 ( ( B3 != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.44/5.65 = B3 )
% 5.44/5.65 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 5.44/5.65 = A )
% 5.44/5.65 => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 5.44/5.65 = one_one_Code_integer )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.44/5.65 != ( times_3573771949741848930nteger @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unitE
% 5.44/5.65 thf(fact_4196_is__unit__div__mult__cancel__left,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( A != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.44/5.65 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult_cancel_left
% 5.44/5.65 thf(fact_4197_is__unit__div__mult__cancel__left,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( A != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.44/5.65 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult_cancel_left
% 5.44/5.65 thf(fact_4198_is__unit__div__mult__cancel__left,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult_cancel_left
% 5.44/5.65 thf(fact_4199_is__unit__div__mult__cancel__right,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ( A != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.44/5.65 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.44/5.65 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult_cancel_right
% 5.44/5.65 thf(fact_4200_is__unit__div__mult__cancel__right,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ( A != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.44/5.65 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.44/5.65 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult_cancel_right
% 5.44/5.65 thf(fact_4201_is__unit__div__mult__cancel__right,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ( A != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.44/5.65 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % is_unit_div_mult_cancel_right
% 5.44/5.65 thf(fact_4202_odd__even__add,axiom,
% 5.44/5.65 ! [A: code_integer,B: code_integer] :
% 5.44/5.65 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_even_add
% 5.44/5.65 thf(fact_4203_odd__even__add,axiom,
% 5.44/5.65 ! [A: nat,B: nat] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.44/5.65 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_even_add
% 5.44/5.65 thf(fact_4204_odd__even__add,axiom,
% 5.44/5.65 ! [A: int,B: int] :
% 5.44/5.65 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.44/5.65 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_even_add
% 5.44/5.65 thf(fact_4205_odd__one,axiom,
% 5.44/5.65 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.44/5.65
% 5.44/5.65 % odd_one
% 5.44/5.65 thf(fact_4206_odd__one,axiom,
% 5.44/5.65 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.44/5.65
% 5.44/5.65 % odd_one
% 5.44/5.65 thf(fact_4207_odd__one,axiom,
% 5.44/5.65 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.44/5.65
% 5.44/5.65 % odd_one
% 5.44/5.65 thf(fact_4208_bit__eq__rec,axiom,
% 5.44/5.65 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.44/5.65 = ( ^ [A4: nat,B4: nat] :
% 5.44/5.65 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 5.44/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) )
% 5.44/5.65 & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide_divide_nat @ B4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % bit_eq_rec
% 5.44/5.65 thf(fact_4209_bit__eq__rec,axiom,
% 5.44/5.65 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.44/5.65 = ( ^ [A4: int,B4: int] :
% 5.44/5.65 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 5.44/5.65 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) )
% 5.44/5.65 & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide_divide_int @ B4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % bit_eq_rec
% 5.44/5.65 thf(fact_4210_bit__eq__rec,axiom,
% 5.44/5.65 ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 5.44/5.65 = ( ^ [A4: code_integer,B4: code_integer] :
% 5.44/5.65 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) )
% 5.44/5.65 & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = ( divide6298287555418463151nteger @ B4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % bit_eq_rec
% 5.44/5.65 thf(fact_4211_dvd__power__iff,axiom,
% 5.44/5.65 ! [X: code_integer,M: nat,N2: nat] :
% 5.44/5.65 ( ( X != zero_z3403309356797280102nteger )
% 5.44/5.65 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.44/5.65 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_iff
% 5.44/5.65 thf(fact_4212_dvd__power__iff,axiom,
% 5.44/5.65 ! [X: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( X != zero_zero_nat )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N2 ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.44/5.65 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_iff
% 5.44/5.65 thf(fact_4213_dvd__power__iff,axiom,
% 5.44/5.65 ! [X: int,M: nat,N2: nat] :
% 5.44/5.65 ( ( X != zero_zero_int )
% 5.44/5.65 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N2 ) )
% 5.44/5.65 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.44/5.65 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_iff
% 5.44/5.65 thf(fact_4214_dvd__power,axiom,
% 5.44/5.65 ! [N2: nat,X: code_integer] :
% 5.44/5.65 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 | ( X = one_one_Code_integer ) )
% 5.44/5.65 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power
% 5.44/5.65 thf(fact_4215_dvd__power,axiom,
% 5.44/5.65 ! [N2: nat,X: extended_enat] :
% 5.44/5.65 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 | ( X = one_on7984719198319812577d_enat ) )
% 5.44/5.65 => ( dvd_dv3785147216227455552d_enat @ X @ ( power_8040749407984259932d_enat @ X @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power
% 5.44/5.65 thf(fact_4216_dvd__power,axiom,
% 5.44/5.65 ! [N2: nat,X: nat] :
% 5.44/5.65 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 | ( X = one_one_nat ) )
% 5.44/5.65 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power
% 5.44/5.65 thf(fact_4217_dvd__power,axiom,
% 5.44/5.65 ! [N2: nat,X: real] :
% 5.44/5.65 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 | ( X = one_one_real ) )
% 5.44/5.65 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power
% 5.44/5.65 thf(fact_4218_dvd__power,axiom,
% 5.44/5.65 ! [N2: nat,X: int] :
% 5.44/5.65 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 | ( X = one_one_int ) )
% 5.44/5.65 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power
% 5.44/5.65 thf(fact_4219_dvd__power,axiom,
% 5.44/5.65 ! [N2: nat,X: complex] :
% 5.44/5.65 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 | ( X = one_one_complex ) )
% 5.44/5.65 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power
% 5.44/5.65 thf(fact_4220_dvd__mult__cancel1,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 5.44/5.65 = ( N2 = one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel1
% 5.44/5.65 thf(fact_4221_dvd__mult__cancel2,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 5.44/5.65 = ( N2 = one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_mult_cancel2
% 5.44/5.65 thf(fact_4222_dvd__minus__add,axiom,
% 5.44/5.65 ! [Q2: nat,N2: nat,R: nat,M: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ Q2 @ N2 )
% 5.44/5.65 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 5.44/5.65 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q2 ) )
% 5.44/5.65 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_minus_add
% 5.44/5.65 thf(fact_4223_power__dvd__imp__le,axiom,
% 5.44/5.65 ! [I2: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 5.44/5.65 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 5.44/5.65 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_dvd_imp_le
% 5.44/5.65 thf(fact_4224_mod__nat__eqI,axiom,
% 5.44/5.65 ! [R: nat,N2: nat,M: nat] :
% 5.44/5.65 ( ( ord_less_nat @ R @ N2 )
% 5.44/5.65 => ( ( ord_less_eq_nat @ R @ M )
% 5.44/5.65 => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R ) )
% 5.44/5.65 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.44/5.65 = R ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod_nat_eqI
% 5.44/5.65 thf(fact_4225_even__two__times__div__two,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_two_times_div_two
% 5.44/5.65 thf(fact_4226_even__two__times__div__two,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_two_times_div_two
% 5.44/5.65 thf(fact_4227_even__two__times__div__two,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = A ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_two_times_div_two
% 5.44/5.65 thf(fact_4228_even__iff__mod__2__eq__zero,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_iff_mod_2_eq_zero
% 5.44/5.65 thf(fact_4229_even__iff__mod__2__eq__zero,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_zero_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_iff_mod_2_eq_zero
% 5.44/5.65 thf(fact_4230_even__iff__mod__2__eq__zero,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_zero_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_iff_mod_2_eq_zero
% 5.44/5.65 thf(fact_4231_odd__iff__mod__2__eq__one,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.65 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_Code_integer ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_iff_mod_2_eq_one
% 5.44/5.65 thf(fact_4232_odd__iff__mod__2__eq__one,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.65 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_nat ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_iff_mod_2_eq_one
% 5.44/5.65 thf(fact_4233_odd__iff__mod__2__eq__one,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.65 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_int ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_iff_mod_2_eq_one
% 5.44/5.65 thf(fact_4234_power__mono__odd,axiom,
% 5.44/5.65 ! [N2: nat,A: real,B: real] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ( ord_less_eq_real @ A @ B )
% 5.44/5.65 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_mono_odd
% 5.44/5.65 thf(fact_4235_power__mono__odd,axiom,
% 5.44/5.65 ! [N2: nat,A: int,B: int] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ( ord_less_eq_int @ A @ B )
% 5.44/5.65 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_mono_odd
% 5.44/5.65 thf(fact_4236_odd__pos,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % odd_pos
% 5.44/5.65 thf(fact_4237_dvd__power__iff__le,axiom,
% 5.44/5.65 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.44/5.65 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 5.44/5.65 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % dvd_power_iff_le
% 5.44/5.65 thf(fact_4238_even__unset__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 | ( M = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_unset_bit_iff
% 5.44/5.65 thf(fact_4239_even__unset__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 | ( M = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_unset_bit_iff
% 5.44/5.65 thf(fact_4240_even__unset__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 | ( M = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_unset_bit_iff
% 5.44/5.65 thf(fact_4241_even__set__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 & ( M != zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_set_bit_iff
% 5.44/5.65 thf(fact_4242_even__set__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 & ( M != zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_set_bit_iff
% 5.44/5.65 thf(fact_4243_even__set__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 & ( M != zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_set_bit_iff
% 5.44/5.65 thf(fact_4244_even__flip__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 != ( M = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_flip_bit_iff
% 5.44/5.65 thf(fact_4245_even__flip__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 != ( M = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_flip_bit_iff
% 5.44/5.65 thf(fact_4246_even__flip__bit__iff,axiom,
% 5.44/5.65 ! [M: nat,A: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 != ( M = zero_zero_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_flip_bit_iff
% 5.44/5.65 thf(fact_4247_even__diff__iff,axiom,
% 5.44/5.65 ! [K: int,L2: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 5.44/5.65 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_diff_iff
% 5.44/5.65 thf(fact_4248_oddE,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ~ ! [B3: code_integer] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % oddE
% 5.44/5.65 thf(fact_4249_oddE,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ~ ! [B3: nat] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % oddE
% 5.44/5.65 thf(fact_4250_oddE,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ~ ! [B3: int] :
% 5.44/5.65 ( A
% 5.44/5.65 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % oddE
% 5.44/5.65 thf(fact_4251_mod2__eq__if,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_z3403309356797280102nteger ) )
% 5.44/5.65 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_Code_integer ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod2_eq_if
% 5.44/5.65 thf(fact_4252_mod2__eq__if,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_zero_nat ) )
% 5.44/5.65 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod2_eq_if
% 5.44/5.65 thf(fact_4253_mod2__eq__if,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = zero_zero_int ) )
% 5.44/5.65 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 = one_one_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % mod2_eq_if
% 5.44/5.65 thf(fact_4254_parity__cases,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 != zero_z3403309356797280102nteger ) )
% 5.44/5.65 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.65 != one_one_Code_integer ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % parity_cases
% 5.44/5.65 thf(fact_4255_parity__cases,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 != zero_zero_nat ) )
% 5.44/5.65 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.65 != one_one_nat ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % parity_cases
% 5.44/5.65 thf(fact_4256_parity__cases,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 != zero_zero_int ) )
% 5.44/5.65 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.65 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.65 != one_one_int ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % parity_cases
% 5.44/5.65 thf(fact_4257_zero__le__power__eq,axiom,
% 5.44/5.65 ! [A: real,N2: nat] :
% 5.44/5.65 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_le_power_eq
% 5.44/5.65 thf(fact_4258_zero__le__power__eq,axiom,
% 5.44/5.65 ! [A: int,N2: nat] :
% 5.44/5.65 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.44/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_le_power_eq
% 5.44/5.65 thf(fact_4259_zero__le__odd__power,axiom,
% 5.44/5.65 ! [N2: nat,A: real] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.44/5.65 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_le_odd_power
% 5.44/5.65 thf(fact_4260_zero__le__odd__power,axiom,
% 5.44/5.65 ! [N2: nat,A: int] :
% 5.44/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.44/5.65 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_le_odd_power
% 5.44/5.65 thf(fact_4261_zero__le__even__power,axiom,
% 5.44/5.65 ! [N2: nat,A: real] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_le_even_power
% 5.44/5.65 thf(fact_4262_zero__le__even__power,axiom,
% 5.44/5.65 ! [N2: nat,A: int] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_le_even_power
% 5.44/5.65 thf(fact_4263_list__decode_Ocases,axiom,
% 5.44/5.65 ! [X: nat] :
% 5.44/5.65 ( ( X != zero_zero_nat )
% 5.44/5.65 => ~ ! [N4: nat] :
% 5.44/5.65 ( X
% 5.44/5.65 != ( suc @ N4 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % list_decode.cases
% 5.44/5.65 thf(fact_4264_zero__less__power__eq,axiom,
% 5.44/5.65 ! [A: real,N2: nat] :
% 5.44/5.65 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.44/5.65 = ( ( N2 = zero_zero_nat )
% 5.44/5.65 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( A != zero_zero_real ) )
% 5.44/5.65 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_less_power_eq
% 5.44/5.65 thf(fact_4265_zero__less__power__eq,axiom,
% 5.44/5.65 ! [A: int,N2: nat] :
% 5.44/5.65 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.44/5.65 = ( ( N2 = zero_zero_nat )
% 5.44/5.65 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( A != zero_zero_int ) )
% 5.44/5.65 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % zero_less_power_eq
% 5.44/5.65 thf(fact_4266_Euclid__induct,axiom,
% 5.44/5.65 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.44/5.65 ( ! [A3: nat,B3: nat] :
% 5.44/5.65 ( ( P @ A3 @ B3 )
% 5.44/5.65 = ( P @ B3 @ A3 ) )
% 5.44/5.65 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 5.44/5.65 => ( ! [A3: nat,B3: nat] :
% 5.44/5.65 ( ( P @ A3 @ B3 )
% 5.44/5.65 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 5.44/5.65 => ( P @ A @ B ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % Euclid_induct
% 5.44/5.65 thf(fact_4267_even__mask__div__iff_H,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( 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 ) ) @ N2 ) ) )
% 5.44/5.65 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mask_div_iff'
% 5.44/5.65 thf(fact_4268_even__mask__div__iff_H,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( 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 ) ) @ N2 ) ) )
% 5.44/5.65 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mask_div_iff'
% 5.44/5.65 thf(fact_4269_even__mask__div__iff_H,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( 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 ) ) @ N2 ) ) )
% 5.44/5.65 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mask_div_iff'
% 5.44/5.65 thf(fact_4270_power__le__zero__eq,axiom,
% 5.44/5.65 ! [A: real,N2: nat] :
% 5.44/5.65 ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.44/5.65 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.44/5.65 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_zero_eq
% 5.44/5.65 thf(fact_4271_power__le__zero__eq,axiom,
% 5.44/5.65 ! [A: int,N2: nat] :
% 5.44/5.65 ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.44/5.65 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.65 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.44/5.65 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % power_le_zero_eq
% 5.44/5.65 thf(fact_4272_even__mask__div__iff,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( 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 ) ) @ N2 ) ) )
% 5.44/5.65 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mask_div_iff
% 5.44/5.65 thf(fact_4273_even__mask__div__iff,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( 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 ) ) @ N2 ) ) )
% 5.44/5.65 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 = zero_zero_int )
% 5.44/5.65 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mask_div_iff
% 5.44/5.65 thf(fact_4274_even__mask__div__iff,axiom,
% 5.44/5.65 ! [M: nat,N2: nat] :
% 5.44/5.65 ( ( 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 ) ) @ N2 ) ) )
% 5.44/5.65 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 = zero_z3403309356797280102nteger )
% 5.44/5.65 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mask_div_iff
% 5.44/5.65 thf(fact_4275_even__mult__exp__div__exp__iff,axiom,
% 5.44/5.65 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.65 ( ( 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 ) ) @ N2 ) ) )
% 5.44/5.65 = ( ( ord_less_nat @ N2 @ M )
% 5.44/5.65 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 = zero_zero_nat )
% 5.44/5.65 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mult_exp_div_exp_iff
% 5.44/5.65 thf(fact_4276_even__mult__exp__div__exp__iff,axiom,
% 5.44/5.65 ! [A: int,M: nat,N2: nat] :
% 5.44/5.65 ( ( 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 ) ) @ N2 ) ) )
% 5.44/5.65 = ( ( ord_less_nat @ N2 @ M )
% 5.44/5.65 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 = zero_zero_int )
% 5.44/5.65 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mult_exp_div_exp_iff
% 5.44/5.65 thf(fact_4277_even__mult__exp__div__exp__iff,axiom,
% 5.44/5.65 ! [A: code_integer,M: nat,N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.65 = ( ( ord_less_nat @ N2 @ M )
% 5.44/5.65 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 = zero_z3403309356797280102nteger )
% 5.44/5.65 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.65 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mult_exp_div_exp_iff
% 5.44/5.65 thf(fact_4278_infinite__growing,axiom,
% 5.44/5.65 ! [X8: set_Extended_enat] :
% 5.44/5.65 ( ( X8 != bot_bo7653980558646680370d_enat )
% 5.44/5.65 => ( ! [X5: extended_enat] :
% 5.44/5.65 ( ( member_Extended_enat @ X5 @ X8 )
% 5.44/5.65 => ? [Xa: extended_enat] :
% 5.44/5.65 ( ( member_Extended_enat @ Xa @ X8 )
% 5.44/5.65 & ( ord_le72135733267957522d_enat @ X5 @ Xa ) ) )
% 5.44/5.65 => ~ ( finite4001608067531595151d_enat @ X8 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_growing
% 5.44/5.65 thf(fact_4279_infinite__growing,axiom,
% 5.44/5.65 ! [X8: set_real] :
% 5.44/5.65 ( ( X8 != bot_bot_set_real )
% 5.44/5.65 => ( ! [X5: real] :
% 5.44/5.65 ( ( member_real @ X5 @ X8 )
% 5.44/5.65 => ? [Xa: real] :
% 5.44/5.65 ( ( member_real @ Xa @ X8 )
% 5.44/5.65 & ( ord_less_real @ X5 @ Xa ) ) )
% 5.44/5.65 => ~ ( finite_finite_real @ X8 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_growing
% 5.44/5.65 thf(fact_4280_infinite__growing,axiom,
% 5.44/5.65 ! [X8: set_num] :
% 5.44/5.65 ( ( X8 != bot_bot_set_num )
% 5.44/5.65 => ( ! [X5: num] :
% 5.44/5.65 ( ( member_num @ X5 @ X8 )
% 5.44/5.65 => ? [Xa: num] :
% 5.44/5.65 ( ( member_num @ Xa @ X8 )
% 5.44/5.65 & ( ord_less_num @ X5 @ Xa ) ) )
% 5.44/5.65 => ~ ( finite_finite_num @ X8 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_growing
% 5.44/5.65 thf(fact_4281_infinite__growing,axiom,
% 5.44/5.65 ! [X8: set_nat] :
% 5.44/5.65 ( ( X8 != bot_bot_set_nat )
% 5.44/5.65 => ( ! [X5: nat] :
% 5.44/5.65 ( ( member_nat @ X5 @ X8 )
% 5.44/5.65 => ? [Xa: nat] :
% 5.44/5.65 ( ( member_nat @ Xa @ X8 )
% 5.44/5.65 & ( ord_less_nat @ X5 @ Xa ) ) )
% 5.44/5.65 => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_growing
% 5.44/5.65 thf(fact_4282_infinite__growing,axiom,
% 5.44/5.65 ! [X8: set_int] :
% 5.44/5.65 ( ( X8 != bot_bot_set_int )
% 5.44/5.65 => ( ! [X5: int] :
% 5.44/5.65 ( ( member_int @ X5 @ X8 )
% 5.44/5.65 => ? [Xa: int] :
% 5.44/5.65 ( ( member_int @ Xa @ X8 )
% 5.44/5.65 & ( ord_less_int @ X5 @ Xa ) ) )
% 5.44/5.65 => ~ ( finite_finite_int @ X8 ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % infinite_growing
% 5.44/5.65 thf(fact_4283_ex__min__if__finite,axiom,
% 5.44/5.65 ! [S: set_Extended_enat] :
% 5.44/5.65 ( ( finite4001608067531595151d_enat @ S )
% 5.44/5.65 => ( ( S != bot_bo7653980558646680370d_enat )
% 5.44/5.65 => ? [X5: extended_enat] :
% 5.44/5.65 ( ( member_Extended_enat @ X5 @ S )
% 5.44/5.65 & ~ ? [Xa: extended_enat] :
% 5.44/5.65 ( ( member_Extended_enat @ Xa @ S )
% 5.44/5.65 & ( ord_le72135733267957522d_enat @ Xa @ X5 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % ex_min_if_finite
% 5.44/5.65 thf(fact_4284_ex__min__if__finite,axiom,
% 5.44/5.65 ! [S: set_real] :
% 5.44/5.65 ( ( finite_finite_real @ S )
% 5.44/5.65 => ( ( S != bot_bot_set_real )
% 5.44/5.65 => ? [X5: real] :
% 5.44/5.65 ( ( member_real @ X5 @ S )
% 5.44/5.65 & ~ ? [Xa: real] :
% 5.44/5.65 ( ( member_real @ Xa @ S )
% 5.44/5.65 & ( ord_less_real @ Xa @ X5 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % ex_min_if_finite
% 5.44/5.65 thf(fact_4285_ex__min__if__finite,axiom,
% 5.44/5.65 ! [S: set_num] :
% 5.44/5.65 ( ( finite_finite_num @ S )
% 5.44/5.65 => ( ( S != bot_bot_set_num )
% 5.44/5.65 => ? [X5: num] :
% 5.44/5.65 ( ( member_num @ X5 @ S )
% 5.44/5.65 & ~ ? [Xa: num] :
% 5.44/5.65 ( ( member_num @ Xa @ S )
% 5.44/5.65 & ( ord_less_num @ Xa @ X5 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % ex_min_if_finite
% 5.44/5.65 thf(fact_4286_ex__min__if__finite,axiom,
% 5.44/5.65 ! [S: set_nat] :
% 5.44/5.65 ( ( finite_finite_nat @ S )
% 5.44/5.65 => ( ( S != bot_bot_set_nat )
% 5.44/5.65 => ? [X5: nat] :
% 5.44/5.65 ( ( member_nat @ X5 @ S )
% 5.44/5.65 & ~ ? [Xa: nat] :
% 5.44/5.65 ( ( member_nat @ Xa @ S )
% 5.44/5.65 & ( ord_less_nat @ Xa @ X5 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % ex_min_if_finite
% 5.44/5.65 thf(fact_4287_ex__min__if__finite,axiom,
% 5.44/5.65 ! [S: set_int] :
% 5.44/5.65 ( ( finite_finite_int @ S )
% 5.44/5.65 => ( ( S != bot_bot_set_int )
% 5.44/5.65 => ? [X5: int] :
% 5.44/5.65 ( ( member_int @ X5 @ S )
% 5.44/5.65 & ~ ? [Xa: int] :
% 5.44/5.65 ( ( member_int @ Xa @ S )
% 5.44/5.65 & ( ord_less_int @ Xa @ X5 ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % ex_min_if_finite
% 5.44/5.65 thf(fact_4288_even__mod__4__div__2,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.65 = ( suc @ zero_zero_nat ) )
% 5.44/5.65 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_mod_4_div_2
% 5.44/5.65 thf(fact_4289_even__even__mod__4__iff,axiom,
% 5.44/5.65 ! [N2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % even_even_mod_4_iff
% 5.44/5.65 thf(fact_4290_inf__period_I4_J,axiom,
% 5.44/5.65 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.44/5.65 => ! [X3: code_integer,K4: code_integer] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ T ) ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % inf_period(4)
% 5.44/5.65 thf(fact_4291_inf__period_I4_J,axiom,
% 5.44/5.65 ! [D: complex,D4: complex,T: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ D @ D4 )
% 5.44/5.65 => ! [X3: complex,K4: complex] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X3 @ T ) ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % inf_period(4)
% 5.44/5.65 thf(fact_4292_inf__period_I4_J,axiom,
% 5.44/5.65 ! [D: real,D4: real,T: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ D @ D4 )
% 5.44/5.65 => ! [X3: real,K4: real] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ T ) ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % inf_period(4)
% 5.44/5.65 thf(fact_4293_inf__period_I4_J,axiom,
% 5.44/5.65 ! [D: int,D4: int,T: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ D @ D4 )
% 5.44/5.65 => ! [X3: int,K4: int] :
% 5.44/5.65 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T ) ) )
% 5.44/5.65 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % inf_period(4)
% 5.44/5.65 thf(fact_4294_inf__period_I3_J,axiom,
% 5.44/5.65 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.44/5.65 => ! [X3: code_integer,K4: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ T ) )
% 5.44/5.65 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % inf_period(3)
% 5.44/5.65 thf(fact_4295_inf__period_I3_J,axiom,
% 5.44/5.65 ! [D: complex,D4: complex,T: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ D @ D4 )
% 5.44/5.65 => ! [X3: complex,K4: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X3 @ T ) )
% 5.44/5.65 = ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % inf_period(3)
% 5.44/5.65 thf(fact_4296_inf__period_I3_J,axiom,
% 5.44/5.65 ! [D: real,D4: real,T: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ D @ D4 )
% 5.44/5.65 => ! [X3: real,K4: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ T ) )
% 5.44/5.65 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % inf_period(3)
% 5.44/5.65 thf(fact_4297_inf__period_I3_J,axiom,
% 5.44/5.65 ! [D: int,D4: int,T: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ D @ D4 )
% 5.44/5.65 => ! [X3: int,K4: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T ) )
% 5.44/5.65 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % inf_period(3)
% 5.44/5.65 thf(fact_4298_unity__coeff__ex,axiom,
% 5.44/5.65 ! [P: code_integer > $o,L2: code_integer] :
% 5.44/5.65 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X2 ) ) )
% 5.44/5.65 = ( ? [X2: code_integer] :
% 5.44/5.65 ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 5.44/5.65 & ( P @ X2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unity_coeff_ex
% 5.44/5.65 thf(fact_4299_unity__coeff__ex,axiom,
% 5.44/5.65 ! [P: extended_enat > $o,L2: extended_enat] :
% 5.44/5.65 ( ( ? [X2: extended_enat] : ( P @ ( times_7803423173614009249d_enat @ L2 @ X2 ) ) )
% 5.44/5.65 = ( ? [X2: extended_enat] :
% 5.44/5.65 ( ( dvd_dv3785147216227455552d_enat @ L2 @ ( plus_p3455044024723400733d_enat @ X2 @ zero_z5237406670263579293d_enat ) )
% 5.44/5.65 & ( P @ X2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unity_coeff_ex
% 5.44/5.65 thf(fact_4300_unity__coeff__ex,axiom,
% 5.44/5.65 ! [P: complex > $o,L2: complex] :
% 5.44/5.65 ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L2 @ X2 ) ) )
% 5.44/5.65 = ( ? [X2: complex] :
% 5.44/5.65 ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 5.44/5.65 & ( P @ X2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unity_coeff_ex
% 5.44/5.65 thf(fact_4301_unity__coeff__ex,axiom,
% 5.44/5.65 ! [P: real > $o,L2: real] :
% 5.44/5.65 ( ( ? [X2: real] : ( P @ ( times_times_real @ L2 @ X2 ) ) )
% 5.44/5.65 = ( ? [X2: real] :
% 5.44/5.65 ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 5.44/5.65 & ( P @ X2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unity_coeff_ex
% 5.44/5.65 thf(fact_4302_unity__coeff__ex,axiom,
% 5.44/5.65 ! [P: nat > $o,L2: nat] :
% 5.44/5.65 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L2 @ X2 ) ) )
% 5.44/5.65 = ( ? [X2: nat] :
% 5.44/5.65 ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 5.44/5.65 & ( P @ X2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unity_coeff_ex
% 5.44/5.65 thf(fact_4303_unity__coeff__ex,axiom,
% 5.44/5.65 ! [P: int > $o,L2: int] :
% 5.44/5.65 ( ( ? [X2: int] : ( P @ ( times_times_int @ L2 @ X2 ) ) )
% 5.44/5.65 = ( ? [X2: int] :
% 5.44/5.65 ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 5.44/5.65 & ( P @ X2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % unity_coeff_ex
% 5.44/5.65 thf(fact_4304_triangle__def,axiom,
% 5.44/5.65 ( nat_triangle
% 5.44/5.65 = ( ^ [N: nat] : ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % triangle_def
% 5.44/5.65 thf(fact_4305_vebt__buildup_Oelims,axiom,
% 5.44/5.65 ! [X: nat,Y: vEBT_VEBT] :
% 5.44/5.65 ( ( ( vEBT_vebt_buildup @ X )
% 5.44/5.65 = Y )
% 5.44/5.65 => ( ( ( X = zero_zero_nat )
% 5.44/5.65 => ( Y
% 5.44/5.65 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.44/5.65 => ( ( ( X
% 5.44/5.65 = ( suc @ zero_zero_nat ) )
% 5.44/5.65 => ( Y
% 5.44/5.65 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.44/5.65 => ~ ! [Va2: nat] :
% 5.44/5.65 ( ( X
% 5.44/5.65 = ( suc @ ( suc @ Va2 ) ) )
% 5.44/5.65 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.44/5.65 => ( Y
% 5.44/5.65 = ( 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 ) ) ) ) ) ) )
% 5.44/5.65 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.44/5.65 => ( Y
% 5.44/5.65 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % vebt_buildup.elims
% 5.44/5.65 thf(fact_4306_flip__bit__0,axiom,
% 5.44/5.65 ! [A: code_integer] :
% 5.44/5.65 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.44/5.65 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % flip_bit_0
% 5.44/5.65 thf(fact_4307_flip__bit__0,axiom,
% 5.44/5.65 ! [A: int] :
% 5.44/5.65 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.44/5.65 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % flip_bit_0
% 5.44/5.65 thf(fact_4308_flip__bit__0,axiom,
% 5.44/5.65 ! [A: nat] :
% 5.44/5.65 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.44/5.65 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % flip_bit_0
% 5.44/5.65 thf(fact_4309_intind,axiom,
% 5.44/5.65 ! [I2: nat,N2: nat,P: nat > $o,X: nat] :
% 5.44/5.65 ( ( ord_less_nat @ I2 @ N2 )
% 5.44/5.65 => ( ( P @ X )
% 5.44/5.65 => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X ) @ I2 ) ) ) ) ).
% 5.44/5.65
% 5.44/5.65 % intind
% 5.44/5.65 thf(fact_4310_intind,axiom,
% 5.44/5.66 ! [I2: nat,N2: nat,P: int > $o,X: int] :
% 5.44/5.66 ( ( ord_less_nat @ I2 @ N2 )
% 5.44/5.66 => ( ( P @ X )
% 5.44/5.66 => ( P @ ( nth_int @ ( replicate_int @ N2 @ X ) @ I2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % intind
% 5.44/5.66 thf(fact_4311_intind,axiom,
% 5.44/5.66 ! [I2: nat,N2: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.44/5.66 ( ( ord_less_nat @ I2 @ N2 )
% 5.44/5.66 => ( ( P @ X )
% 5.44/5.66 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) @ I2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % intind
% 5.44/5.66 thf(fact_4312_of__bool__less__eq__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.44/5.66 = ( P
% 5.44/5.66 => Q ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_eq_iff
% 5.44/5.66 thf(fact_4313_of__bool__less__eq__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.44/5.66 = ( P
% 5.44/5.66 => Q ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_eq_iff
% 5.44/5.66 thf(fact_4314_of__bool__less__eq__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.44/5.66 = ( P
% 5.44/5.66 => Q ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_eq_iff
% 5.44/5.66 thf(fact_4315_of__bool__less__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ ( zero_n1046097342994218471d_enat @ P ) @ ( zero_n1046097342994218471d_enat @ Q ) )
% 5.44/5.66 = ( ~ P
% 5.44/5.66 & Q ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_iff
% 5.44/5.66 thf(fact_4316_of__bool__less__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.44/5.66 = ( ~ P
% 5.44/5.66 & Q ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_iff
% 5.44/5.66 thf(fact_4317_of__bool__less__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.44/5.66 = ( ~ P
% 5.44/5.66 & Q ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_iff
% 5.44/5.66 thf(fact_4318_of__bool__less__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.44/5.66 = ( ~ P
% 5.44/5.66 & Q ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_iff
% 5.44/5.66 thf(fact_4319_of__bool__less__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.44/5.66 = ( ~ P
% 5.44/5.66 & Q ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_iff
% 5.44/5.66 thf(fact_4320_of__bool__eq_I2_J,axiom,
% 5.44/5.66 ( ( zero_n1046097342994218471d_enat @ $true )
% 5.44/5.66 = one_on7984719198319812577d_enat ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq(2)
% 5.44/5.66 thf(fact_4321_of__bool__eq_I2_J,axiom,
% 5.44/5.66 ( ( zero_n1201886186963655149omplex @ $true )
% 5.44/5.66 = one_one_complex ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq(2)
% 5.44/5.66 thf(fact_4322_of__bool__eq_I2_J,axiom,
% 5.44/5.66 ( ( zero_n3304061248610475627l_real @ $true )
% 5.44/5.66 = one_one_real ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq(2)
% 5.44/5.66 thf(fact_4323_of__bool__eq_I2_J,axiom,
% 5.44/5.66 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.44/5.66 = one_one_nat ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq(2)
% 5.44/5.66 thf(fact_4324_of__bool__eq_I2_J,axiom,
% 5.44/5.66 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq(2)
% 5.44/5.66 thf(fact_4325_of__bool__eq_I2_J,axiom,
% 5.44/5.66 ( ( zero_n356916108424825756nteger @ $true )
% 5.44/5.66 = one_one_Code_integer ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq(2)
% 5.44/5.66 thf(fact_4326_of__bool__eq__1__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ( zero_n1046097342994218471d_enat @ P )
% 5.44/5.66 = one_on7984719198319812577d_enat )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq_1_iff
% 5.44/5.66 thf(fact_4327_of__bool__eq__1__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.44/5.66 = one_one_complex )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq_1_iff
% 5.44/5.66 thf(fact_4328_of__bool__eq__1__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.44/5.66 = one_one_real )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq_1_iff
% 5.44/5.66 thf(fact_4329_of__bool__eq__1__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.44/5.66 = one_one_nat )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq_1_iff
% 5.44/5.66 thf(fact_4330_of__bool__eq__1__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.44/5.66 = one_one_int )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq_1_iff
% 5.44/5.66 thf(fact_4331_of__bool__eq__1__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ( zero_n356916108424825756nteger @ P )
% 5.44/5.66 = one_one_Code_integer )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_eq_1_iff
% 5.44/5.66 thf(fact_4332_replicate__eq__replicate,axiom,
% 5.44/5.66 ! [M: nat,X: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.44/5.66 ( ( ( replicate_VEBT_VEBT @ M @ X )
% 5.44/5.66 = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 5.44/5.66 = ( ( M = N2 )
% 5.44/5.66 & ( ( M != zero_zero_nat )
% 5.44/5.66 => ( X = Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_eq_replicate
% 5.44/5.66 thf(fact_4333_length__replicate,axiom,
% 5.44/5.66 ! [N2: nat,X: vEBT_VEBT] :
% 5.44/5.66 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.44/5.66 = N2 ) ).
% 5.44/5.66
% 5.44/5.66 % length_replicate
% 5.44/5.66 thf(fact_4334_length__replicate,axiom,
% 5.44/5.66 ! [N2: nat,X: $o] :
% 5.44/5.66 ( ( size_size_list_o @ ( replicate_o @ N2 @ X ) )
% 5.44/5.66 = N2 ) ).
% 5.44/5.66
% 5.44/5.66 % length_replicate
% 5.44/5.66 thf(fact_4335_length__replicate,axiom,
% 5.44/5.66 ! [N2: nat,X: nat] :
% 5.44/5.66 ( ( size_size_list_nat @ ( replicate_nat @ N2 @ X ) )
% 5.44/5.66 = N2 ) ).
% 5.44/5.66
% 5.44/5.66 % length_replicate
% 5.44/5.66 thf(fact_4336_length__replicate,axiom,
% 5.44/5.66 ! [N2: nat,X: int] :
% 5.44/5.66 ( ( size_size_list_int @ ( replicate_int @ N2 @ X ) )
% 5.44/5.66 = N2 ) ).
% 5.44/5.66
% 5.44/5.66 % length_replicate
% 5.44/5.66 thf(fact_4337_of__bool__or__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( zero_n2687167440665602831ol_nat
% 5.44/5.66 @ ( P
% 5.44/5.66 | Q ) )
% 5.44/5.66 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_or_iff
% 5.44/5.66 thf(fact_4338_of__bool__or__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( zero_n2684676970156552555ol_int
% 5.44/5.66 @ ( P
% 5.44/5.66 | Q ) )
% 5.44/5.66 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_or_iff
% 5.44/5.66 thf(fact_4339_of__bool__or__iff,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( zero_n356916108424825756nteger
% 5.44/5.66 @ ( P
% 5.44/5.66 | Q ) )
% 5.44/5.66 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_or_iff
% 5.44/5.66 thf(fact_4340_zero__less__of__bool__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % zero_less_of_bool_iff
% 5.44/5.66 thf(fact_4341_zero__less__of__bool__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % zero_less_of_bool_iff
% 5.44/5.66 thf(fact_4342_zero__less__of__bool__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % zero_less_of_bool_iff
% 5.44/5.66 thf(fact_4343_zero__less__of__bool__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.44/5.66 = P ) ).
% 5.44/5.66
% 5.44/5.66 % zero_less_of_bool_iff
% 5.44/5.66 thf(fact_4344_of__bool__less__one__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.44/5.66 = ~ P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_one_iff
% 5.44/5.66 thf(fact_4345_of__bool__less__one__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.44/5.66 = ~ P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_one_iff
% 5.44/5.66 thf(fact_4346_of__bool__less__one__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.44/5.66 = ~ P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_one_iff
% 5.44/5.66 thf(fact_4347_of__bool__less__one__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.44/5.66 = ~ P ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_one_iff
% 5.44/5.66 thf(fact_4348_of__bool__not__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.44/5.66 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_not_iff
% 5.44/5.66 thf(fact_4349_of__bool__not__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.44/5.66 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_not_iff
% 5.44/5.66 thf(fact_4350_of__bool__not__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.44/5.66 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_not_iff
% 5.44/5.66 thf(fact_4351_of__bool__not__iff,axiom,
% 5.44/5.66 ! [P: $o] :
% 5.44/5.66 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.44/5.66 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_not_iff
% 5.44/5.66 thf(fact_4352_Suc__0__mod__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.66 = ( zero_n2687167440665602831ol_nat
% 5.44/5.66 @ ( N2
% 5.44/5.66 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Suc_0_mod_eq
% 5.44/5.66 thf(fact_4353_Ball__set__replicate,axiom,
% 5.44/5.66 ! [N2: nat,A: int,P: int > $o] :
% 5.44/5.66 ( ( ! [X2: int] :
% 5.44/5.66 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.44/5.66 => ( P @ X2 ) ) )
% 5.44/5.66 = ( ( P @ A )
% 5.44/5.66 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Ball_set_replicate
% 5.44/5.66 thf(fact_4354_Ball__set__replicate,axiom,
% 5.44/5.66 ! [N2: nat,A: nat,P: nat > $o] :
% 5.44/5.66 ( ( ! [X2: nat] :
% 5.44/5.66 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 5.44/5.66 => ( P @ X2 ) ) )
% 5.44/5.66 = ( ( P @ A )
% 5.44/5.66 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Ball_set_replicate
% 5.44/5.66 thf(fact_4355_Ball__set__replicate,axiom,
% 5.44/5.66 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.44/5.66 ( ( ! [X2: vEBT_VEBT] :
% 5.44/5.66 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.44/5.66 => ( P @ X2 ) ) )
% 5.44/5.66 = ( ( P @ A )
% 5.44/5.66 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Ball_set_replicate
% 5.44/5.66 thf(fact_4356_Bex__set__replicate,axiom,
% 5.44/5.66 ! [N2: nat,A: int,P: int > $o] :
% 5.44/5.66 ( ( ? [X2: int] :
% 5.44/5.66 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.44/5.66 & ( P @ X2 ) ) )
% 5.44/5.66 = ( ( P @ A )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Bex_set_replicate
% 5.44/5.66 thf(fact_4357_Bex__set__replicate,axiom,
% 5.44/5.66 ! [N2: nat,A: nat,P: nat > $o] :
% 5.44/5.66 ( ( ? [X2: nat] :
% 5.44/5.66 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 5.44/5.66 & ( P @ X2 ) ) )
% 5.44/5.66 = ( ( P @ A )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Bex_set_replicate
% 5.44/5.66 thf(fact_4358_Bex__set__replicate,axiom,
% 5.44/5.66 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.44/5.66 ( ( ? [X2: vEBT_VEBT] :
% 5.44/5.66 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.44/5.66 & ( P @ X2 ) ) )
% 5.44/5.66 = ( ( P @ A )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Bex_set_replicate
% 5.44/5.66 thf(fact_4359_in__set__replicate,axiom,
% 5.44/5.66 ! [X: real,N2: nat,Y: real] :
% 5.44/5.66 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % in_set_replicate
% 5.44/5.66 thf(fact_4360_in__set__replicate,axiom,
% 5.44/5.66 ! [X: complex,N2: nat,Y: complex] :
% 5.44/5.66 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N2 @ Y ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % in_set_replicate
% 5.44/5.66 thf(fact_4361_in__set__replicate,axiom,
% 5.44/5.66 ! [X: product_prod_nat_nat,N2: nat,Y: product_prod_nat_nat] :
% 5.44/5.66 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N2 @ Y ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % in_set_replicate
% 5.44/5.66 thf(fact_4362_in__set__replicate,axiom,
% 5.44/5.66 ! [X: int,N2: nat,Y: int] :
% 5.44/5.66 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % in_set_replicate
% 5.44/5.66 thf(fact_4363_in__set__replicate,axiom,
% 5.44/5.66 ! [X: nat,N2: nat,Y: nat] :
% 5.44/5.66 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % in_set_replicate
% 5.44/5.66 thf(fact_4364_in__set__replicate,axiom,
% 5.44/5.66 ! [X: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.44/5.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 & ( N2 != zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % in_set_replicate
% 5.44/5.66 thf(fact_4365_nth__replicate,axiom,
% 5.44/5.66 ! [I2: nat,N2: nat,X: nat] :
% 5.44/5.66 ( ( ord_less_nat @ I2 @ N2 )
% 5.44/5.66 => ( ( nth_nat @ ( replicate_nat @ N2 @ X ) @ I2 )
% 5.44/5.66 = X ) ) ).
% 5.44/5.66
% 5.44/5.66 % nth_replicate
% 5.44/5.66 thf(fact_4366_nth__replicate,axiom,
% 5.44/5.66 ! [I2: nat,N2: nat,X: int] :
% 5.44/5.66 ( ( ord_less_nat @ I2 @ N2 )
% 5.44/5.66 => ( ( nth_int @ ( replicate_int @ N2 @ X ) @ I2 )
% 5.44/5.66 = X ) ) ).
% 5.44/5.66
% 5.44/5.66 % nth_replicate
% 5.44/5.66 thf(fact_4367_nth__replicate,axiom,
% 5.44/5.66 ! [I2: nat,N2: nat,X: vEBT_VEBT] :
% 5.44/5.66 ( ( ord_less_nat @ I2 @ N2 )
% 5.44/5.66 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) @ I2 )
% 5.44/5.66 = X ) ) ).
% 5.44/5.66
% 5.44/5.66 % nth_replicate
% 5.44/5.66 thf(fact_4368_triangle__Suc,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( nat_triangle @ ( suc @ N2 ) )
% 5.44/5.66 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % triangle_Suc
% 5.44/5.66 thf(fact_4369_odd__of__bool__self,axiom,
% 5.44/5.66 ! [P5: $o] :
% 5.44/5.66 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P5 ) ) )
% 5.44/5.66 = P5 ) ).
% 5.44/5.66
% 5.44/5.66 % odd_of_bool_self
% 5.44/5.66 thf(fact_4370_odd__of__bool__self,axiom,
% 5.44/5.66 ! [P5: $o] :
% 5.44/5.66 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P5 ) ) )
% 5.44/5.66 = P5 ) ).
% 5.44/5.66
% 5.44/5.66 % odd_of_bool_self
% 5.44/5.66 thf(fact_4371_odd__of__bool__self,axiom,
% 5.44/5.66 ! [P5: $o] :
% 5.44/5.66 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P5 ) ) )
% 5.44/5.66 = P5 ) ).
% 5.44/5.66
% 5.44/5.66 % odd_of_bool_self
% 5.44/5.66 thf(fact_4372_of__bool__half__eq__0,axiom,
% 5.44/5.66 ! [B: $o] :
% 5.44/5.66 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = zero_zero_nat ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_half_eq_0
% 5.44/5.66 thf(fact_4373_of__bool__half__eq__0,axiom,
% 5.44/5.66 ! [B: $o] :
% 5.44/5.66 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_half_eq_0
% 5.44/5.66 thf(fact_4374_of__bool__half__eq__0,axiom,
% 5.44/5.66 ! [B: $o] :
% 5.44/5.66 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_half_eq_0
% 5.44/5.66 thf(fact_4375_bits__1__div__exp,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % bits_1_div_exp
% 5.44/5.66 thf(fact_4376_bits__1__div__exp,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % bits_1_div_exp
% 5.44/5.66 thf(fact_4377_bits__1__div__exp,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % bits_1_div_exp
% 5.44/5.66 thf(fact_4378_one__div__2__pow__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_div_2_pow_eq
% 5.44/5.66 thf(fact_4379_one__div__2__pow__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_div_2_pow_eq
% 5.44/5.66 thf(fact_4380_one__div__2__pow__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_div_2_pow_eq
% 5.44/5.66 thf(fact_4381_one__mod__2__pow__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_mod_2_pow_eq
% 5.44/5.66 thf(fact_4382_one__mod__2__pow__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_mod_2_pow_eq
% 5.44/5.66 thf(fact_4383_one__mod__2__pow__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_mod_2_pow_eq
% 5.44/5.66 thf(fact_4384_dvd__antisym,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( dvd_dvd_nat @ M @ N2 )
% 5.44/5.66 => ( ( dvd_dvd_nat @ N2 @ M )
% 5.44/5.66 => ( M = N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_antisym
% 5.44/5.66 thf(fact_4385_of__bool__conj,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( zero_n1201886186963655149omplex
% 5.44/5.66 @ ( P
% 5.44/5.66 & Q ) )
% 5.44/5.66 = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_conj
% 5.44/5.66 thf(fact_4386_of__bool__conj,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( zero_n3304061248610475627l_real
% 5.44/5.66 @ ( P
% 5.44/5.66 & Q ) )
% 5.44/5.66 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_conj
% 5.44/5.66 thf(fact_4387_of__bool__conj,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( zero_n2687167440665602831ol_nat
% 5.44/5.66 @ ( P
% 5.44/5.66 & Q ) )
% 5.44/5.66 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_conj
% 5.44/5.66 thf(fact_4388_of__bool__conj,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( zero_n2684676970156552555ol_int
% 5.44/5.66 @ ( P
% 5.44/5.66 & Q ) )
% 5.44/5.66 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_conj
% 5.44/5.66 thf(fact_4389_of__bool__conj,axiom,
% 5.44/5.66 ! [P: $o,Q: $o] :
% 5.44/5.66 ( ( zero_n356916108424825756nteger
% 5.44/5.66 @ ( P
% 5.44/5.66 & Q ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_conj
% 5.44/5.66 thf(fact_4390_zero__less__eq__of__bool,axiom,
% 5.44/5.66 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_less_eq_of_bool
% 5.44/5.66 thf(fact_4391_zero__less__eq__of__bool,axiom,
% 5.44/5.66 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_less_eq_of_bool
% 5.44/5.66 thf(fact_4392_zero__less__eq__of__bool,axiom,
% 5.44/5.66 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_less_eq_of_bool
% 5.44/5.66 thf(fact_4393_zero__less__eq__of__bool,axiom,
% 5.44/5.66 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_less_eq_of_bool
% 5.44/5.66 thf(fact_4394_of__bool__less__eq__one,axiom,
% 5.44/5.66 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_eq_one
% 5.44/5.66 thf(fact_4395_of__bool__less__eq__one,axiom,
% 5.44/5.66 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_eq_one
% 5.44/5.66 thf(fact_4396_of__bool__less__eq__one,axiom,
% 5.44/5.66 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_eq_one
% 5.44/5.66 thf(fact_4397_of__bool__less__eq__one,axiom,
% 5.44/5.66 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_less_eq_one
% 5.44/5.66 thf(fact_4398_of__bool__def,axiom,
% 5.44/5.66 ( zero_n1046097342994218471d_enat
% 5.44/5.66 = ( ^ [P4: $o] : ( if_Extended_enat @ P4 @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_def
% 5.44/5.66 thf(fact_4399_of__bool__def,axiom,
% 5.44/5.66 ( zero_n1201886186963655149omplex
% 5.44/5.66 = ( ^ [P4: $o] : ( if_complex @ P4 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_def
% 5.44/5.66 thf(fact_4400_of__bool__def,axiom,
% 5.44/5.66 ( zero_n3304061248610475627l_real
% 5.44/5.66 = ( ^ [P4: $o] : ( if_real @ P4 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_def
% 5.44/5.66 thf(fact_4401_of__bool__def,axiom,
% 5.44/5.66 ( zero_n2687167440665602831ol_nat
% 5.44/5.66 = ( ^ [P4: $o] : ( if_nat @ P4 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_def
% 5.44/5.66 thf(fact_4402_of__bool__def,axiom,
% 5.44/5.66 ( zero_n2684676970156552555ol_int
% 5.44/5.66 = ( ^ [P4: $o] : ( if_int @ P4 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_def
% 5.44/5.66 thf(fact_4403_of__bool__def,axiom,
% 5.44/5.66 ( zero_n356916108424825756nteger
% 5.44/5.66 = ( ^ [P4: $o] : ( if_Code_integer @ P4 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_def
% 5.44/5.66 thf(fact_4404_split__of__bool,axiom,
% 5.44/5.66 ! [P: extended_enat > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n1046097342994218471d_enat @ P5 ) )
% 5.44/5.66 = ( ( P5
% 5.44/5.66 => ( P @ one_on7984719198319812577d_enat ) )
% 5.44/5.66 & ( ~ P5
% 5.44/5.66 => ( P @ zero_z5237406670263579293d_enat ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool
% 5.44/5.66 thf(fact_4405_split__of__bool,axiom,
% 5.44/5.66 ! [P: complex > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 5.44/5.66 = ( ( P5
% 5.44/5.66 => ( P @ one_one_complex ) )
% 5.44/5.66 & ( ~ P5
% 5.44/5.66 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool
% 5.44/5.66 thf(fact_4406_split__of__bool,axiom,
% 5.44/5.66 ! [P: real > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 5.44/5.66 = ( ( P5
% 5.44/5.66 => ( P @ one_one_real ) )
% 5.44/5.66 & ( ~ P5
% 5.44/5.66 => ( P @ zero_zero_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool
% 5.44/5.66 thf(fact_4407_split__of__bool,axiom,
% 5.44/5.66 ! [P: nat > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 5.44/5.66 = ( ( P5
% 5.44/5.66 => ( P @ one_one_nat ) )
% 5.44/5.66 & ( ~ P5
% 5.44/5.66 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool
% 5.44/5.66 thf(fact_4408_split__of__bool,axiom,
% 5.44/5.66 ! [P: int > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 5.44/5.66 = ( ( P5
% 5.44/5.66 => ( P @ one_one_int ) )
% 5.44/5.66 & ( ~ P5
% 5.44/5.66 => ( P @ zero_zero_int ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool
% 5.44/5.66 thf(fact_4409_split__of__bool,axiom,
% 5.44/5.66 ! [P: code_integer > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 5.44/5.66 = ( ( P5
% 5.44/5.66 => ( P @ one_one_Code_integer ) )
% 5.44/5.66 & ( ~ P5
% 5.44/5.66 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool
% 5.44/5.66 thf(fact_4410_split__of__bool__asm,axiom,
% 5.44/5.66 ! [P: extended_enat > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n1046097342994218471d_enat @ P5 ) )
% 5.44/5.66 = ( ~ ( ( P5
% 5.44/5.66 & ~ ( P @ one_on7984719198319812577d_enat ) )
% 5.44/5.66 | ( ~ P5
% 5.44/5.66 & ~ ( P @ zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool_asm
% 5.44/5.66 thf(fact_4411_split__of__bool__asm,axiom,
% 5.44/5.66 ! [P: complex > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 5.44/5.66 = ( ~ ( ( P5
% 5.44/5.66 & ~ ( P @ one_one_complex ) )
% 5.44/5.66 | ( ~ P5
% 5.44/5.66 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool_asm
% 5.44/5.66 thf(fact_4412_split__of__bool__asm,axiom,
% 5.44/5.66 ! [P: real > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 5.44/5.66 = ( ~ ( ( P5
% 5.44/5.66 & ~ ( P @ one_one_real ) )
% 5.44/5.66 | ( ~ P5
% 5.44/5.66 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool_asm
% 5.44/5.66 thf(fact_4413_split__of__bool__asm,axiom,
% 5.44/5.66 ! [P: nat > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 5.44/5.66 = ( ~ ( ( P5
% 5.44/5.66 & ~ ( P @ one_one_nat ) )
% 5.44/5.66 | ( ~ P5
% 5.44/5.66 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool_asm
% 5.44/5.66 thf(fact_4414_split__of__bool__asm,axiom,
% 5.44/5.66 ! [P: int > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 5.44/5.66 = ( ~ ( ( P5
% 5.44/5.66 & ~ ( P @ one_one_int ) )
% 5.44/5.66 | ( ~ P5
% 5.44/5.66 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool_asm
% 5.44/5.66 thf(fact_4415_split__of__bool__asm,axiom,
% 5.44/5.66 ! [P: code_integer > $o,P5: $o] :
% 5.44/5.66 ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 5.44/5.66 = ( ~ ( ( P5
% 5.44/5.66 & ~ ( P @ one_one_Code_integer ) )
% 5.44/5.66 | ( ~ P5
% 5.44/5.66 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % split_of_bool_asm
% 5.44/5.66 thf(fact_4416_replicate__eqI,axiom,
% 5.44/5.66 ! [Xs2: list_real,N2: nat,X: real] :
% 5.44/5.66 ( ( ( size_size_list_real @ Xs2 )
% 5.44/5.66 = N2 )
% 5.44/5.66 => ( ! [Y5: real] :
% 5.44/5.66 ( ( member_real @ Y5 @ ( set_real2 @ Xs2 ) )
% 5.44/5.66 => ( Y5 = X ) )
% 5.44/5.66 => ( Xs2
% 5.44/5.66 = ( replicate_real @ N2 @ X ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_eqI
% 5.44/5.66 thf(fact_4417_replicate__eqI,axiom,
% 5.44/5.66 ! [Xs2: list_complex,N2: nat,X: complex] :
% 5.44/5.66 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.44/5.66 = N2 )
% 5.44/5.66 => ( ! [Y5: complex] :
% 5.44/5.66 ( ( member_complex @ Y5 @ ( set_complex2 @ Xs2 ) )
% 5.44/5.66 => ( Y5 = X ) )
% 5.44/5.66 => ( Xs2
% 5.44/5.66 = ( replicate_complex @ N2 @ X ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_eqI
% 5.44/5.66 thf(fact_4418_replicate__eqI,axiom,
% 5.44/5.66 ! [Xs2: list_P6011104703257516679at_nat,N2: nat,X: product_prod_nat_nat] :
% 5.44/5.66 ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 5.44/5.66 = N2 )
% 5.44/5.66 => ( ! [Y5: product_prod_nat_nat] :
% 5.44/5.66 ( ( member8440522571783428010at_nat @ Y5 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.44/5.66 => ( Y5 = X ) )
% 5.44/5.66 => ( Xs2
% 5.44/5.66 = ( replic4235873036481779905at_nat @ N2 @ X ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_eqI
% 5.44/5.66 thf(fact_4419_replicate__eqI,axiom,
% 5.44/5.66 ! [Xs2: list_VEBT_VEBT,N2: nat,X: vEBT_VEBT] :
% 5.44/5.66 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.44/5.66 = N2 )
% 5.44/5.66 => ( ! [Y5: vEBT_VEBT] :
% 5.44/5.66 ( ( member_VEBT_VEBT @ Y5 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.66 => ( Y5 = X ) )
% 5.44/5.66 => ( Xs2
% 5.44/5.66 = ( replicate_VEBT_VEBT @ N2 @ X ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_eqI
% 5.44/5.66 thf(fact_4420_replicate__eqI,axiom,
% 5.44/5.66 ! [Xs2: list_o,N2: nat,X: $o] :
% 5.44/5.66 ( ( ( size_size_list_o @ Xs2 )
% 5.44/5.66 = N2 )
% 5.44/5.66 => ( ! [Y5: $o] :
% 5.44/5.66 ( ( member_o @ Y5 @ ( set_o2 @ Xs2 ) )
% 5.44/5.66 => ( Y5 = X ) )
% 5.44/5.66 => ( Xs2
% 5.44/5.66 = ( replicate_o @ N2 @ X ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_eqI
% 5.44/5.66 thf(fact_4421_replicate__eqI,axiom,
% 5.44/5.66 ! [Xs2: list_nat,N2: nat,X: nat] :
% 5.44/5.66 ( ( ( size_size_list_nat @ Xs2 )
% 5.44/5.66 = N2 )
% 5.44/5.66 => ( ! [Y5: nat] :
% 5.44/5.66 ( ( member_nat @ Y5 @ ( set_nat2 @ Xs2 ) )
% 5.44/5.66 => ( Y5 = X ) )
% 5.44/5.66 => ( Xs2
% 5.44/5.66 = ( replicate_nat @ N2 @ X ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_eqI
% 5.44/5.66 thf(fact_4422_replicate__eqI,axiom,
% 5.44/5.66 ! [Xs2: list_int,N2: nat,X: int] :
% 5.44/5.66 ( ( ( size_size_list_int @ Xs2 )
% 5.44/5.66 = N2 )
% 5.44/5.66 => ( ! [Y5: int] :
% 5.44/5.66 ( ( member_int @ Y5 @ ( set_int2 @ Xs2 ) )
% 5.44/5.66 => ( Y5 = X ) )
% 5.44/5.66 => ( Xs2
% 5.44/5.66 = ( replicate_int @ N2 @ X ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_eqI
% 5.44/5.66 thf(fact_4423_replicate__length__same,axiom,
% 5.44/5.66 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.44/5.66 ( ! [X5: vEBT_VEBT] :
% 5.44/5.66 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.44/5.66 => ( X5 = X ) )
% 5.44/5.66 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 5.44/5.66 = Xs2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_length_same
% 5.44/5.66 thf(fact_4424_replicate__length__same,axiom,
% 5.44/5.66 ! [Xs2: list_o,X: $o] :
% 5.44/5.66 ( ! [X5: $o] :
% 5.44/5.66 ( ( member_o @ X5 @ ( set_o2 @ Xs2 ) )
% 5.44/5.66 => ( X5 = X ) )
% 5.44/5.66 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 5.44/5.66 = Xs2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_length_same
% 5.44/5.66 thf(fact_4425_replicate__length__same,axiom,
% 5.44/5.66 ! [Xs2: list_nat,X: nat] :
% 5.44/5.66 ( ! [X5: nat] :
% 5.44/5.66 ( ( member_nat @ X5 @ ( set_nat2 @ Xs2 ) )
% 5.44/5.66 => ( X5 = X ) )
% 5.44/5.66 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 5.44/5.66 = Xs2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_length_same
% 5.44/5.66 thf(fact_4426_replicate__length__same,axiom,
% 5.44/5.66 ! [Xs2: list_int,X: int] :
% 5.44/5.66 ( ! [X5: int] :
% 5.44/5.66 ( ( member_int @ X5 @ ( set_int2 @ Xs2 ) )
% 5.44/5.66 => ( X5 = X ) )
% 5.44/5.66 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 5.44/5.66 = Xs2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % replicate_length_same
% 5.44/5.66 thf(fact_4427_pinf_I1_J,axiom,
% 5.44/5.66 ! [P: extended_enat > $o,P6: extended_enat > $o,Q: extended_enat > $o,Q5: extended_enat > $o] :
% 5.44/5.66 ( ? [Z3: extended_enat] :
% 5.44/5.66 ! [X5: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: extended_enat] :
% 5.44/5.66 ! [X5: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(1)
% 5.44/5.66 thf(fact_4428_pinf_I1_J,axiom,
% 5.44/5.66 ! [P: real > $o,P6: real > $o,Q: real > $o,Q5: real > $o] :
% 5.44/5.66 ( ? [Z3: real] :
% 5.44/5.66 ! [X5: real] :
% 5.44/5.66 ( ( ord_less_real @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: real] :
% 5.44/5.66 ! [X5: real] :
% 5.44/5.66 ( ( ord_less_real @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(1)
% 5.44/5.66 thf(fact_4429_pinf_I1_J,axiom,
% 5.44/5.66 ! [P: num > $o,P6: num > $o,Q: num > $o,Q5: num > $o] :
% 5.44/5.66 ( ? [Z3: num] :
% 5.44/5.66 ! [X5: num] :
% 5.44/5.66 ( ( ord_less_num @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: num] :
% 5.44/5.66 ! [X5: num] :
% 5.44/5.66 ( ( ord_less_num @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(1)
% 5.44/5.66 thf(fact_4430_pinf_I1_J,axiom,
% 5.44/5.66 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q5: nat > $o] :
% 5.44/5.66 ( ? [Z3: nat] :
% 5.44/5.66 ! [X5: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: nat] :
% 5.44/5.66 ! [X5: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(1)
% 5.44/5.66 thf(fact_4431_pinf_I1_J,axiom,
% 5.44/5.66 ! [P: int > $o,P6: int > $o,Q: int > $o,Q5: int > $o] :
% 5.44/5.66 ( ? [Z3: int] :
% 5.44/5.66 ! [X5: int] :
% 5.44/5.66 ( ( ord_less_int @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: int] :
% 5.44/5.66 ! [X5: int] :
% 5.44/5.66 ( ( ord_less_int @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(1)
% 5.44/5.66 thf(fact_4432_pinf_I2_J,axiom,
% 5.44/5.66 ! [P: extended_enat > $o,P6: extended_enat > $o,Q: extended_enat > $o,Q5: extended_enat > $o] :
% 5.44/5.66 ( ? [Z3: extended_enat] :
% 5.44/5.66 ! [X5: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: extended_enat] :
% 5.44/5.66 ! [X5: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(2)
% 5.44/5.66 thf(fact_4433_pinf_I2_J,axiom,
% 5.44/5.66 ! [P: real > $o,P6: real > $o,Q: real > $o,Q5: real > $o] :
% 5.44/5.66 ( ? [Z3: real] :
% 5.44/5.66 ! [X5: real] :
% 5.44/5.66 ( ( ord_less_real @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: real] :
% 5.44/5.66 ! [X5: real] :
% 5.44/5.66 ( ( ord_less_real @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(2)
% 5.44/5.66 thf(fact_4434_pinf_I2_J,axiom,
% 5.44/5.66 ! [P: num > $o,P6: num > $o,Q: num > $o,Q5: num > $o] :
% 5.44/5.66 ( ? [Z3: num] :
% 5.44/5.66 ! [X5: num] :
% 5.44/5.66 ( ( ord_less_num @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: num] :
% 5.44/5.66 ! [X5: num] :
% 5.44/5.66 ( ( ord_less_num @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(2)
% 5.44/5.66 thf(fact_4435_pinf_I2_J,axiom,
% 5.44/5.66 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q5: nat > $o] :
% 5.44/5.66 ( ? [Z3: nat] :
% 5.44/5.66 ! [X5: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: nat] :
% 5.44/5.66 ! [X5: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(2)
% 5.44/5.66 thf(fact_4436_pinf_I2_J,axiom,
% 5.44/5.66 ! [P: int > $o,P6: int > $o,Q: int > $o,Q5: int > $o] :
% 5.44/5.66 ( ? [Z3: int] :
% 5.44/5.66 ! [X5: int] :
% 5.44/5.66 ( ( ord_less_int @ Z3 @ X5 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: int] :
% 5.44/5.66 ! [X5: int] :
% 5.44/5.66 ( ( ord_less_int @ Z3 @ X5 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(2)
% 5.44/5.66 thf(fact_4437_pinf_I3_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(3)
% 5.44/5.66 thf(fact_4438_pinf_I3_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(3)
% 5.44/5.66 thf(fact_4439_pinf_I3_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(3)
% 5.44/5.66 thf(fact_4440_pinf_I3_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(3)
% 5.44/5.66 thf(fact_4441_pinf_I3_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(3)
% 5.44/5.66 thf(fact_4442_pinf_I4_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(4)
% 5.44/5.66 thf(fact_4443_pinf_I4_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(4)
% 5.44/5.66 thf(fact_4444_pinf_I4_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(4)
% 5.44/5.66 thf(fact_4445_pinf_I4_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(4)
% 5.44/5.66 thf(fact_4446_pinf_I4_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(4)
% 5.44/5.66 thf(fact_4447_pinf_I5_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_le72135733267957522d_enat @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(5)
% 5.44/5.66 thf(fact_4448_pinf_I5_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_less_real @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(5)
% 5.44/5.66 thf(fact_4449_pinf_I5_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_less_num @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(5)
% 5.44/5.66 thf(fact_4450_pinf_I5_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_less_nat @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(5)
% 5.44/5.66 thf(fact_4451_pinf_I5_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_less_int @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(5)
% 5.44/5.66 thf(fact_4452_pinf_I7_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ( ord_le72135733267957522d_enat @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(7)
% 5.44/5.66 thf(fact_4453_pinf_I7_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ( ord_less_real @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(7)
% 5.44/5.66 thf(fact_4454_pinf_I7_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ Z4 @ X3 )
% 5.44/5.66 => ( ord_less_num @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(7)
% 5.44/5.66 thf(fact_4455_pinf_I7_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ( ord_less_nat @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(7)
% 5.44/5.66 thf(fact_4456_pinf_I7_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ( ord_less_int @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(7)
% 5.44/5.66 thf(fact_4457_minf_I1_J,axiom,
% 5.44/5.66 ! [P: extended_enat > $o,P6: extended_enat > $o,Q: extended_enat > $o,Q5: extended_enat > $o] :
% 5.44/5.66 ( ? [Z3: extended_enat] :
% 5.44/5.66 ! [X5: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: extended_enat] :
% 5.44/5.66 ! [X5: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(1)
% 5.44/5.66 thf(fact_4458_minf_I1_J,axiom,
% 5.44/5.66 ! [P: real > $o,P6: real > $o,Q: real > $o,Q5: real > $o] :
% 5.44/5.66 ( ? [Z3: real] :
% 5.44/5.66 ! [X5: real] :
% 5.44/5.66 ( ( ord_less_real @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: real] :
% 5.44/5.66 ! [X5: real] :
% 5.44/5.66 ( ( ord_less_real @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(1)
% 5.44/5.66 thf(fact_4459_minf_I1_J,axiom,
% 5.44/5.66 ! [P: num > $o,P6: num > $o,Q: num > $o,Q5: num > $o] :
% 5.44/5.66 ( ? [Z3: num] :
% 5.44/5.66 ! [X5: num] :
% 5.44/5.66 ( ( ord_less_num @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: num] :
% 5.44/5.66 ! [X5: num] :
% 5.44/5.66 ( ( ord_less_num @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(1)
% 5.44/5.66 thf(fact_4460_minf_I1_J,axiom,
% 5.44/5.66 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q5: nat > $o] :
% 5.44/5.66 ( ? [Z3: nat] :
% 5.44/5.66 ! [X5: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: nat] :
% 5.44/5.66 ! [X5: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(1)
% 5.44/5.66 thf(fact_4461_minf_I1_J,axiom,
% 5.44/5.66 ! [P: int > $o,P6: int > $o,Q: int > $o,Q5: int > $o] :
% 5.44/5.66 ( ? [Z3: int] :
% 5.44/5.66 ! [X5: int] :
% 5.44/5.66 ( ( ord_less_int @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: int] :
% 5.44/5.66 ! [X5: int] :
% 5.44/5.66 ( ( ord_less_int @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 & ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(1)
% 5.44/5.66 thf(fact_4462_minf_I2_J,axiom,
% 5.44/5.66 ! [P: extended_enat > $o,P6: extended_enat > $o,Q: extended_enat > $o,Q5: extended_enat > $o] :
% 5.44/5.66 ( ? [Z3: extended_enat] :
% 5.44/5.66 ! [X5: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: extended_enat] :
% 5.44/5.66 ! [X5: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(2)
% 5.44/5.66 thf(fact_4463_minf_I2_J,axiom,
% 5.44/5.66 ! [P: real > $o,P6: real > $o,Q: real > $o,Q5: real > $o] :
% 5.44/5.66 ( ? [Z3: real] :
% 5.44/5.66 ! [X5: real] :
% 5.44/5.66 ( ( ord_less_real @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: real] :
% 5.44/5.66 ! [X5: real] :
% 5.44/5.66 ( ( ord_less_real @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(2)
% 5.44/5.66 thf(fact_4464_minf_I2_J,axiom,
% 5.44/5.66 ! [P: num > $o,P6: num > $o,Q: num > $o,Q5: num > $o] :
% 5.44/5.66 ( ? [Z3: num] :
% 5.44/5.66 ! [X5: num] :
% 5.44/5.66 ( ( ord_less_num @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: num] :
% 5.44/5.66 ! [X5: num] :
% 5.44/5.66 ( ( ord_less_num @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(2)
% 5.44/5.66 thf(fact_4465_minf_I2_J,axiom,
% 5.44/5.66 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q5: nat > $o] :
% 5.44/5.66 ( ? [Z3: nat] :
% 5.44/5.66 ! [X5: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: nat] :
% 5.44/5.66 ! [X5: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(2)
% 5.44/5.66 thf(fact_4466_minf_I2_J,axiom,
% 5.44/5.66 ! [P: int > $o,P6: int > $o,Q: int > $o,Q5: int > $o] :
% 5.44/5.66 ( ? [Z3: int] :
% 5.44/5.66 ! [X5: int] :
% 5.44/5.66 ( ( ord_less_int @ X5 @ Z3 )
% 5.44/5.66 => ( ( P @ X5 )
% 5.44/5.66 = ( P6 @ X5 ) ) )
% 5.44/5.66 => ( ? [Z3: int] :
% 5.44/5.66 ! [X5: int] :
% 5.44/5.66 ( ( ord_less_int @ X5 @ Z3 )
% 5.44/5.66 => ( ( Q @ X5 )
% 5.44/5.66 = ( Q5 @ X5 ) ) )
% 5.44/5.66 => ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P6 @ X3 )
% 5.44/5.66 | ( Q5 @ X3 ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(2)
% 5.44/5.66 thf(fact_4467_minf_I3_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(3)
% 5.44/5.66 thf(fact_4468_minf_I3_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(3)
% 5.44/5.66 thf(fact_4469_minf_I3_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(3)
% 5.44/5.66 thf(fact_4470_minf_I3_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(3)
% 5.44/5.66 thf(fact_4471_minf_I3_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(3)
% 5.44/5.66 thf(fact_4472_minf_I4_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(4)
% 5.44/5.66 thf(fact_4473_minf_I4_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(4)
% 5.44/5.66 thf(fact_4474_minf_I4_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(4)
% 5.44/5.66 thf(fact_4475_minf_I4_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(4)
% 5.44/5.66 thf(fact_4476_minf_I4_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ( X3 != T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(4)
% 5.44/5.66 thf(fact_4477_minf_I5_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ( ord_le72135733267957522d_enat @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(5)
% 5.44/5.66 thf(fact_4478_minf_I5_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ( ord_less_real @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(5)
% 5.44/5.66 thf(fact_4479_minf_I5_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ X3 @ Z4 )
% 5.44/5.66 => ( ord_less_num @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(5)
% 5.44/5.66 thf(fact_4480_minf_I5_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ( ord_less_nat @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(5)
% 5.44/5.66 thf(fact_4481_minf_I5_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ( ord_less_int @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(5)
% 5.44/5.66 thf(fact_4482_minf_I7_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_le72135733267957522d_enat @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(7)
% 5.44/5.66 thf(fact_4483_minf_I7_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_less_real @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(7)
% 5.44/5.66 thf(fact_4484_minf_I7_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_less_num @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(7)
% 5.44/5.66 thf(fact_4485_minf_I7_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_less_nat @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(7)
% 5.44/5.66 thf(fact_4486_minf_I7_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_less_int @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(7)
% 5.44/5.66 thf(fact_4487_of__bool__odd__eq__mod__2,axiom,
% 5.44/5.66 ! [A: nat] :
% 5.44/5.66 ( ( zero_n2687167440665602831ol_nat
% 5.44/5.66 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.66 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_odd_eq_mod_2
% 5.44/5.66 thf(fact_4488_of__bool__odd__eq__mod__2,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( zero_n2684676970156552555ol_int
% 5.44/5.66 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.66 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_odd_eq_mod_2
% 5.44/5.66 thf(fact_4489_of__bool__odd__eq__mod__2,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( zero_n356916108424825756nteger
% 5.44/5.66 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.66 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % of_bool_odd_eq_mod_2
% 5.44/5.66 thf(fact_4490_bits__induct,axiom,
% 5.44/5.66 ! [P: nat > $o,A: nat] :
% 5.44/5.66 ( ! [A3: nat] :
% 5.44/5.66 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = A3 )
% 5.44/5.66 => ( P @ A3 ) )
% 5.44/5.66 => ( ! [A3: nat,B3: $o] :
% 5.44/5.66 ( ( P @ A3 )
% 5.44/5.66 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = A3 )
% 5.44/5.66 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.44/5.66 => ( P @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % bits_induct
% 5.44/5.66 thf(fact_4491_bits__induct,axiom,
% 5.44/5.66 ! [P: int > $o,A: int] :
% 5.44/5.66 ( ! [A3: int] :
% 5.44/5.66 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.66 = A3 )
% 5.44/5.66 => ( P @ A3 ) )
% 5.44/5.66 => ( ! [A3: int,B3: $o] :
% 5.44/5.66 ( ( P @ A3 )
% 5.44/5.66 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.66 = A3 )
% 5.44/5.66 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.44/5.66 => ( P @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % bits_induct
% 5.44/5.66 thf(fact_4492_bits__induct,axiom,
% 5.44/5.66 ! [P: code_integer > $o,A: code_integer] :
% 5.44/5.66 ( ! [A3: code_integer] :
% 5.44/5.66 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.66 = A3 )
% 5.44/5.66 => ( P @ A3 ) )
% 5.44/5.66 => ( ! [A3: code_integer,B3: $o] :
% 5.44/5.66 ( ( P @ A3 )
% 5.44/5.66 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.66 = A3 )
% 5.44/5.66 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.44/5.66 => ( P @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % bits_induct
% 5.44/5.66 thf(fact_4493_pinf_I6_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_le2932123472753598470d_enat @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(6)
% 5.44/5.66 thf(fact_4494_pinf_I6_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_less_eq_real @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(6)
% 5.44/5.66 thf(fact_4495_pinf_I6_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_less_eq_num @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(6)
% 5.44/5.66 thf(fact_4496_pinf_I6_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_less_eq_nat @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(6)
% 5.44/5.66 thf(fact_4497_pinf_I6_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ~ ( ord_less_eq_int @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(6)
% 5.44/5.66 thf(fact_4498_pinf_I8_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ( ord_le2932123472753598470d_enat @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(8)
% 5.44/5.66 thf(fact_4499_pinf_I8_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ( ord_less_eq_real @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(8)
% 5.44/5.66 thf(fact_4500_pinf_I8_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ Z4 @ X3 )
% 5.44/5.66 => ( ord_less_eq_num @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(8)
% 5.44/5.66 thf(fact_4501_pinf_I8_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ( ord_less_eq_nat @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(8)
% 5.44/5.66 thf(fact_4502_pinf_I8_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ( ord_less_eq_int @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(8)
% 5.44/5.66 thf(fact_4503_minf_I6_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ( ord_le2932123472753598470d_enat @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(6)
% 5.44/5.66 thf(fact_4504_minf_I6_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ( ord_less_eq_real @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(6)
% 5.44/5.66 thf(fact_4505_minf_I6_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ X3 @ Z4 )
% 5.44/5.66 => ( ord_less_eq_num @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(6)
% 5.44/5.66 thf(fact_4506_minf_I6_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ( ord_less_eq_nat @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(6)
% 5.44/5.66 thf(fact_4507_minf_I6_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ( ord_less_eq_int @ X3 @ T ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(6)
% 5.44/5.66 thf(fact_4508_minf_I8_J,axiom,
% 5.44/5.66 ! [T: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_le2932123472753598470d_enat @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(8)
% 5.44/5.66 thf(fact_4509_minf_I8_J,axiom,
% 5.44/5.66 ! [T: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_less_eq_real @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(8)
% 5.44/5.66 thf(fact_4510_minf_I8_J,axiom,
% 5.44/5.66 ! [T: num] :
% 5.44/5.66 ? [Z4: num] :
% 5.44/5.66 ! [X3: num] :
% 5.44/5.66 ( ( ord_less_num @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_less_eq_num @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(8)
% 5.44/5.66 thf(fact_4511_minf_I8_J,axiom,
% 5.44/5.66 ! [T: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_less_eq_nat @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(8)
% 5.44/5.66 thf(fact_4512_minf_I8_J,axiom,
% 5.44/5.66 ! [T: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ~ ( ord_less_eq_int @ T @ X3 ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(8)
% 5.44/5.66 thf(fact_4513_exp__mod__exp,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % exp_mod_exp
% 5.44/5.66 thf(fact_4514_exp__mod__exp,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % exp_mod_exp
% 5.44/5.66 thf(fact_4515_exp__mod__exp,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % exp_mod_exp
% 5.44/5.66 thf(fact_4516_inf__period_I1_J,axiom,
% 5.44/5.66 ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 5.44/5.66 ( ! [X5: complex,K2: complex] :
% 5.44/5.66 ( ( P @ X5 )
% 5.44/5.66 = ( P @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ( ! [X5: complex,K2: complex] :
% 5.44/5.66 ( ( Q @ X5 )
% 5.44/5.66 = ( Q @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ! [X3: complex,K4: complex] :
% 5.44/5.66 ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K4 @ D4 ) ) )
% 5.44/5.66 & ( Q @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % inf_period(1)
% 5.44/5.66 thf(fact_4517_inf__period_I1_J,axiom,
% 5.44/5.66 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.44/5.66 ( ! [X5: real,K2: real] :
% 5.44/5.66 ( ( P @ X5 )
% 5.44/5.66 = ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ( ! [X5: real,K2: real] :
% 5.44/5.66 ( ( Q @ X5 )
% 5.44/5.66 = ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ! [X3: real,K4: real] :
% 5.44/5.66 ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.44/5.66 & ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % inf_period(1)
% 5.44/5.66 thf(fact_4518_inf__period_I1_J,axiom,
% 5.44/5.66 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.44/5.66 ( ! [X5: int,K2: int] :
% 5.44/5.66 ( ( P @ X5 )
% 5.44/5.66 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ( ! [X5: int,K2: int] :
% 5.44/5.66 ( ( Q @ X5 )
% 5.44/5.66 = ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ! [X3: int,K4: int] :
% 5.44/5.66 ( ( ( P @ X3 )
% 5.44/5.66 & ( Q @ X3 ) )
% 5.44/5.66 = ( ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.44/5.66 & ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % inf_period(1)
% 5.44/5.66 thf(fact_4519_inf__period_I2_J,axiom,
% 5.44/5.66 ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 5.44/5.66 ( ! [X5: complex,K2: complex] :
% 5.44/5.66 ( ( P @ X5 )
% 5.44/5.66 = ( P @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ( ! [X5: complex,K2: complex] :
% 5.44/5.66 ( ( Q @ X5 )
% 5.44/5.66 = ( Q @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ! [X3: complex,K4: complex] :
% 5.44/5.66 ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K4 @ D4 ) ) )
% 5.44/5.66 | ( Q @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % inf_period(2)
% 5.44/5.66 thf(fact_4520_inf__period_I2_J,axiom,
% 5.44/5.66 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.44/5.66 ( ! [X5: real,K2: real] :
% 5.44/5.66 ( ( P @ X5 )
% 5.44/5.66 = ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ( ! [X5: real,K2: real] :
% 5.44/5.66 ( ( Q @ X5 )
% 5.44/5.66 = ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ! [X3: real,K4: real] :
% 5.44/5.66 ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.44/5.66 | ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % inf_period(2)
% 5.44/5.66 thf(fact_4521_inf__period_I2_J,axiom,
% 5.44/5.66 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.44/5.66 ( ! [X5: int,K2: int] :
% 5.44/5.66 ( ( P @ X5 )
% 5.44/5.66 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ( ! [X5: int,K2: int] :
% 5.44/5.66 ( ( Q @ X5 )
% 5.44/5.66 = ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.44/5.66 => ! [X3: int,K4: int] :
% 5.44/5.66 ( ( ( P @ X3 )
% 5.44/5.66 | ( Q @ X3 ) )
% 5.44/5.66 = ( ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.44/5.66 | ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % inf_period(2)
% 5.44/5.66 thf(fact_4522_exp__div__exp__eq,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_times_nat
% 5.44/5.66 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.66 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.44/5.66 != zero_zero_nat )
% 5.44/5.66 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.44/5.66 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % exp_div_exp_eq
% 5.44/5.66 thf(fact_4523_exp__div__exp__eq,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_times_int
% 5.44/5.66 @ ( zero_n2684676970156552555ol_int
% 5.44/5.66 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.44/5.66 != zero_zero_int )
% 5.44/5.66 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.44/5.66 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % exp_div_exp_eq
% 5.44/5.66 thf(fact_4524_exp__div__exp__eq,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_3573771949741848930nteger
% 5.44/5.66 @ ( zero_n356916108424825756nteger
% 5.44/5.66 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.44/5.66 != zero_z3403309356797280102nteger )
% 5.44/5.66 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.44/5.66 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % exp_div_exp_eq
% 5.44/5.66 thf(fact_4525_vebt__buildup_Osimps_I3_J,axiom,
% 5.44/5.66 ! [Va: nat] :
% 5.44/5.66 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.44/5.66 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.44/5.66 = ( 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 ) ) ) ) ) ) )
% 5.44/5.66 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.44/5.66 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.44/5.66 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % vebt_buildup.simps(3)
% 5.44/5.66 thf(fact_4526_pinf_I9_J,axiom,
% 5.44/5.66 ! [D: code_integer,S3: code_integer] :
% 5.44/5.66 ? [Z4: code_integer] :
% 5.44/5.66 ! [X3: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ Z4 @ X3 )
% 5.44/5.66 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(9)
% 5.44/5.66 thf(fact_4527_pinf_I9_J,axiom,
% 5.44/5.66 ! [D: extended_enat,S3: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ( ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(9)
% 5.44/5.66 thf(fact_4528_pinf_I9_J,axiom,
% 5.44/5.66 ! [D: real,S3: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(9)
% 5.44/5.66 thf(fact_4529_pinf_I9_J,axiom,
% 5.44/5.66 ! [D: nat,S3: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(9)
% 5.44/5.66 thf(fact_4530_pinf_I9_J,axiom,
% 5.44/5.66 ! [D: int,S3: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(9)
% 5.44/5.66 thf(fact_4531_pinf_I10_J,axiom,
% 5.44/5.66 ! [D: code_integer,S3: code_integer] :
% 5.44/5.66 ? [Z4: code_integer] :
% 5.44/5.66 ! [X3: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ Z4 @ X3 )
% 5.44/5.66 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(10)
% 5.44/5.66 thf(fact_4532_pinf_I10_J,axiom,
% 5.44/5.66 ! [D: extended_enat,S3: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ Z4 @ X3 )
% 5.44/5.66 => ( ( ~ ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(10)
% 5.44/5.66 thf(fact_4533_pinf_I10_J,axiom,
% 5.44/5.66 ! [D: real,S3: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ Z4 @ X3 )
% 5.44/5.66 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(10)
% 5.44/5.66 thf(fact_4534_pinf_I10_J,axiom,
% 5.44/5.66 ! [D: nat,S3: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ Z4 @ X3 )
% 5.44/5.66 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(10)
% 5.44/5.66 thf(fact_4535_pinf_I10_J,axiom,
% 5.44/5.66 ! [D: int,S3: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ Z4 @ X3 )
% 5.44/5.66 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pinf(10)
% 5.44/5.66 thf(fact_4536_minf_I9_J,axiom,
% 5.44/5.66 ! [D: code_integer,S3: code_integer] :
% 5.44/5.66 ? [Z4: code_integer] :
% 5.44/5.66 ! [X3: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ X3 @ Z4 )
% 5.44/5.66 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(9)
% 5.44/5.66 thf(fact_4537_minf_I9_J,axiom,
% 5.44/5.66 ! [D: extended_enat,S3: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ( ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(9)
% 5.44/5.66 thf(fact_4538_minf_I9_J,axiom,
% 5.44/5.66 ! [D: real,S3: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(9)
% 5.44/5.66 thf(fact_4539_minf_I9_J,axiom,
% 5.44/5.66 ! [D: nat,S3: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(9)
% 5.44/5.66 thf(fact_4540_minf_I9_J,axiom,
% 5.44/5.66 ! [D: int,S3: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S3 ) )
% 5.44/5.66 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(9)
% 5.44/5.66 thf(fact_4541_minf_I10_J,axiom,
% 5.44/5.66 ! [D: code_integer,S3: code_integer] :
% 5.44/5.66 ? [Z4: code_integer] :
% 5.44/5.66 ! [X3: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ X3 @ Z4 )
% 5.44/5.66 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(10)
% 5.44/5.66 thf(fact_4542_minf_I10_J,axiom,
% 5.44/5.66 ! [D: extended_enat,S3: extended_enat] :
% 5.44/5.66 ? [Z4: extended_enat] :
% 5.44/5.66 ! [X3: extended_enat] :
% 5.44/5.66 ( ( ord_le72135733267957522d_enat @ X3 @ Z4 )
% 5.44/5.66 => ( ( ~ ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dv3785147216227455552d_enat @ D @ ( plus_p3455044024723400733d_enat @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(10)
% 5.44/5.66 thf(fact_4543_minf_I10_J,axiom,
% 5.44/5.66 ! [D: real,S3: real] :
% 5.44/5.66 ? [Z4: real] :
% 5.44/5.66 ! [X3: real] :
% 5.44/5.66 ( ( ord_less_real @ X3 @ Z4 )
% 5.44/5.66 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(10)
% 5.44/5.66 thf(fact_4544_minf_I10_J,axiom,
% 5.44/5.66 ! [D: nat,S3: nat] :
% 5.44/5.66 ? [Z4: nat] :
% 5.44/5.66 ! [X3: nat] :
% 5.44/5.66 ( ( ord_less_nat @ X3 @ Z4 )
% 5.44/5.66 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(10)
% 5.44/5.66 thf(fact_4545_minf_I10_J,axiom,
% 5.44/5.66 ! [D: int,S3: int] :
% 5.44/5.66 ? [Z4: int] :
% 5.44/5.66 ! [X3: int] :
% 5.44/5.66 ( ( ord_less_int @ X3 @ Z4 )
% 5.44/5.66 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S3 ) ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S3 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minf(10)
% 5.44/5.66 thf(fact_4546_vebt__buildup_Opelims,axiom,
% 5.44/5.66 ! [X: nat,Y: vEBT_VEBT] :
% 5.44/5.66 ( ( ( vEBT_vebt_buildup @ X )
% 5.44/5.66 = Y )
% 5.44/5.66 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.44/5.66 => ( ( ( X = zero_zero_nat )
% 5.44/5.66 => ( ( Y
% 5.44/5.66 = ( vEBT_Leaf @ $false @ $false ) )
% 5.44/5.66 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.44/5.66 => ( ( ( X
% 5.44/5.66 = ( suc @ zero_zero_nat ) )
% 5.44/5.66 => ( ( Y
% 5.44/5.66 = ( vEBT_Leaf @ $false @ $false ) )
% 5.44/5.66 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.44/5.66 => ~ ! [Va2: nat] :
% 5.44/5.66 ( ( X
% 5.44/5.66 = ( suc @ ( suc @ Va2 ) ) )
% 5.44/5.66 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.44/5.66 => ( Y
% 5.44/5.66 = ( 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 ) ) ) ) ) ) )
% 5.44/5.66 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.44/5.66 => ( Y
% 5.44/5.66 = ( 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 ) ) ) ) ) ) ) ) )
% 5.44/5.66 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % vebt_buildup.pelims
% 5.44/5.66 thf(fact_4547_option_Osize__gen_I2_J,axiom,
% 5.44/5.66 ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.44/5.66 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.44/5.66 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % option.size_gen(2)
% 5.44/5.66 thf(fact_4548_option_Osize__gen_I2_J,axiom,
% 5.44/5.66 ! [X: nat > nat,X22: nat] :
% 5.44/5.66 ( ( size_option_nat @ X @ ( some_nat @ X22 ) )
% 5.44/5.66 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % option.size_gen(2)
% 5.44/5.66 thf(fact_4549_option_Osize__gen_I2_J,axiom,
% 5.44/5.66 ! [X: num > nat,X22: num] :
% 5.44/5.66 ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 5.44/5.66 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % option.size_gen(2)
% 5.44/5.66 thf(fact_4550_signed__take__bit__Suc,axiom,
% 5.44/5.66 ! [N2: nat,A: code_integer] :
% 5.44/5.66 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_Suc
% 5.44/5.66 thf(fact_4551_signed__take__bit__Suc,axiom,
% 5.44/5.66 ! [N2: nat,A: int] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 5.44/5.66 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_Suc
% 5.44/5.66 thf(fact_4552_set__decode__0,axiom,
% 5.44/5.66 ! [X: nat] :
% 5.44/5.66 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.44/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % set_decode_0
% 5.44/5.66 thf(fact_4553_set__decode__Suc,axiom,
% 5.44/5.66 ! [N2: nat,X: nat] :
% 5.44/5.66 ( ( member_nat @ ( suc @ N2 ) @ ( nat_set_decode @ X ) )
% 5.44/5.66 = ( member_nat @ N2 @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % set_decode_Suc
% 5.44/5.66 thf(fact_4554_diff__shunt__var,axiom,
% 5.44/5.66 ! [X: set_int,Y: set_int] :
% 5.44/5.66 ( ( ( minus_minus_set_int @ X @ Y )
% 5.44/5.66 = bot_bot_set_int )
% 5.44/5.66 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_shunt_var
% 5.44/5.66 thf(fact_4555_diff__shunt__var,axiom,
% 5.44/5.66 ! [X: set_real,Y: set_real] :
% 5.44/5.66 ( ( ( minus_minus_set_real @ X @ Y )
% 5.44/5.66 = bot_bot_set_real )
% 5.44/5.66 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_shunt_var
% 5.44/5.66 thf(fact_4556_diff__shunt__var,axiom,
% 5.44/5.66 ! [X: set_nat,Y: set_nat] :
% 5.44/5.66 ( ( ( minus_minus_set_nat @ X @ Y )
% 5.44/5.66 = bot_bot_set_nat )
% 5.44/5.66 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_shunt_var
% 5.44/5.66 thf(fact_4557_add__scale__eq__noteq,axiom,
% 5.44/5.66 ! [R: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.44/5.66 ( ( R != zero_zero_complex )
% 5.44/5.66 => ( ( ( A = B )
% 5.44/5.66 & ( C != D ) )
% 5.44/5.66 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 5.44/5.66 != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_scale_eq_noteq
% 5.44/5.66 thf(fact_4558_add__scale__eq__noteq,axiom,
% 5.44/5.66 ! [R: real,A: real,B: real,C: real,D: real] :
% 5.44/5.66 ( ( R != zero_zero_real )
% 5.44/5.66 => ( ( ( A = B )
% 5.44/5.66 & ( C != D ) )
% 5.44/5.66 => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 5.44/5.66 != ( plus_plus_real @ B @ ( times_times_real @ R @ D ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_scale_eq_noteq
% 5.44/5.66 thf(fact_4559_add__scale__eq__noteq,axiom,
% 5.44/5.66 ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.66 ( ( R != zero_zero_nat )
% 5.44/5.66 => ( ( ( A = B )
% 5.44/5.66 & ( C != D ) )
% 5.44/5.66 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 5.44/5.66 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_scale_eq_noteq
% 5.44/5.66 thf(fact_4560_add__scale__eq__noteq,axiom,
% 5.44/5.66 ! [R: int,A: int,B: int,C: int,D: int] :
% 5.44/5.66 ( ( R != zero_zero_int )
% 5.44/5.66 => ( ( ( A = B )
% 5.44/5.66 & ( C != D ) )
% 5.44/5.66 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 5.44/5.66 != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_scale_eq_noteq
% 5.44/5.66 thf(fact_4561_signed__take__bit__of__0,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_of_0
% 5.44/5.66 thf(fact_4562_signed__take__bit__Suc__1,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_Suc_1
% 5.44/5.66 thf(fact_4563_signed__take__bit__numeral__of__1,axiom,
% 5.44/5.66 ! [K: num] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_numeral_of_1
% 5.44/5.66 thf(fact_4564_signed__take__bit__Suc__bit0,axiom,
% 5.44/5.66 ! [N2: nat,K: num] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.44/5.66 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_Suc_bit0
% 5.44/5.66 thf(fact_4565_signed__take__bit__mult,axiom,
% 5.44/5.66 ! [N2: nat,K: int,L2: int] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L2 ) ) )
% 5.44/5.66 = ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_mult
% 5.44/5.66 thf(fact_4566_signed__take__bit__add,axiom,
% 5.44/5.66 ! [N2: nat,K: int,L2: int] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L2 ) ) )
% 5.44/5.66 = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_add
% 5.44/5.66 thf(fact_4567_signed__take__bit__diff,axiom,
% 5.44/5.66 ! [N2: nat,K: int,L2: int] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L2 ) ) )
% 5.44/5.66 = ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_diff
% 5.44/5.66 thf(fact_4568_subset__decode__imp__le,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 5.44/5.66 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % subset_decode_imp_le
% 5.44/5.66 thf(fact_4569_signed__take__bit__int__less__exp,axiom,
% 5.44/5.66 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_int_less_exp
% 5.44/5.66 thf(fact_4570_even__signed__take__bit__iff,axiom,
% 5.44/5.66 ! [M: nat,A: code_integer] :
% 5.44/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.44/5.66 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % even_signed_take_bit_iff
% 5.44/5.66 thf(fact_4571_even__signed__take__bit__iff,axiom,
% 5.44/5.66 ! [M: nat,A: int] :
% 5.44/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.44/5.66 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % even_signed_take_bit_iff
% 5.44/5.66 thf(fact_4572_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.44/5.66 ! [K: int,N2: nat] :
% 5.44/5.66 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.44/5.66 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_int_greater_eq_self_iff
% 5.44/5.66 thf(fact_4573_signed__take__bit__int__less__self__iff,axiom,
% 5.44/5.66 ! [N2: nat,K: int] :
% 5.44/5.66 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.44/5.66 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_int_less_self_iff
% 5.44/5.66 thf(fact_4574_add__0__iff,axiom,
% 5.44/5.66 ! [B: complex,A: complex] :
% 5.44/5.66 ( ( B
% 5.44/5.66 = ( plus_plus_complex @ B @ A ) )
% 5.44/5.66 = ( A = zero_zero_complex ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_0_iff
% 5.44/5.66 thf(fact_4575_add__0__iff,axiom,
% 5.44/5.66 ! [B: real,A: real] :
% 5.44/5.66 ( ( B
% 5.44/5.66 = ( plus_plus_real @ B @ A ) )
% 5.44/5.66 = ( A = zero_zero_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_0_iff
% 5.44/5.66 thf(fact_4576_add__0__iff,axiom,
% 5.44/5.66 ! [B: nat,A: nat] :
% 5.44/5.66 ( ( B
% 5.44/5.66 = ( plus_plus_nat @ B @ A ) )
% 5.44/5.66 = ( A = zero_zero_nat ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_0_iff
% 5.44/5.66 thf(fact_4577_add__0__iff,axiom,
% 5.44/5.66 ! [B: int,A: int] :
% 5.44/5.66 ( ( B
% 5.44/5.66 = ( plus_plus_int @ B @ A ) )
% 5.44/5.66 = ( A = zero_zero_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_0_iff
% 5.44/5.66 thf(fact_4578_crossproduct__eq,axiom,
% 5.44/5.66 ! [W: complex,Y: complex,X: complex,Z: complex] :
% 5.44/5.66 ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y ) @ ( times_times_complex @ X @ Z ) )
% 5.44/5.66 = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X @ Y ) ) )
% 5.44/5.66 = ( ( W = X )
% 5.44/5.66 | ( Y = Z ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % crossproduct_eq
% 5.44/5.66 thf(fact_4579_crossproduct__eq,axiom,
% 5.44/5.66 ! [W: real,Y: real,X: real,Z: real] :
% 5.44/5.66 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X @ Z ) )
% 5.44/5.66 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y ) ) )
% 5.44/5.66 = ( ( W = X )
% 5.44/5.66 | ( Y = Z ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % crossproduct_eq
% 5.44/5.66 thf(fact_4580_crossproduct__eq,axiom,
% 5.44/5.66 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 5.44/5.66 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 5.44/5.66 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 5.44/5.66 = ( ( W = X )
% 5.44/5.66 | ( Y = Z ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % crossproduct_eq
% 5.44/5.66 thf(fact_4581_crossproduct__eq,axiom,
% 5.44/5.66 ! [W: int,Y: int,X: int,Z: int] :
% 5.44/5.66 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 5.44/5.66 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 5.44/5.66 = ( ( W = X )
% 5.44/5.66 | ( Y = Z ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % crossproduct_eq
% 5.44/5.66 thf(fact_4582_crossproduct__noteq,axiom,
% 5.44/5.66 ! [A: complex,B: complex,C: complex,D: complex] :
% 5.44/5.66 ( ( ( A != B )
% 5.44/5.66 & ( C != D ) )
% 5.44/5.66 = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) )
% 5.44/5.66 != ( plus_plus_complex @ ( times_times_complex @ A @ D ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % crossproduct_noteq
% 5.44/5.66 thf(fact_4583_crossproduct__noteq,axiom,
% 5.44/5.66 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.66 ( ( ( A != B )
% 5.44/5.66 & ( C != D ) )
% 5.44/5.66 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.44/5.66 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % crossproduct_noteq
% 5.44/5.66 thf(fact_4584_crossproduct__noteq,axiom,
% 5.44/5.66 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.44/5.66 ( ( ( A != B )
% 5.44/5.66 & ( C != D ) )
% 5.44/5.66 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.44/5.66 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % crossproduct_noteq
% 5.44/5.66 thf(fact_4585_crossproduct__noteq,axiom,
% 5.44/5.66 ! [A: int,B: int,C: int,D: int] :
% 5.44/5.66 ( ( ( A != B )
% 5.44/5.66 & ( C != D ) )
% 5.44/5.66 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.44/5.66 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % crossproduct_noteq
% 5.44/5.66 thf(fact_4586_signed__take__bit__int__less__eq,axiom,
% 5.44/5.66 ! [N2: nat,K: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.44/5.66 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_int_less_eq
% 5.44/5.66 thf(fact_4587_option_Osize__gen_I1_J,axiom,
% 5.44/5.66 ! [X: product_prod_nat_nat > nat] :
% 5.44/5.66 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 5.44/5.66 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.66
% 5.44/5.66 % option.size_gen(1)
% 5.44/5.66 thf(fact_4588_option_Osize__gen_I1_J,axiom,
% 5.44/5.66 ! [X: nat > nat] :
% 5.44/5.66 ( ( size_option_nat @ X @ none_nat )
% 5.44/5.66 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.66
% 5.44/5.66 % option.size_gen(1)
% 5.44/5.66 thf(fact_4589_option_Osize__gen_I1_J,axiom,
% 5.44/5.66 ! [X: num > nat] :
% 5.44/5.66 ( ( size_option_num @ X @ none_num )
% 5.44/5.66 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.66
% 5.44/5.66 % option.size_gen(1)
% 5.44/5.66 thf(fact_4590_set__decode__def,axiom,
% 5.44/5.66 ( nat_set_decode
% 5.44/5.66 = ( ^ [X2: nat] :
% 5.44/5.66 ( collect_nat
% 5.44/5.66 @ ^ [N: nat] :
% 5.44/5.66 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % set_decode_def
% 5.44/5.66 thf(fact_4591_signed__take__bit__rec,axiom,
% 5.44/5.66 ( bit_ri6519982836138164636nteger
% 5.44/5.66 = ( ^ [N: nat,A4: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_rec
% 5.44/5.66 thf(fact_4592_signed__take__bit__rec,axiom,
% 5.44/5.66 ( bit_ri631733984087533419it_int
% 5.44/5.66 = ( ^ [N: nat,A4: int] : ( if_int @ ( N = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_rec
% 5.44/5.66 thf(fact_4593_artanh__def,axiom,
% 5.44/5.66 ( artanh_real
% 5.44/5.66 = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % artanh_def
% 5.44/5.66 thf(fact_4594_divmod__step__def,axiom,
% 5.44/5.66 ( unique5026877609467782581ep_nat
% 5.44/5.66 = ( ^ [L: num] :
% 5.44/5.66 ( produc2626176000494625587at_nat
% 5.44/5.66 @ ^ [Q4: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R4 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divmod_step_def
% 5.44/5.66 thf(fact_4595_divmod__step__def,axiom,
% 5.44/5.66 ( unique5024387138958732305ep_int
% 5.44/5.66 = ( ^ [L: num] :
% 5.44/5.66 ( produc4245557441103728435nt_int
% 5.44/5.66 @ ^ [Q4: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R4 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divmod_step_def
% 5.44/5.66 thf(fact_4596_divmod__step__def,axiom,
% 5.44/5.66 ( unique4921790084139445826nteger
% 5.44/5.66 = ( ^ [L: num] :
% 5.44/5.66 ( produc6916734918728496179nteger
% 5.44/5.66 @ ^ [Q4: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R4 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divmod_step_def
% 5.44/5.66 thf(fact_4597_even__set__encode__iff,axiom,
% 5.44/5.66 ! [A2: set_nat] :
% 5.44/5.66 ( ( finite_finite_nat @ A2 )
% 5.44/5.66 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.44/5.66 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % even_set_encode_iff
% 5.44/5.66 thf(fact_4598_take__bit__rec,axiom,
% 5.44/5.66 ( bit_se1745604003318907178nteger
% 5.44/5.66 = ( ^ [N: nat,A4: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_rec
% 5.44/5.66 thf(fact_4599_take__bit__rec,axiom,
% 5.44/5.66 ( bit_se2923211474154528505it_int
% 5.44/5.66 = ( ^ [N: nat,A4: int] : ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_rec
% 5.44/5.66 thf(fact_4600_take__bit__rec,axiom,
% 5.44/5.66 ( bit_se2925701944663578781it_nat
% 5.44/5.66 = ( ^ [N: nat,A4: nat] : ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_rec
% 5.44/5.66 thf(fact_4601_num_Osize__gen_I2_J,axiom,
% 5.44/5.66 ! [X22: num] :
% 5.44/5.66 ( ( size_num @ ( bit0 @ X22 ) )
% 5.44/5.66 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % num.size_gen(2)
% 5.44/5.66 thf(fact_4602_power__numeral,axiom,
% 5.44/5.66 ! [K: num,L2: num] :
% 5.44/5.66 ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.44/5.66 = ( numera1916890842035813515d_enat @ ( pow @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_numeral
% 5.44/5.66 thf(fact_4603_power__numeral,axiom,
% 5.44/5.66 ! [K: num,L2: num] :
% 5.44/5.66 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.44/5.66 = ( numera6690914467698888265omplex @ ( pow @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_numeral
% 5.44/5.66 thf(fact_4604_power__numeral,axiom,
% 5.44/5.66 ! [K: num,L2: num] :
% 5.44/5.66 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.44/5.66 = ( numeral_numeral_real @ ( pow @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_numeral
% 5.44/5.66 thf(fact_4605_power__numeral,axiom,
% 5.44/5.66 ! [K: num,L2: num] :
% 5.44/5.66 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.44/5.66 = ( numeral_numeral_nat @ ( pow @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_numeral
% 5.44/5.66 thf(fact_4606_power__numeral,axiom,
% 5.44/5.66 ! [K: num,L2: num] :
% 5.44/5.66 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.44/5.66 = ( numeral_numeral_int @ ( pow @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_numeral
% 5.44/5.66 thf(fact_4607_Compl__anti__mono,axiom,
% 5.44/5.66 ! [A2: set_real,B2: set_real] :
% 5.44/5.66 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.66 => ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ B2 ) @ ( uminus612125837232591019t_real @ A2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Compl_anti_mono
% 5.44/5.66 thf(fact_4608_Compl__anti__mono,axiom,
% 5.44/5.66 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.66 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.66 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ B2 ) @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Compl_anti_mono
% 5.44/5.66 thf(fact_4609_Compl__subset__Compl__iff,axiom,
% 5.44/5.66 ! [A2: set_real,B2: set_real] :
% 5.44/5.66 ( ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( uminus612125837232591019t_real @ B2 ) )
% 5.44/5.66 = ( ord_less_eq_set_real @ B2 @ A2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % Compl_subset_Compl_iff
% 5.44/5.66 thf(fact_4610_Compl__subset__Compl__iff,axiom,
% 5.44/5.66 ! [A2: set_nat,B2: set_nat] :
% 5.44/5.66 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B2 ) )
% 5.44/5.66 = ( ord_less_eq_set_nat @ B2 @ A2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % Compl_subset_Compl_iff
% 5.44/5.66 thf(fact_4611_neg__le__iff__le,axiom,
% 5.44/5.66 ! [B: real,A: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.44/5.66 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_le_iff_le
% 5.44/5.66 thf(fact_4612_neg__le__iff__le,axiom,
% 5.44/5.66 ! [B: code_integer,A: code_integer] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.44/5.66 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_le_iff_le
% 5.44/5.66 thf(fact_4613_neg__le__iff__le,axiom,
% 5.44/5.66 ! [B: int,A: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.44/5.66 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_le_iff_le
% 5.44/5.66 thf(fact_4614_compl__le__compl__iff,axiom,
% 5.44/5.66 ! [X: set_real,Y: set_real] :
% 5.44/5.66 ( ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ X ) @ ( uminus612125837232591019t_real @ Y ) )
% 5.44/5.66 = ( ord_less_eq_set_real @ Y @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % compl_le_compl_iff
% 5.44/5.66 thf(fact_4615_compl__le__compl__iff,axiom,
% 5.44/5.66 ! [X: set_nat,Y: set_nat] :
% 5.44/5.66 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 5.44/5.66 = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % compl_le_compl_iff
% 5.44/5.66 thf(fact_4616_neg__less__iff__less,axiom,
% 5.44/5.66 ! [B: real,A: real] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.44/5.66 = ( ord_less_real @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_iff_less
% 5.44/5.66 thf(fact_4617_neg__less__iff__less,axiom,
% 5.44/5.66 ! [B: int,A: int] :
% 5.44/5.66 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.44/5.66 = ( ord_less_int @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_iff_less
% 5.44/5.66 thf(fact_4618_neg__less__iff__less,axiom,
% 5.44/5.66 ! [B: code_integer,A: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.44/5.66 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_iff_less
% 5.44/5.66 thf(fact_4619_neg__numeral__eq__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( M = N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_eq_iff
% 5.44/5.66 thf(fact_4620_neg__numeral__eq__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( M = N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_eq_iff
% 5.44/5.66 thf(fact_4621_neg__numeral__eq__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.44/5.66 = ( M = N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_eq_iff
% 5.44/5.66 thf(fact_4622_neg__numeral__eq__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( M = N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_eq_iff
% 5.44/5.66 thf(fact_4623_mult__minus__right,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus_right
% 5.44/5.66 thf(fact_4624_mult__minus__right,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus_right
% 5.44/5.66 thf(fact_4625_mult__minus__right,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus_right
% 5.44/5.66 thf(fact_4626_mult__minus__right,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus_right
% 5.44/5.66 thf(fact_4627_minus__mult__minus,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( times_times_real @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mult_minus
% 5.44/5.66 thf(fact_4628_minus__mult__minus,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( times_times_int @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mult_minus
% 5.44/5.66 thf(fact_4629_minus__mult__minus,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.44/5.66 = ( times_times_complex @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mult_minus
% 5.44/5.66 thf(fact_4630_minus__mult__minus,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mult_minus
% 5.44/5.66 thf(fact_4631_mult__minus__left,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.44/5.66 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus_left
% 5.44/5.66 thf(fact_4632_mult__minus__left,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.44/5.66 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus_left
% 5.44/5.66 thf(fact_4633_mult__minus__left,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus_left
% 5.44/5.66 thf(fact_4634_mult__minus__left,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus_left
% 5.44/5.66 thf(fact_4635_minus__add__distrib,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.44/5.66 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_add_distrib
% 5.44/5.66 thf(fact_4636_minus__add__distrib,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.44/5.66 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_add_distrib
% 5.44/5.66 thf(fact_4637_minus__add__distrib,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.44/5.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_add_distrib
% 5.44/5.66 thf(fact_4638_minus__add__distrib,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_add_distrib
% 5.44/5.66 thf(fact_4639_minus__add__cancel,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.44/5.66 = B ) ).
% 5.44/5.66
% 5.44/5.66 % minus_add_cancel
% 5.44/5.66 thf(fact_4640_minus__add__cancel,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.44/5.66 = B ) ).
% 5.44/5.66
% 5.44/5.66 % minus_add_cancel
% 5.44/5.66 thf(fact_4641_minus__add__cancel,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.44/5.66 = B ) ).
% 5.44/5.66
% 5.44/5.66 % minus_add_cancel
% 5.44/5.66 thf(fact_4642_minus__add__cancel,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.44/5.66 = B ) ).
% 5.44/5.66
% 5.44/5.66 % minus_add_cancel
% 5.44/5.66 thf(fact_4643_add__minus__cancel,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.44/5.66 = B ) ).
% 5.44/5.66
% 5.44/5.66 % add_minus_cancel
% 5.44/5.66 thf(fact_4644_add__minus__cancel,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.44/5.66 = B ) ).
% 5.44/5.66
% 5.44/5.66 % add_minus_cancel
% 5.44/5.66 thf(fact_4645_add__minus__cancel,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.44/5.66 = B ) ).
% 5.44/5.66
% 5.44/5.66 % add_minus_cancel
% 5.44/5.66 thf(fact_4646_add__minus__cancel,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.44/5.66 = B ) ).
% 5.44/5.66
% 5.44/5.66 % add_minus_cancel
% 5.44/5.66 thf(fact_4647_div__minus__minus,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( divide_divide_int @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % div_minus_minus
% 5.44/5.66 thf(fact_4648_div__minus__minus,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % div_minus_minus
% 5.44/5.66 thf(fact_4649_ln__less__cancel__iff,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.66 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.44/5.66 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_less_cancel_iff
% 5.44/5.66 thf(fact_4650_ln__inj__iff,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.66 => ( ( ( ln_ln_real @ X )
% 5.44/5.66 = ( ln_ln_real @ Y ) )
% 5.44/5.66 = ( X = Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_inj_iff
% 5.44/5.66 thf(fact_4651_mod__minus__minus,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus_minus
% 5.44/5.66 thf(fact_4652_mod__minus__minus,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus_minus
% 5.44/5.66 thf(fact_4653_take__bit__of__0,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_0
% 5.44/5.66 thf(fact_4654_take__bit__of__0,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 5.44/5.66 = zero_zero_nat ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_0
% 5.44/5.66 thf(fact_4655_real__add__minus__iff,axiom,
% 5.44/5.66 ! [X: real,A: real] :
% 5.44/5.66 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 5.44/5.66 = zero_zero_real )
% 5.44/5.66 = ( X = A ) ) ).
% 5.44/5.66
% 5.44/5.66 % real_add_minus_iff
% 5.44/5.66 thf(fact_4656_concat__bit__of__zero__2,axiom,
% 5.44/5.66 ! [N2: nat,K: int] :
% 5.44/5.66 ( ( bit_concat_bit @ N2 @ K @ zero_zero_int )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.44/5.66
% 5.44/5.66 % concat_bit_of_zero_2
% 5.44/5.66 thf(fact_4657_case__prod__conv,axiom,
% 5.44/5.66 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.44/5.66 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.44/5.66 = ( F @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_conv
% 5.44/5.66 thf(fact_4658_case__prod__conv,axiom,
% 5.44/5.66 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.44/5.66 ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.44/5.66 = ( F @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_conv
% 5.44/5.66 thf(fact_4659_case__prod__conv,axiom,
% 5.44/5.66 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.44/5.66 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.44/5.66 = ( F @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_conv
% 5.44/5.66 thf(fact_4660_case__prod__conv,axiom,
% 5.44/5.66 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.44/5.66 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.44/5.66 = ( F @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_conv
% 5.44/5.66 thf(fact_4661_case__prod__conv,axiom,
% 5.44/5.66 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.44/5.66 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.44/5.66 = ( F @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_conv
% 5.44/5.66 thf(fact_4662_neg__0__le__iff__le,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.44/5.66 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_0_le_iff_le
% 5.44/5.66 thf(fact_4663_neg__0__le__iff__le,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.44/5.66 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_0_le_iff_le
% 5.44/5.66 thf(fact_4664_neg__0__le__iff__le,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.44/5.66 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_0_le_iff_le
% 5.44/5.66 thf(fact_4665_neg__le__0__iff__le,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.44/5.66 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_le_0_iff_le
% 5.44/5.66 thf(fact_4666_neg__le__0__iff__le,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.44/5.66 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_le_0_iff_le
% 5.44/5.66 thf(fact_4667_neg__le__0__iff__le,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.44/5.66 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_le_0_iff_le
% 5.44/5.66 thf(fact_4668_less__eq__neg__nonpos,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.44/5.66 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_eq_neg_nonpos
% 5.44/5.66 thf(fact_4669_less__eq__neg__nonpos,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.44/5.66 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_eq_neg_nonpos
% 5.44/5.66 thf(fact_4670_less__eq__neg__nonpos,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.44/5.66 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_eq_neg_nonpos
% 5.44/5.66 thf(fact_4671_neg__less__eq__nonneg,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.44/5.66 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_eq_nonneg
% 5.44/5.66 thf(fact_4672_neg__less__eq__nonneg,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.44/5.66 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_eq_nonneg
% 5.44/5.66 thf(fact_4673_neg__less__eq__nonneg,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.44/5.66 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_eq_nonneg
% 5.44/5.66 thf(fact_4674_neg__less__0__iff__less,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.44/5.66 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_0_iff_less
% 5.44/5.66 thf(fact_4675_neg__less__0__iff__less,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.44/5.66 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_0_iff_less
% 5.44/5.66 thf(fact_4676_neg__less__0__iff__less,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.44/5.66 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_0_iff_less
% 5.44/5.66 thf(fact_4677_neg__0__less__iff__less,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.44/5.66 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_0_less_iff_less
% 5.44/5.66 thf(fact_4678_neg__0__less__iff__less,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.44/5.66 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_0_less_iff_less
% 5.44/5.66 thf(fact_4679_neg__0__less__iff__less,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.44/5.66 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_0_less_iff_less
% 5.44/5.66 thf(fact_4680_neg__less__pos,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.44/5.66 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_pos
% 5.44/5.66 thf(fact_4681_neg__less__pos,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.44/5.66 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_pos
% 5.44/5.66 thf(fact_4682_neg__less__pos,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.44/5.66 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_pos
% 5.44/5.66 thf(fact_4683_less__neg__neg,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.44/5.66 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_neg_neg
% 5.44/5.66 thf(fact_4684_less__neg__neg,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.44/5.66 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_neg_neg
% 5.44/5.66 thf(fact_4685_less__neg__neg,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.44/5.66 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_neg_neg
% 5.44/5.66 thf(fact_4686_add_Oright__inverse,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.44/5.66 = zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % add.right_inverse
% 5.44/5.66 thf(fact_4687_add_Oright__inverse,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % add.right_inverse
% 5.44/5.66 thf(fact_4688_add_Oright__inverse,axiom,
% 5.44/5.66 ! [A: complex] :
% 5.44/5.66 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.44/5.66 = zero_zero_complex ) ).
% 5.44/5.66
% 5.44/5.66 % add.right_inverse
% 5.44/5.66 thf(fact_4689_add_Oright__inverse,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % add.right_inverse
% 5.44/5.66 thf(fact_4690_ab__left__minus,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.44/5.66 = zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % ab_left_minus
% 5.44/5.66 thf(fact_4691_ab__left__minus,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % ab_left_minus
% 5.44/5.66 thf(fact_4692_ab__left__minus,axiom,
% 5.44/5.66 ! [A: complex] :
% 5.44/5.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.44/5.66 = zero_zero_complex ) ).
% 5.44/5.66
% 5.44/5.66 % ab_left_minus
% 5.44/5.66 thf(fact_4693_ab__left__minus,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % ab_left_minus
% 5.44/5.66 thf(fact_4694_add__neg__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_simps(3)
% 5.44/5.66 thf(fact_4695_add__neg__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_simps(3)
% 5.44/5.66 thf(fact_4696_add__neg__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_simps(3)
% 5.44/5.66 thf(fact_4697_add__neg__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_simps(3)
% 5.44/5.66 thf(fact_4698_mult__minus1,axiom,
% 5.44/5.66 ! [Z: real] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.44/5.66 = ( uminus_uminus_real @ Z ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus1
% 5.44/5.66 thf(fact_4699_mult__minus1,axiom,
% 5.44/5.66 ! [Z: int] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.44/5.66 = ( uminus_uminus_int @ Z ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus1
% 5.44/5.66 thf(fact_4700_mult__minus1,axiom,
% 5.44/5.66 ! [Z: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus1
% 5.44/5.66 thf(fact_4701_mult__minus1,axiom,
% 5.44/5.66 ! [Z: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus1
% 5.44/5.66 thf(fact_4702_mult__minus1__right,axiom,
% 5.44/5.66 ! [Z: real] :
% 5.44/5.66 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = ( uminus_uminus_real @ Z ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus1_right
% 5.44/5.66 thf(fact_4703_mult__minus1__right,axiom,
% 5.44/5.66 ! [Z: int] :
% 5.44/5.66 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( uminus_uminus_int @ Z ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus1_right
% 5.44/5.66 thf(fact_4704_mult__minus1__right,axiom,
% 5.44/5.66 ! [Z: complex] :
% 5.44/5.66 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus1_right
% 5.44/5.66 thf(fact_4705_mult__minus1__right,axiom,
% 5.44/5.66 ! [Z: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_minus1_right
% 5.44/5.66 thf(fact_4706_diff__minus__eq__add,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( plus_plus_real @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_minus_eq_add
% 5.44/5.66 thf(fact_4707_diff__minus__eq__add,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( plus_plus_int @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_minus_eq_add
% 5.44/5.66 thf(fact_4708_diff__minus__eq__add,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.44/5.66 = ( plus_plus_complex @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_minus_eq_add
% 5.44/5.66 thf(fact_4709_diff__minus__eq__add,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_minus_eq_add
% 5.44/5.66 thf(fact_4710_uminus__add__conv__diff,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.44/5.66 = ( minus_minus_real @ B @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_add_conv_diff
% 5.44/5.66 thf(fact_4711_uminus__add__conv__diff,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.44/5.66 = ( minus_minus_int @ B @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_add_conv_diff
% 5.44/5.66 thf(fact_4712_uminus__add__conv__diff,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.44/5.66 = ( minus_minus_complex @ B @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_add_conv_diff
% 5.44/5.66 thf(fact_4713_uminus__add__conv__diff,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.44/5.66 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_add_conv_diff
% 5.44/5.66 thf(fact_4714_div__minus1__right,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( uminus_uminus_int @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % div_minus1_right
% 5.44/5.66 thf(fact_4715_div__minus1__right,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % div_minus1_right
% 5.44/5.66 thf(fact_4716_divide__minus1,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = ( uminus_uminus_real @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_minus1
% 5.44/5.66 thf(fact_4717_divide__minus1,axiom,
% 5.44/5.66 ! [X: complex] :
% 5.44/5.66 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_minus1
% 5.44/5.66 thf(fact_4718_minus__mod__self1,axiom,
% 5.44/5.66 ! [B: int,A: int] :
% 5.44/5.66 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.44/5.66 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mod_self1
% 5.44/5.66 thf(fact_4719_minus__mod__self1,axiom,
% 5.44/5.66 ! [B: code_integer,A: code_integer] :
% 5.44/5.66 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.44/5.66 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mod_self1
% 5.44/5.66 thf(fact_4720_ln__le__cancel__iff,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.66 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.44/5.66 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_le_cancel_iff
% 5.44/5.66 thf(fact_4721_take__bit__0,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_0
% 5.44/5.66 thf(fact_4722_take__bit__0,axiom,
% 5.44/5.66 ! [A: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.44/5.66 = zero_zero_nat ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_0
% 5.44/5.66 thf(fact_4723_ln__less__zero__iff,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.44/5.66 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_less_zero_iff
% 5.44/5.66 thf(fact_4724_ln__gt__zero__iff,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.44/5.66 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_gt_zero_iff
% 5.44/5.66 thf(fact_4725_ln__eq__zero__iff,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ( ln_ln_real @ X )
% 5.44/5.66 = zero_zero_real )
% 5.44/5.66 = ( X = one_one_real ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_eq_zero_iff
% 5.44/5.66 thf(fact_4726_take__bit__Suc__1,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_1
% 5.44/5.66 thf(fact_4727_take__bit__Suc__1,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.44/5.66 = one_one_nat ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_1
% 5.44/5.66 thf(fact_4728_take__bit__numeral__1,axiom,
% 5.44/5.66 ! [L2: num] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_numeral_1
% 5.44/5.66 thf(fact_4729_take__bit__numeral__1,axiom,
% 5.44/5.66 ! [L2: num] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 5.44/5.66 = one_one_nat ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_numeral_1
% 5.44/5.66 thf(fact_4730_ln__one,axiom,
% 5.44/5.66 ( ( ln_ln_real @ one_one_real )
% 5.44/5.66 = zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % ln_one
% 5.44/5.66 thf(fact_4731_signed__take__bit__of__minus__1,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_of_minus_1
% 5.44/5.66 thf(fact_4732_signed__take__bit__of__minus__1,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_of_minus_1
% 5.44/5.66 thf(fact_4733_dbl__simps_I1_J,axiom,
% 5.44/5.66 ! [K: num] :
% 5.44/5.66 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dbl_simps(1)
% 5.44/5.66 thf(fact_4734_dbl__simps_I1_J,axiom,
% 5.44/5.66 ! [K: num] :
% 5.44/5.66 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dbl_simps(1)
% 5.44/5.66 thf(fact_4735_dbl__simps_I1_J,axiom,
% 5.44/5.66 ! [K: num] :
% 5.44/5.66 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dbl_simps(1)
% 5.44/5.66 thf(fact_4736_dbl__simps_I1_J,axiom,
% 5.44/5.66 ! [K: num] :
% 5.44/5.66 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dbl_simps(1)
% 5.44/5.66 thf(fact_4737_add__neg__numeral__special_I7_J,axiom,
% 5.44/5.66 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(7)
% 5.44/5.66 thf(fact_4738_add__neg__numeral__special_I7_J,axiom,
% 5.44/5.66 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(7)
% 5.44/5.66 thf(fact_4739_add__neg__numeral__special_I7_J,axiom,
% 5.44/5.66 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = zero_zero_complex ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(7)
% 5.44/5.66 thf(fact_4740_add__neg__numeral__special_I7_J,axiom,
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(7)
% 5.44/5.66 thf(fact_4741_add__neg__numeral__special_I8_J,axiom,
% 5.44/5.66 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.44/5.66 = zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(8)
% 5.44/5.66 thf(fact_4742_add__neg__numeral__special_I8_J,axiom,
% 5.44/5.66 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(8)
% 5.44/5.66 thf(fact_4743_add__neg__numeral__special_I8_J,axiom,
% 5.44/5.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.44/5.66 = zero_zero_complex ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(8)
% 5.44/5.66 thf(fact_4744_add__neg__numeral__special_I8_J,axiom,
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(8)
% 5.44/5.66 thf(fact_4745_diff__numeral__special_I12_J,axiom,
% 5.44/5.66 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(12)
% 5.44/5.66 thf(fact_4746_diff__numeral__special_I12_J,axiom,
% 5.44/5.66 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(12)
% 5.44/5.66 thf(fact_4747_diff__numeral__special_I12_J,axiom,
% 5.44/5.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = zero_zero_complex ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(12)
% 5.44/5.66 thf(fact_4748_diff__numeral__special_I12_J,axiom,
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(12)
% 5.44/5.66 thf(fact_4749_numeral__eq__neg__one__iff,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.66 = ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = ( N2 = one ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_eq_neg_one_iff
% 5.44/5.66 thf(fact_4750_numeral__eq__neg__one__iff,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.66 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( N2 = one ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_eq_neg_one_iff
% 5.44/5.66 thf(fact_4751_numeral__eq__neg__one__iff,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = ( N2 = one ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_eq_neg_one_iff
% 5.44/5.66 thf(fact_4752_numeral__eq__neg__one__iff,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( N2 = one ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_eq_neg_one_iff
% 5.44/5.66 thf(fact_4753_neg__one__eq__numeral__iff,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( ( uminus_uminus_real @ one_one_real )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( N2 = one ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_eq_numeral_iff
% 5.44/5.66 thf(fact_4754_neg__one__eq__numeral__iff,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( ( uminus_uminus_int @ one_one_int )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( N2 = one ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_eq_numeral_iff
% 5.44/5.66 thf(fact_4755_neg__one__eq__numeral__iff,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.44/5.66 = ( N2 = one ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_eq_numeral_iff
% 5.44/5.66 thf(fact_4756_neg__one__eq__numeral__iff,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( N2 = one ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_eq_numeral_iff
% 5.44/5.66 thf(fact_4757_left__minus__one__mult__self,axiom,
% 5.44/5.66 ! [N2: nat,A: real] :
% 5.44/5.66 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ A ) )
% 5.44/5.66 = A ) ).
% 5.44/5.66
% 5.44/5.66 % left_minus_one_mult_self
% 5.44/5.66 thf(fact_4758_left__minus__one__mult__self,axiom,
% 5.44/5.66 ! [N2: nat,A: int] :
% 5.44/5.66 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 5.44/5.66 = A ) ).
% 5.44/5.66
% 5.44/5.66 % left_minus_one_mult_self
% 5.44/5.66 thf(fact_4759_left__minus__one__mult__self,axiom,
% 5.44/5.66 ! [N2: nat,A: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ A ) )
% 5.44/5.66 = A ) ).
% 5.44/5.66
% 5.44/5.66 % left_minus_one_mult_self
% 5.44/5.66 thf(fact_4760_left__minus__one__mult__self,axiom,
% 5.44/5.66 ! [N2: nat,A: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 5.44/5.66 = A ) ).
% 5.44/5.66
% 5.44/5.66 % left_minus_one_mult_self
% 5.44/5.66 thf(fact_4761_minus__one__mult__self,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) )
% 5.44/5.66 = one_one_real ) ).
% 5.44/5.66
% 5.44/5.66 % minus_one_mult_self
% 5.44/5.66 thf(fact_4762_minus__one__mult__self,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % minus_one_mult_self
% 5.44/5.66 thf(fact_4763_minus__one__mult__self,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) )
% 5.44/5.66 = one_one_complex ) ).
% 5.44/5.66
% 5.44/5.66 % minus_one_mult_self
% 5.44/5.66 thf(fact_4764_minus__one__mult__self,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 5.44/5.66 = one_one_Code_integer ) ).
% 5.44/5.66
% 5.44/5.66 % minus_one_mult_self
% 5.44/5.66 thf(fact_4765_mod__minus1__right,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus1_right
% 5.44/5.66 thf(fact_4766_mod__minus1__right,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus1_right
% 5.44/5.66 thf(fact_4767_max__number__of_I4_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(4)
% 5.44/5.66 thf(fact_4768_max__number__of_I4_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.44/5.66 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(4)
% 5.44/5.66 thf(fact_4769_max__number__of_I4_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(4)
% 5.44/5.66 thf(fact_4770_max__number__of_I3_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.66 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.66 = ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.66 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(3)
% 5.44/5.66 thf(fact_4771_max__number__of_I3_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.44/5.66 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.44/5.66 = ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.44/5.66 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(3)
% 5.44/5.66 thf(fact_4772_max__number__of_I3_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.66 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.66 = ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.66 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(3)
% 5.44/5.66 thf(fact_4773_max__number__of_I2_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.66 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(2)
% 5.44/5.66 thf(fact_4774_max__number__of_I2_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.44/5.66 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.44/5.66 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(2)
% 5.44/5.66 thf(fact_4775_max__number__of_I2_J,axiom,
% 5.44/5.66 ! [U: num,V: num] :
% 5.44/5.66 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.66 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % max_number_of(2)
% 5.44/5.66 thf(fact_4776_take__bit__of__1__eq__0__iff,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.44/5.66 = zero_zero_int )
% 5.44/5.66 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_1_eq_0_iff
% 5.44/5.66 thf(fact_4777_take__bit__of__1__eq__0__iff,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.44/5.66 = zero_zero_nat )
% 5.44/5.66 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_1_eq_0_iff
% 5.44/5.66 thf(fact_4778_ln__le__zero__iff,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.44/5.66 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_le_zero_iff
% 5.44/5.66 thf(fact_4779_ln__ge__zero__iff,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.44/5.66 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_ge_zero_iff
% 5.44/5.66 thf(fact_4780_semiring__norm_I168_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: real] :
% 5.44/5.66 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.44/5.66 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(168)
% 5.44/5.66 thf(fact_4781_semiring__norm_I168_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: int] :
% 5.44/5.66 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.44/5.66 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(168)
% 5.44/5.66 thf(fact_4782_semiring__norm_I168_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: complex] :
% 5.44/5.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.44/5.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(168)
% 5.44/5.66 thf(fact_4783_semiring__norm_I168_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: code_integer] :
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(168)
% 5.44/5.66 thf(fact_4784_diff__numeral__simps_I2_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_simps(2)
% 5.44/5.66 thf(fact_4785_diff__numeral__simps_I2_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_simps(2)
% 5.44/5.66 thf(fact_4786_diff__numeral__simps_I2_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.44/5.66 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_simps(2)
% 5.44/5.66 thf(fact_4787_diff__numeral__simps_I2_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_simps(2)
% 5.44/5.66 thf(fact_4788_diff__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_simps(3)
% 5.44/5.66 thf(fact_4789_diff__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_simps(3)
% 5.44/5.66 thf(fact_4790_diff__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_simps(3)
% 5.44/5.66 thf(fact_4791_diff__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_simps(3)
% 5.44/5.66 thf(fact_4792_semiring__norm_I170_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: real] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 5.44/5.66 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(170)
% 5.44/5.66 thf(fact_4793_semiring__norm_I170_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: int] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 5.44/5.66 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(170)
% 5.44/5.66 thf(fact_4794_semiring__norm_I170_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 5.44/5.66 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(170)
% 5.44/5.66 thf(fact_4795_semiring__norm_I170_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(170)
% 5.44/5.66 thf(fact_4796_semiring__norm_I171_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: real] :
% 5.44/5.66 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.44/5.66 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(171)
% 5.44/5.66 thf(fact_4797_semiring__norm_I171_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: int] :
% 5.44/5.66 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.44/5.66 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(171)
% 5.44/5.66 thf(fact_4798_semiring__norm_I171_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.44/5.66 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(171)
% 5.44/5.66 thf(fact_4799_semiring__norm_I171_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(171)
% 5.44/5.66 thf(fact_4800_semiring__norm_I172_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: real] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.44/5.66 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(172)
% 5.44/5.66 thf(fact_4801_semiring__norm_I172_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: int] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.44/5.66 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(172)
% 5.44/5.66 thf(fact_4802_semiring__norm_I172_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.44/5.66 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(172)
% 5.44/5.66 thf(fact_4803_semiring__norm_I172_J,axiom,
% 5.44/5.66 ! [V: num,W: num,Y: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % semiring_norm(172)
% 5.44/5.66 thf(fact_4804_mult__neg__numeral__simps_I1_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(1)
% 5.44/5.66 thf(fact_4805_mult__neg__numeral__simps_I1_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(1)
% 5.44/5.66 thf(fact_4806_mult__neg__numeral__simps_I1_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.44/5.66 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(1)
% 5.44/5.66 thf(fact_4807_mult__neg__numeral__simps_I1_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(1)
% 5.44/5.66 thf(fact_4808_mult__neg__numeral__simps_I2_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(2)
% 5.44/5.66 thf(fact_4809_mult__neg__numeral__simps_I2_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(2)
% 5.44/5.66 thf(fact_4810_mult__neg__numeral__simps_I2_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(2)
% 5.44/5.66 thf(fact_4811_mult__neg__numeral__simps_I2_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(2)
% 5.44/5.66 thf(fact_4812_mult__neg__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(3)
% 5.44/5.66 thf(fact_4813_mult__neg__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(3)
% 5.44/5.66 thf(fact_4814_mult__neg__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(3)
% 5.44/5.66 thf(fact_4815_mult__neg__numeral__simps_I3_J,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_neg_numeral_simps(3)
% 5.44/5.66 thf(fact_4816_neg__numeral__le__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_iff
% 5.44/5.66 thf(fact_4817_neg__numeral__le__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_iff
% 5.44/5.66 thf(fact_4818_neg__numeral__le__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_iff
% 5.44/5.66 thf(fact_4819_neg__numeral__less__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( ord_less_num @ N2 @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_iff
% 5.44/5.66 thf(fact_4820_neg__numeral__less__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( ord_less_num @ N2 @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_iff
% 5.44/5.66 thf(fact_4821_neg__numeral__less__iff,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( ord_less_num @ N2 @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_iff
% 5.44/5.66 thf(fact_4822_take__bit__of__Suc__0,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.44/5.66 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_Suc_0
% 5.44/5.66 thf(fact_4823_not__neg__one__le__neg__numeral__iff,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.44/5.66 = ( M != one ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_neg_one_le_neg_numeral_iff
% 5.44/5.66 thf(fact_4824_not__neg__one__le__neg__numeral__iff,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.44/5.66 = ( M != one ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_neg_one_le_neg_numeral_iff
% 5.44/5.66 thf(fact_4825_not__neg__one__le__neg__numeral__iff,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.44/5.66 = ( M != one ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_neg_one_le_neg_numeral_iff
% 5.44/5.66 thf(fact_4826_le__divide__eq__numeral1_I2_J,axiom,
% 5.44/5.66 ! [A: real,B: real,W: num] :
% 5.44/5.66 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.44/5.66 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_divide_eq_numeral1(2)
% 5.44/5.66 thf(fact_4827_divide__le__eq__numeral1_I2_J,axiom,
% 5.44/5.66 ! [B: real,W: num,A: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.44/5.66 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_le_eq_numeral1(2)
% 5.44/5.66 thf(fact_4828_eq__divide__eq__numeral1_I2_J,axiom,
% 5.44/5.66 ! [A: real,B: real,W: num] :
% 5.44/5.66 ( ( A
% 5.44/5.66 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.44/5.66 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.66 != zero_zero_real )
% 5.44/5.66 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.66 = B ) )
% 5.44/5.66 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.66 = zero_zero_real )
% 5.44/5.66 => ( A = zero_zero_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_divide_eq_numeral1(2)
% 5.44/5.66 thf(fact_4829_eq__divide__eq__numeral1_I2_J,axiom,
% 5.44/5.66 ! [A: complex,B: complex,W: num] :
% 5.44/5.66 ( ( A
% 5.44/5.66 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.44/5.66 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.66 != zero_zero_complex )
% 5.44/5.66 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.66 = B ) )
% 5.44/5.66 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.66 = zero_zero_complex )
% 5.44/5.66 => ( A = zero_zero_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_divide_eq_numeral1(2)
% 5.44/5.66 thf(fact_4830_divide__eq__eq__numeral1_I2_J,axiom,
% 5.44/5.66 ! [B: real,W: num,A: real] :
% 5.44/5.66 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.66 = A )
% 5.44/5.66 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.66 != zero_zero_real )
% 5.44/5.66 => ( B
% 5.44/5.66 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.44/5.66 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.66 = zero_zero_real )
% 5.44/5.66 => ( A = zero_zero_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_eq_eq_numeral1(2)
% 5.44/5.66 thf(fact_4831_divide__eq__eq__numeral1_I2_J,axiom,
% 5.44/5.66 ! [B: complex,W: num,A: complex] :
% 5.44/5.66 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.66 = A )
% 5.44/5.66 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.66 != zero_zero_complex )
% 5.44/5.66 => ( B
% 5.44/5.66 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.44/5.66 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.66 = zero_zero_complex )
% 5.44/5.66 => ( A = zero_zero_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_eq_eq_numeral1(2)
% 5.44/5.66 thf(fact_4832_neg__numeral__less__neg__one__iff,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = ( M != one ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_neg_one_iff
% 5.44/5.66 thf(fact_4833_neg__numeral__less__neg__one__iff,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( M != one ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_neg_one_iff
% 5.44/5.66 thf(fact_4834_neg__numeral__less__neg__one__iff,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( M != one ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_neg_one_iff
% 5.44/5.66 thf(fact_4835_less__divide__eq__numeral1_I2_J,axiom,
% 5.44/5.66 ! [A: real,B: real,W: num] :
% 5.44/5.66 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.44/5.66 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_divide_eq_numeral1(2)
% 5.44/5.66 thf(fact_4836_divide__less__eq__numeral1_I2_J,axiom,
% 5.44/5.66 ! [B: real,W: num,A: real] :
% 5.44/5.66 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.44/5.66 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_less_eq_numeral1(2)
% 5.44/5.66 thf(fact_4837_power2__minus,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_minus
% 5.44/5.66 thf(fact_4838_power2__minus,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_minus
% 5.44/5.66 thf(fact_4839_power2__minus,axiom,
% 5.44/5.66 ! [A: complex] :
% 5.44/5.66 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_minus
% 5.44/5.66 thf(fact_4840_power2__minus,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_minus
% 5.44/5.66 thf(fact_4841_take__bit__of__1,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 5.44/5.66 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_1
% 5.44/5.66 thf(fact_4842_take__bit__of__1,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.44/5.66 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_1
% 5.44/5.66 thf(fact_4843_take__bit__of__1,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.44/5.66 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_1
% 5.44/5.66 thf(fact_4844_add__neg__numeral__special_I9_J,axiom,
% 5.44/5.66 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(9)
% 5.44/5.66 thf(fact_4845_add__neg__numeral__special_I9_J,axiom,
% 5.44/5.66 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(9)
% 5.44/5.66 thf(fact_4846_add__neg__numeral__special_I9_J,axiom,
% 5.44/5.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(9)
% 5.44/5.66 thf(fact_4847_add__neg__numeral__special_I9_J,axiom,
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_neg_numeral_special(9)
% 5.44/5.66 thf(fact_4848_diff__numeral__special_I10_J,axiom,
% 5.44/5.66 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(10)
% 5.44/5.66 thf(fact_4849_diff__numeral__special_I10_J,axiom,
% 5.44/5.66 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(10)
% 5.44/5.66 thf(fact_4850_diff__numeral__special_I10_J,axiom,
% 5.44/5.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(10)
% 5.44/5.66 thf(fact_4851_diff__numeral__special_I10_J,axiom,
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(10)
% 5.44/5.66 thf(fact_4852_diff__numeral__special_I11_J,axiom,
% 5.44/5.66 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(11)
% 5.44/5.66 thf(fact_4853_diff__numeral__special_I11_J,axiom,
% 5.44/5.66 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(11)
% 5.44/5.66 thf(fact_4854_diff__numeral__special_I11_J,axiom,
% 5.44/5.66 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(11)
% 5.44/5.66 thf(fact_4855_diff__numeral__special_I11_J,axiom,
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(11)
% 5.44/5.66 thf(fact_4856_minus__1__div__2__eq,axiom,
% 5.44/5.66 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_1_div_2_eq
% 5.44/5.66 thf(fact_4857_minus__1__div__2__eq,axiom,
% 5.44/5.66 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_1_div_2_eq
% 5.44/5.66 thf(fact_4858_minus__1__mod__2__eq,axiom,
% 5.44/5.66 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % minus_1_mod_2_eq
% 5.44/5.66 thf(fact_4859_minus__1__mod__2__eq,axiom,
% 5.44/5.66 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.66 = one_one_Code_integer ) ).
% 5.44/5.66
% 5.44/5.66 % minus_1_mod_2_eq
% 5.44/5.66 thf(fact_4860_bits__minus__1__mod__2__eq,axiom,
% 5.44/5.66 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % bits_minus_1_mod_2_eq
% 5.44/5.66 thf(fact_4861_bits__minus__1__mod__2__eq,axiom,
% 5.44/5.66 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.66 = one_one_Code_integer ) ).
% 5.44/5.66
% 5.44/5.66 % bits_minus_1_mod_2_eq
% 5.44/5.66 thf(fact_4862_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.44/5.66 ! [A: real,N2: nat] :
% 5.44/5.66 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Power.ring_1_class.power_minus_even
% 5.44/5.66 thf(fact_4863_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.44/5.66 ! [A: int,N2: nat] :
% 5.44/5.66 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Power.ring_1_class.power_minus_even
% 5.44/5.66 thf(fact_4864_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.44/5.66 ! [A: complex,N2: nat] :
% 5.44/5.66 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Power.ring_1_class.power_minus_even
% 5.44/5.66 thf(fact_4865_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.44/5.66 ! [A: code_integer,N2: nat] :
% 5.44/5.66 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Power.ring_1_class.power_minus_even
% 5.44/5.66 thf(fact_4866_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.44/5.66 ! [N2: nat,A: real] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.44/5.66 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Parity.ring_1_class.power_minus_even
% 5.44/5.66 thf(fact_4867_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.44/5.66 ! [N2: nat,A: int] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.44/5.66 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Parity.ring_1_class.power_minus_even
% 5.44/5.66 thf(fact_4868_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.44/5.66 ! [N2: nat,A: complex] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.44/5.66 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Parity.ring_1_class.power_minus_even
% 5.44/5.66 thf(fact_4869_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.44/5.66 ! [N2: nat,A: code_integer] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.44/5.66 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % Parity.ring_1_class.power_minus_even
% 5.44/5.66 thf(fact_4870_power__minus__odd,axiom,
% 5.44/5.66 ! [N2: nat,A: real] :
% 5.44/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.44/5.66 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus_odd
% 5.44/5.66 thf(fact_4871_power__minus__odd,axiom,
% 5.44/5.66 ! [N2: nat,A: int] :
% 5.44/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.44/5.66 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus_odd
% 5.44/5.66 thf(fact_4872_power__minus__odd,axiom,
% 5.44/5.66 ! [N2: nat,A: complex] :
% 5.44/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus_odd
% 5.44/5.66 thf(fact_4873_power__minus__odd,axiom,
% 5.44/5.66 ! [N2: nat,A: code_integer] :
% 5.44/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus_odd
% 5.44/5.66 thf(fact_4874_even__take__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,A: code_integer] :
% 5.44/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 5.44/5.66 = ( ( N2 = zero_zero_nat )
% 5.44/5.66 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % even_take_bit_eq
% 5.44/5.66 thf(fact_4875_even__take__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,A: int] :
% 5.44/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.44/5.66 = ( ( N2 = zero_zero_nat )
% 5.44/5.66 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % even_take_bit_eq
% 5.44/5.66 thf(fact_4876_even__take__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,A: nat] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 5.44/5.66 = ( ( N2 = zero_zero_nat )
% 5.44/5.66 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % even_take_bit_eq
% 5.44/5.66 thf(fact_4877_diff__numeral__special_I4_J,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(4)
% 5.44/5.66 thf(fact_4878_diff__numeral__special_I4_J,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(4)
% 5.44/5.66 thf(fact_4879_diff__numeral__special_I4_J,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(4)
% 5.44/5.66 thf(fact_4880_diff__numeral__special_I4_J,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(4)
% 5.44/5.66 thf(fact_4881_diff__numeral__special_I3_J,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.66 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(3)
% 5.44/5.66 thf(fact_4882_diff__numeral__special_I3_J,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.66 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(3)
% 5.44/5.66 thf(fact_4883_diff__numeral__special_I3_J,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.44/5.66 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(3)
% 5.44/5.66 thf(fact_4884_diff__numeral__special_I3_J,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.66 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_numeral_special(3)
% 5.44/5.66 thf(fact_4885_signed__take__bit__Suc__minus__bit0,axiom,
% 5.44/5.66 ! [N2: nat,K: num] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.44/5.66 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_Suc_minus_bit0
% 5.44/5.66 thf(fact_4886_dbl__simps_I4_J,axiom,
% 5.44/5.66 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dbl_simps(4)
% 5.44/5.66 thf(fact_4887_dbl__simps_I4_J,axiom,
% 5.44/5.66 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dbl_simps(4)
% 5.44/5.66 thf(fact_4888_dbl__simps_I4_J,axiom,
% 5.44/5.66 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dbl_simps(4)
% 5.44/5.66 thf(fact_4889_dbl__simps_I4_J,axiom,
% 5.44/5.66 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dbl_simps(4)
% 5.44/5.66 thf(fact_4890_power__minus1__even,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = one_one_real ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus1_even
% 5.44/5.66 thf(fact_4891_power__minus1__even,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus1_even
% 5.44/5.66 thf(fact_4892_power__minus1__even,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = one_one_complex ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus1_even
% 5.44/5.66 thf(fact_4893_power__minus1__even,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = one_one_Code_integer ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus1_even
% 5.44/5.66 thf(fact_4894_neg__one__even__power,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.44/5.66 = one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_even_power
% 5.44/5.66 thf(fact_4895_neg__one__even__power,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.44/5.66 = one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_even_power
% 5.44/5.66 thf(fact_4896_neg__one__even__power,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.44/5.66 = one_one_complex ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_even_power
% 5.44/5.66 thf(fact_4897_neg__one__even__power,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.44/5.66 = one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_even_power
% 5.44/5.66 thf(fact_4898_neg__one__odd__power,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.44/5.66 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_odd_power
% 5.44/5.66 thf(fact_4899_neg__one__odd__power,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.44/5.66 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_odd_power
% 5.44/5.66 thf(fact_4900_neg__one__odd__power,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_odd_power
% 5.44/5.66 thf(fact_4901_neg__one__odd__power,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_odd_power
% 5.44/5.66 thf(fact_4902_take__bit__Suc__0,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.44/5.66 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_0
% 5.44/5.66 thf(fact_4903_take__bit__Suc__0,axiom,
% 5.44/5.66 ! [A: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.44/5.66 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_0
% 5.44/5.66 thf(fact_4904_signed__take__bit__0,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_0
% 5.44/5.66 thf(fact_4905_signed__take__bit__0,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.44/5.66 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_0
% 5.44/5.66 thf(fact_4906_take__bit__of__exp,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_exp
% 5.44/5.66 thf(fact_4907_take__bit__of__exp,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_exp
% 5.44/5.66 thf(fact_4908_take__bit__of__exp,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_exp
% 5.44/5.66 thf(fact_4909_take__bit__of__2,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_2
% 5.44/5.66 thf(fact_4910_take__bit__of__2,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_2
% 5.44/5.66 thf(fact_4911_take__bit__of__2,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_of_2
% 5.44/5.66 thf(fact_4912_signed__take__bit__minus,axiom,
% 5.44/5.66 ! [N2: nat,K: int] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) )
% 5.44/5.66 = ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_minus
% 5.44/5.66 thf(fact_4913_take__bit__add,axiom,
% 5.44/5.66 ! [N2: nat,A: int,B: int] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_add
% 5.44/5.66 thf(fact_4914_take__bit__add,axiom,
% 5.44/5.66 ! [N2: nat,A: nat,B: nat] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 5.44/5.66 = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_add
% 5.44/5.66 thf(fact_4915_take__bit__tightened,axiom,
% 5.44/5.66 ! [N2: nat,A: int,B: int,M: nat] :
% 5.44/5.66 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.44/5.66 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_tightened
% 5.44/5.66 thf(fact_4916_take__bit__tightened,axiom,
% 5.44/5.66 ! [N2: nat,A: nat,B: nat,M: nat] :
% 5.44/5.66 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.44/5.66 = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 5.44/5.66 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.66 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.44/5.66 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_tightened
% 5.44/5.66 thf(fact_4917_take__bit__nat__less__eq__self,axiom,
% 5.44/5.66 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_nat_less_eq_self
% 5.44/5.66 thf(fact_4918_take__bit__tightened__less__eq__nat,axiom,
% 5.44/5.66 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.66 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.66 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_tightened_less_eq_nat
% 5.44/5.66 thf(fact_4919_take__bit__mult,axiom,
% 5.44/5.66 ! [N2: nat,K: int,L2: int] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L2 ) ) )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_mult
% 5.44/5.66 thf(fact_4920_le__minus__iff,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_iff
% 5.44/5.66 thf(fact_4921_le__minus__iff,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_iff
% 5.44/5.66 thf(fact_4922_le__minus__iff,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_iff
% 5.44/5.66 thf(fact_4923_minus__le__iff,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.44/5.66 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_le_iff
% 5.44/5.66 thf(fact_4924_minus__le__iff,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.44/5.66 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_le_iff
% 5.44/5.66 thf(fact_4925_minus__le__iff,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.44/5.66 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_le_iff
% 5.44/5.66 thf(fact_4926_le__imp__neg__le,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.66 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_imp_neg_le
% 5.44/5.66 thf(fact_4927_le__imp__neg__le,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.44/5.66 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_imp_neg_le
% 5.44/5.66 thf(fact_4928_le__imp__neg__le,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.66 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_imp_neg_le
% 5.44/5.66 thf(fact_4929_compl__mono,axiom,
% 5.44/5.66 ! [X: set_real,Y: set_real] :
% 5.44/5.66 ( ( ord_less_eq_set_real @ X @ Y )
% 5.44/5.66 => ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ Y ) @ ( uminus612125837232591019t_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % compl_mono
% 5.44/5.66 thf(fact_4930_compl__mono,axiom,
% 5.44/5.66 ! [X: set_nat,Y: set_nat] :
% 5.44/5.66 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.44/5.66 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % compl_mono
% 5.44/5.66 thf(fact_4931_compl__le__swap1,axiom,
% 5.44/5.66 ! [Y: set_real,X: set_real] :
% 5.44/5.66 ( ( ord_less_eq_set_real @ Y @ ( uminus612125837232591019t_real @ X ) )
% 5.44/5.66 => ( ord_less_eq_set_real @ X @ ( uminus612125837232591019t_real @ Y ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % compl_le_swap1
% 5.44/5.66 thf(fact_4932_compl__le__swap1,axiom,
% 5.44/5.66 ! [Y: set_nat,X: set_nat] :
% 5.44/5.66 ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 5.44/5.66 => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % compl_le_swap1
% 5.44/5.66 thf(fact_4933_compl__le__swap2,axiom,
% 5.44/5.66 ! [Y: set_real,X: set_real] :
% 5.44/5.66 ( ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ Y ) @ X )
% 5.44/5.66 => ( ord_less_eq_set_real @ ( uminus612125837232591019t_real @ X ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % compl_le_swap2
% 5.44/5.66 thf(fact_4934_compl__le__swap2,axiom,
% 5.44/5.66 ! [Y: set_nat,X: set_nat] :
% 5.44/5.66 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 5.44/5.66 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % compl_le_swap2
% 5.44/5.66 thf(fact_4935_minus__less__iff,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.44/5.66 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_less_iff
% 5.44/5.66 thf(fact_4936_minus__less__iff,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.44/5.66 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_less_iff
% 5.44/5.66 thf(fact_4937_minus__less__iff,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.44/5.66 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_less_iff
% 5.44/5.66 thf(fact_4938_less__minus__iff,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_iff
% 5.44/5.66 thf(fact_4939_less__minus__iff,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_iff
% 5.44/5.66 thf(fact_4940_less__minus__iff,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_iff
% 5.44/5.66 thf(fact_4941_verit__negate__coefficient_I2_J,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ord_less_real @ A @ B )
% 5.44/5.66 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % verit_negate_coefficient(2)
% 5.44/5.66 thf(fact_4942_verit__negate__coefficient_I2_J,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ord_less_int @ A @ B )
% 5.44/5.66 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % verit_negate_coefficient(2)
% 5.44/5.66 thf(fact_4943_verit__negate__coefficient_I2_J,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.44/5.66 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % verit_negate_coefficient(2)
% 5.44/5.66 thf(fact_4944_numeral__neq__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( numeral_numeral_real @ M )
% 5.44/5.66 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_neq_neg_numeral
% 5.44/5.66 thf(fact_4945_numeral__neq__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( numeral_numeral_int @ M )
% 5.44/5.66 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_neq_neg_numeral
% 5.44/5.66 thf(fact_4946_numeral__neq__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( numera6690914467698888265omplex @ M )
% 5.44/5.66 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_neq_neg_numeral
% 5.44/5.66 thf(fact_4947_numeral__neq__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( numera6620942414471956472nteger @ M )
% 5.44/5.66 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_neq_neg_numeral
% 5.44/5.66 thf(fact_4948_neg__numeral__neq__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.44/5.66 != ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_neq_numeral
% 5.44/5.66 thf(fact_4949_neg__numeral__neq__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.44/5.66 != ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_neq_numeral
% 5.44/5.66 thf(fact_4950_neg__numeral__neq__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.44/5.66 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_neq_numeral
% 5.44/5.66 thf(fact_4951_neg__numeral__neq__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.44/5.66 != ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_neq_numeral
% 5.44/5.66 thf(fact_4952_minus__mult__commute,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.44/5.66 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mult_commute
% 5.44/5.66 thf(fact_4953_minus__mult__commute,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.44/5.66 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mult_commute
% 5.44/5.66 thf(fact_4954_minus__mult__commute,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.44/5.66 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mult_commute
% 5.44/5.66 thf(fact_4955_minus__mult__commute,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.44/5.66 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_mult_commute
% 5.44/5.66 thf(fact_4956_square__eq__iff,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ( times_times_real @ A @ A )
% 5.44/5.66 = ( times_times_real @ B @ B ) )
% 5.44/5.66 = ( ( A = B )
% 5.44/5.66 | ( A
% 5.44/5.66 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % square_eq_iff
% 5.44/5.66 thf(fact_4957_square__eq__iff,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ( times_times_int @ A @ A )
% 5.44/5.66 = ( times_times_int @ B @ B ) )
% 5.44/5.66 = ( ( A = B )
% 5.44/5.66 | ( A
% 5.44/5.66 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % square_eq_iff
% 5.44/5.66 thf(fact_4958_square__eq__iff,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( ( times_times_complex @ A @ A )
% 5.44/5.66 = ( times_times_complex @ B @ B ) )
% 5.44/5.66 = ( ( A = B )
% 5.44/5.66 | ( A
% 5.44/5.66 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % square_eq_iff
% 5.44/5.66 thf(fact_4959_square__eq__iff,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.44/5.66 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.44/5.66 = ( ( A = B )
% 5.44/5.66 | ( A
% 5.44/5.66 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % square_eq_iff
% 5.44/5.66 thf(fact_4960_add_Oinverse__distrib__swap,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.44/5.66 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add.inverse_distrib_swap
% 5.44/5.66 thf(fact_4961_add_Oinverse__distrib__swap,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.44/5.66 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add.inverse_distrib_swap
% 5.44/5.66 thf(fact_4962_add_Oinverse__distrib__swap,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.44/5.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add.inverse_distrib_swap
% 5.44/5.66 thf(fact_4963_add_Oinverse__distrib__swap,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add.inverse_distrib_swap
% 5.44/5.66 thf(fact_4964_group__cancel_Oneg1,axiom,
% 5.44/5.66 ! [A2: real,K: real,A: real] :
% 5.44/5.66 ( ( A2
% 5.44/5.66 = ( plus_plus_real @ K @ A ) )
% 5.44/5.66 => ( ( uminus_uminus_real @ A2 )
% 5.44/5.66 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % group_cancel.neg1
% 5.44/5.66 thf(fact_4965_group__cancel_Oneg1,axiom,
% 5.44/5.66 ! [A2: int,K: int,A: int] :
% 5.44/5.66 ( ( A2
% 5.44/5.66 = ( plus_plus_int @ K @ A ) )
% 5.44/5.66 => ( ( uminus_uminus_int @ A2 )
% 5.44/5.66 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % group_cancel.neg1
% 5.44/5.66 thf(fact_4966_group__cancel_Oneg1,axiom,
% 5.44/5.66 ! [A2: complex,K: complex,A: complex] :
% 5.44/5.66 ( ( A2
% 5.44/5.66 = ( plus_plus_complex @ K @ A ) )
% 5.44/5.66 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.44/5.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % group_cancel.neg1
% 5.44/5.66 thf(fact_4967_group__cancel_Oneg1,axiom,
% 5.44/5.66 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.44/5.66 ( ( A2
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.44/5.66 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % group_cancel.neg1
% 5.44/5.66 thf(fact_4968_is__num__normalize_I8_J,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.44/5.66 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % is_num_normalize(8)
% 5.44/5.66 thf(fact_4969_is__num__normalize_I8_J,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.44/5.66 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % is_num_normalize(8)
% 5.44/5.66 thf(fact_4970_is__num__normalize_I8_J,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.44/5.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % is_num_normalize(8)
% 5.44/5.66 thf(fact_4971_is__num__normalize_I8_J,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % is_num_normalize(8)
% 5.44/5.66 thf(fact_4972_one__neq__neg__one,axiom,
% 5.44/5.66 ( one_one_real
% 5.44/5.66 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_neq_neg_one
% 5.44/5.66 thf(fact_4973_one__neq__neg__one,axiom,
% 5.44/5.66 ( one_one_int
% 5.44/5.66 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_neq_neg_one
% 5.44/5.66 thf(fact_4974_one__neq__neg__one,axiom,
% 5.44/5.66 ( one_one_complex
% 5.44/5.66 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_neq_neg_one
% 5.44/5.66 thf(fact_4975_one__neq__neg__one,axiom,
% 5.44/5.66 ( one_one_Code_integer
% 5.44/5.66 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_neq_neg_one
% 5.44/5.66 thf(fact_4976_take__bit__diff,axiom,
% 5.44/5.66 ! [N2: nat,K: int,L2: int] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L2 ) ) )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_diff
% 5.44/5.66 thf(fact_4977_minus__diff__minus,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_diff_minus
% 5.44/5.66 thf(fact_4978_minus__diff__minus,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_diff_minus
% 5.44/5.66 thf(fact_4979_minus__diff__minus,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_diff_minus
% 5.44/5.66 thf(fact_4980_minus__diff__minus,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_diff_minus
% 5.44/5.66 thf(fact_4981_div__minus__right,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % div_minus_right
% 5.44/5.66 thf(fact_4982_div__minus__right,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % div_minus_right
% 5.44/5.66 thf(fact_4983_minus__divide__left,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.66 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_left
% 5.44/5.66 thf(fact_4984_minus__divide__left,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.66 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_left
% 5.44/5.66 thf(fact_4985_minus__divide__divide,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( divide_divide_real @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_divide
% 5.44/5.66 thf(fact_4986_minus__divide__divide,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.44/5.66 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_divide
% 5.44/5.66 thf(fact_4987_minus__divide__right,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.66 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_right
% 5.44/5.66 thf(fact_4988_minus__divide__right,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.66 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_right
% 5.44/5.66 thf(fact_4989_old_Oprod_Ocase,axiom,
% 5.44/5.66 ! [F: nat > nat > $o,X1: nat,X22: nat] :
% 5.44/5.66 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.44/5.66 = ( F @ X1 @ X22 ) ) ).
% 5.44/5.66
% 5.44/5.66 % old.prod.case
% 5.44/5.66 thf(fact_4990_old_Oprod_Ocase,axiom,
% 5.44/5.66 ! [F: nat > nat > nat,X1: nat,X22: nat] :
% 5.44/5.66 ( ( produc6842872674320459806at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.44/5.66 = ( F @ X1 @ X22 ) ) ).
% 5.44/5.66
% 5.44/5.66 % old.prod.case
% 5.44/5.66 thf(fact_4991_old_Oprod_Ocase,axiom,
% 5.44/5.66 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 5.44/5.66 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.44/5.66 = ( F @ X1 @ X22 ) ) ).
% 5.44/5.66
% 5.44/5.66 % old.prod.case
% 5.44/5.66 thf(fact_4992_old_Oprod_Ocase,axiom,
% 5.44/5.66 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 5.44/5.66 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.44/5.66 = ( F @ X1 @ X22 ) ) ).
% 5.44/5.66
% 5.44/5.66 % old.prod.case
% 5.44/5.66 thf(fact_4993_old_Oprod_Ocase,axiom,
% 5.44/5.66 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 5.44/5.66 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.44/5.66 = ( F @ X1 @ X22 ) ) ).
% 5.44/5.66
% 5.44/5.66 % old.prod.case
% 5.44/5.66 thf(fact_4994_mod__minus__right,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus_right
% 5.44/5.66 thf(fact_4995_mod__minus__right,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus_right
% 5.44/5.66 thf(fact_4996_mod__minus__cong,axiom,
% 5.44/5.66 ! [A: int,B: int,A6: int] :
% 5.44/5.66 ( ( ( modulo_modulo_int @ A @ B )
% 5.44/5.66 = ( modulo_modulo_int @ A6 @ B ) )
% 5.44/5.66 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.44/5.66 = ( modulo_modulo_int @ ( uminus_uminus_int @ A6 ) @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus_cong
% 5.44/5.66 thf(fact_4997_mod__minus__cong,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer,A6: code_integer] :
% 5.44/5.66 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.44/5.66 = ( modulo364778990260209775nteger @ A6 @ B ) )
% 5.44/5.66 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.44/5.66 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A6 ) @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus_cong
% 5.44/5.66 thf(fact_4998_mod__minus__eq,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.44/5.66 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus_eq
% 5.44/5.66 thf(fact_4999_mod__minus__eq,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.44/5.66 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mod_minus_eq
% 5.44/5.66 thf(fact_5000_concat__bit__take__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,B: int] :
% 5.44/5.66 ( ( bit_concat_bit @ N2 @ ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.44/5.66 = ( bit_concat_bit @ N2 @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % concat_bit_take_bit_eq
% 5.44/5.66 thf(fact_5001_concat__bit__eq__iff,axiom,
% 5.44/5.66 ! [N2: nat,K: int,L2: int,R: int,S3: int] :
% 5.44/5.66 ( ( ( bit_concat_bit @ N2 @ K @ L2 )
% 5.44/5.66 = ( bit_concat_bit @ N2 @ R @ S3 ) )
% 5.44/5.66 = ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ R ) )
% 5.44/5.66 & ( L2 = S3 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % concat_bit_eq_iff
% 5.44/5.66 thf(fact_5002_cond__case__prod__eta,axiom,
% 5.44/5.66 ! [F: nat > nat > $o,G: product_prod_nat_nat > $o] :
% 5.44/5.66 ( ! [X5: nat,Y5: nat] :
% 5.44/5.66 ( ( F @ X5 @ Y5 )
% 5.44/5.66 = ( G @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
% 5.44/5.66 => ( ( produc6081775807080527818_nat_o @ F )
% 5.44/5.66 = G ) ) ).
% 5.44/5.66
% 5.44/5.66 % cond_case_prod_eta
% 5.44/5.66 thf(fact_5003_cond__case__prod__eta,axiom,
% 5.44/5.66 ! [F: nat > nat > nat,G: product_prod_nat_nat > nat] :
% 5.44/5.66 ( ! [X5: nat,Y5: nat] :
% 5.44/5.66 ( ( F @ X5 @ Y5 )
% 5.44/5.66 = ( G @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
% 5.44/5.66 => ( ( produc6842872674320459806at_nat @ F )
% 5.44/5.66 = G ) ) ).
% 5.44/5.66
% 5.44/5.66 % cond_case_prod_eta
% 5.44/5.66 thf(fact_5004_cond__case__prod__eta,axiom,
% 5.44/5.66 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.44/5.66 ( ! [X5: nat,Y5: nat] :
% 5.44/5.66 ( ( F @ X5 @ Y5 )
% 5.44/5.66 = ( G @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
% 5.44/5.66 => ( ( produc27273713700761075at_nat @ F )
% 5.44/5.66 = G ) ) ).
% 5.44/5.66
% 5.44/5.66 % cond_case_prod_eta
% 5.44/5.66 thf(fact_5005_cond__case__prod__eta,axiom,
% 5.44/5.66 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.44/5.66 ( ! [X5: nat,Y5: nat] :
% 5.44/5.66 ( ( F @ X5 @ Y5 )
% 5.44/5.66 = ( G @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) )
% 5.44/5.66 => ( ( produc8739625826339149834_nat_o @ F )
% 5.44/5.66 = G ) ) ).
% 5.44/5.66
% 5.44/5.66 % cond_case_prod_eta
% 5.44/5.66 thf(fact_5006_cond__case__prod__eta,axiom,
% 5.44/5.66 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.44/5.66 ( ! [X5: int,Y5: int] :
% 5.44/5.66 ( ( F @ X5 @ Y5 )
% 5.44/5.66 = ( G @ ( product_Pair_int_int @ X5 @ Y5 ) ) )
% 5.44/5.66 => ( ( produc4245557441103728435nt_int @ F )
% 5.44/5.66 = G ) ) ).
% 5.44/5.66
% 5.44/5.66 % cond_case_prod_eta
% 5.44/5.66 thf(fact_5007_case__prod__eta,axiom,
% 5.44/5.66 ! [F: product_prod_nat_nat > $o] :
% 5.44/5.66 ( ( produc6081775807080527818_nat_o
% 5.44/5.66 @ ^ [X2: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) )
% 5.44/5.66 = F ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_eta
% 5.44/5.66 thf(fact_5008_case__prod__eta,axiom,
% 5.44/5.66 ! [F: product_prod_nat_nat > nat] :
% 5.44/5.66 ( ( produc6842872674320459806at_nat
% 5.44/5.66 @ ^ [X2: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) )
% 5.44/5.66 = F ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_eta
% 5.44/5.66 thf(fact_5009_case__prod__eta,axiom,
% 5.44/5.66 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.44/5.66 ( ( produc27273713700761075at_nat
% 5.44/5.66 @ ^ [X2: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) )
% 5.44/5.66 = F ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_eta
% 5.44/5.66 thf(fact_5010_case__prod__eta,axiom,
% 5.44/5.66 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.44/5.66 ( ( produc8739625826339149834_nat_o
% 5.44/5.66 @ ^ [X2: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) )
% 5.44/5.66 = F ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_eta
% 5.44/5.66 thf(fact_5011_case__prod__eta,axiom,
% 5.44/5.66 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.44/5.66 ( ( produc4245557441103728435nt_int
% 5.44/5.66 @ ^ [X2: int,Y3: int] : ( F @ ( product_Pair_int_int @ X2 @ Y3 ) ) )
% 5.44/5.66 = F ) ).
% 5.44/5.66
% 5.44/5.66 % case_prod_eta
% 5.44/5.66 thf(fact_5012_case__prodE2,axiom,
% 5.44/5.66 ! [Q: $o > $o,P: nat > nat > $o,Z: product_prod_nat_nat] :
% 5.44/5.66 ( ( Q @ ( produc6081775807080527818_nat_o @ P @ Z ) )
% 5.44/5.66 => ~ ! [X5: nat,Y5: nat] :
% 5.44/5.66 ( ( Z
% 5.44/5.66 = ( product_Pair_nat_nat @ X5 @ Y5 ) )
% 5.44/5.66 => ~ ( Q @ ( P @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prodE2
% 5.44/5.66 thf(fact_5013_case__prodE2,axiom,
% 5.44/5.66 ! [Q: nat > $o,P: nat > nat > nat,Z: product_prod_nat_nat] :
% 5.44/5.66 ( ( Q @ ( produc6842872674320459806at_nat @ P @ Z ) )
% 5.44/5.66 => ~ ! [X5: nat,Y5: nat] :
% 5.44/5.66 ( ( Z
% 5.44/5.66 = ( product_Pair_nat_nat @ X5 @ Y5 ) )
% 5.44/5.66 => ~ ( Q @ ( P @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prodE2
% 5.44/5.66 thf(fact_5014_case__prodE2,axiom,
% 5.44/5.66 ! [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] :
% 5.44/5.66 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.44/5.66 => ~ ! [X5: nat,Y5: nat] :
% 5.44/5.66 ( ( Z
% 5.44/5.66 = ( product_Pair_nat_nat @ X5 @ Y5 ) )
% 5.44/5.66 => ~ ( Q @ ( P @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prodE2
% 5.44/5.66 thf(fact_5015_case__prodE2,axiom,
% 5.44/5.66 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.44/5.66 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.44/5.66 => ~ ! [X5: nat,Y5: nat] :
% 5.44/5.66 ( ( Z
% 5.44/5.66 = ( product_Pair_nat_nat @ X5 @ Y5 ) )
% 5.44/5.66 => ~ ( Q @ ( P @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prodE2
% 5.44/5.66 thf(fact_5016_case__prodE2,axiom,
% 5.44/5.66 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.44/5.66 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.44/5.66 => ~ ! [X5: int,Y5: int] :
% 5.44/5.66 ( ( Z
% 5.44/5.66 = ( product_Pair_int_int @ X5 @ Y5 ) )
% 5.44/5.66 => ~ ( Q @ ( P @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % case_prodE2
% 5.44/5.66 thf(fact_5017_ln__add__one__self__le__self2,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.66 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_add_one_self_le_self2
% 5.44/5.66 thf(fact_5018_ln__less__self,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_less_self
% 5.44/5.66 thf(fact_5019_take__bit__tightened__less__eq__int,axiom,
% 5.44/5.66 ! [M: nat,N2: nat,K: int] :
% 5.44/5.66 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.66 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_tightened_less_eq_int
% 5.44/5.66 thf(fact_5020_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,A: int,B: int] :
% 5.44/5.66 ( ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 5.44/5.66 = ( bit_ri631733984087533419it_int @ N2 @ B ) )
% 5.44/5.66 = ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_eq_iff_take_bit_eq
% 5.44/5.66 thf(fact_5021_take__bit__nonnegative,axiom,
% 5.44/5.66 ! [N2: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_nonnegative
% 5.44/5.66 thf(fact_5022_take__bit__int__less__eq__self__iff,axiom,
% 5.44/5.66 ! [N2: nat,K: int] :
% 5.44/5.66 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.44/5.66 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_int_less_eq_self_iff
% 5.44/5.66 thf(fact_5023_not__take__bit__negative,axiom,
% 5.44/5.66 ! [N2: nat,K: int] :
% 5.44/5.66 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % not_take_bit_negative
% 5.44/5.66 thf(fact_5024_take__bit__int__greater__self__iff,axiom,
% 5.44/5.66 ! [K: int,N2: nat] :
% 5.44/5.66 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.44/5.66 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_int_greater_self_iff
% 5.44/5.66 thf(fact_5025_signed__take__bit__take__bit,axiom,
% 5.44/5.66 ! [M: nat,N2: nat,A: int] :
% 5.44/5.66 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.44/5.66 = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % signed_take_bit_take_bit
% 5.44/5.66 thf(fact_5026_not__numeral__le__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_le_neg_numeral
% 5.44/5.66 thf(fact_5027_not__numeral__le__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_le_neg_numeral
% 5.44/5.66 thf(fact_5028_not__numeral__le__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_le_neg_numeral
% 5.44/5.66 thf(fact_5029_neg__numeral__le__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_numeral
% 5.44/5.66 thf(fact_5030_neg__numeral__le__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_numeral
% 5.44/5.66 thf(fact_5031_neg__numeral__le__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_numeral
% 5.44/5.66 thf(fact_5032_zero__neq__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( zero_zero_real
% 5.44/5.66 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_neq_neg_numeral
% 5.44/5.66 thf(fact_5033_zero__neq__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( zero_zero_int
% 5.44/5.66 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_neq_neg_numeral
% 5.44/5.66 thf(fact_5034_zero__neq__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( zero_zero_complex
% 5.44/5.66 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_neq_neg_numeral
% 5.44/5.66 thf(fact_5035_zero__neq__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( zero_z3403309356797280102nteger
% 5.44/5.66 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_neq_neg_numeral
% 5.44/5.66 thf(fact_5036_not__numeral__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_less_neg_numeral
% 5.44/5.66 thf(fact_5037_not__numeral__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_less_neg_numeral
% 5.44/5.66 thf(fact_5038_not__numeral__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] :
% 5.44/5.66 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_less_neg_numeral
% 5.44/5.66 thf(fact_5039_neg__numeral__less__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_numeral
% 5.44/5.66 thf(fact_5040_neg__numeral__less__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_numeral
% 5.44/5.66 thf(fact_5041_neg__numeral__less__numeral,axiom,
% 5.44/5.66 ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_numeral
% 5.44/5.66 thf(fact_5042_neg__eq__iff__add__eq__0,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ( uminus_uminus_real @ A )
% 5.44/5.66 = B )
% 5.44/5.66 = ( ( plus_plus_real @ A @ B )
% 5.44/5.66 = zero_zero_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_eq_iff_add_eq_0
% 5.44/5.66 thf(fact_5043_neg__eq__iff__add__eq__0,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ( uminus_uminus_int @ A )
% 5.44/5.66 = B )
% 5.44/5.66 = ( ( plus_plus_int @ A @ B )
% 5.44/5.66 = zero_zero_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_eq_iff_add_eq_0
% 5.44/5.66 thf(fact_5044_neg__eq__iff__add__eq__0,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( ( uminus1482373934393186551omplex @ A )
% 5.44/5.66 = B )
% 5.44/5.66 = ( ( plus_plus_complex @ A @ B )
% 5.44/5.66 = zero_zero_complex ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_eq_iff_add_eq_0
% 5.44/5.66 thf(fact_5045_neg__eq__iff__add__eq__0,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ( uminus1351360451143612070nteger @ A )
% 5.44/5.66 = B )
% 5.44/5.66 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_eq_iff_add_eq_0
% 5.44/5.66 thf(fact_5046_eq__neg__iff__add__eq__0,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( A
% 5.44/5.66 = ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( ( plus_plus_real @ A @ B )
% 5.44/5.66 = zero_zero_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_neg_iff_add_eq_0
% 5.44/5.66 thf(fact_5047_eq__neg__iff__add__eq__0,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( A
% 5.44/5.66 = ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( ( plus_plus_int @ A @ B )
% 5.44/5.66 = zero_zero_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_neg_iff_add_eq_0
% 5.44/5.66 thf(fact_5048_eq__neg__iff__add__eq__0,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( A
% 5.44/5.66 = ( uminus1482373934393186551omplex @ B ) )
% 5.44/5.66 = ( ( plus_plus_complex @ A @ B )
% 5.44/5.66 = zero_zero_complex ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_neg_iff_add_eq_0
% 5.44/5.66 thf(fact_5049_eq__neg__iff__add__eq__0,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( A
% 5.44/5.66 = ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_neg_iff_add_eq_0
% 5.44/5.66 thf(fact_5050_add_Oinverse__unique,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ( plus_plus_real @ A @ B )
% 5.44/5.66 = zero_zero_real )
% 5.44/5.66 => ( ( uminus_uminus_real @ A )
% 5.44/5.66 = B ) ) ).
% 5.44/5.66
% 5.44/5.66 % add.inverse_unique
% 5.44/5.66 thf(fact_5051_add_Oinverse__unique,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ( plus_plus_int @ A @ B )
% 5.44/5.66 = zero_zero_int )
% 5.44/5.66 => ( ( uminus_uminus_int @ A )
% 5.44/5.66 = B ) ) ).
% 5.44/5.66
% 5.44/5.66 % add.inverse_unique
% 5.44/5.66 thf(fact_5052_add_Oinverse__unique,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( ( plus_plus_complex @ A @ B )
% 5.44/5.66 = zero_zero_complex )
% 5.44/5.66 => ( ( uminus1482373934393186551omplex @ A )
% 5.44/5.66 = B ) ) ).
% 5.44/5.66
% 5.44/5.66 % add.inverse_unique
% 5.44/5.66 thf(fact_5053_add_Oinverse__unique,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.44/5.66 = zero_z3403309356797280102nteger )
% 5.44/5.66 => ( ( uminus1351360451143612070nteger @ A )
% 5.44/5.66 = B ) ) ).
% 5.44/5.66
% 5.44/5.66 % add.inverse_unique
% 5.44/5.66 thf(fact_5054_ab__group__add__class_Oab__left__minus,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.44/5.66 = zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % ab_group_add_class.ab_left_minus
% 5.44/5.66 thf(fact_5055_ab__group__add__class_Oab__left__minus,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.44/5.66 = zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % ab_group_add_class.ab_left_minus
% 5.44/5.66 thf(fact_5056_ab__group__add__class_Oab__left__minus,axiom,
% 5.44/5.66 ! [A: complex] :
% 5.44/5.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.44/5.66 = zero_zero_complex ) ).
% 5.44/5.66
% 5.44/5.66 % ab_group_add_class.ab_left_minus
% 5.44/5.66 thf(fact_5057_ab__group__add__class_Oab__left__minus,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.44/5.66 = zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % ab_group_add_class.ab_left_minus
% 5.44/5.66 thf(fact_5058_add__eq__0__iff,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ( plus_plus_real @ A @ B )
% 5.44/5.66 = zero_zero_real )
% 5.44/5.66 = ( B
% 5.44/5.66 = ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_eq_0_iff
% 5.44/5.66 thf(fact_5059_add__eq__0__iff,axiom,
% 5.44/5.66 ! [A: int,B: int] :
% 5.44/5.66 ( ( ( plus_plus_int @ A @ B )
% 5.44/5.66 = zero_zero_int )
% 5.44/5.66 = ( B
% 5.44/5.66 = ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_eq_0_iff
% 5.44/5.66 thf(fact_5060_add__eq__0__iff,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( ( plus_plus_complex @ A @ B )
% 5.44/5.66 = zero_zero_complex )
% 5.44/5.66 = ( B
% 5.44/5.66 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_eq_0_iff
% 5.44/5.66 thf(fact_5061_add__eq__0__iff,axiom,
% 5.44/5.66 ! [A: code_integer,B: code_integer] :
% 5.44/5.66 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.44/5.66 = zero_z3403309356797280102nteger )
% 5.44/5.66 = ( B
% 5.44/5.66 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_eq_0_iff
% 5.44/5.66 thf(fact_5062_le__minus__one__simps_I4_J,axiom,
% 5.44/5.66 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(4)
% 5.44/5.66 thf(fact_5063_le__minus__one__simps_I4_J,axiom,
% 5.44/5.66 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(4)
% 5.44/5.66 thf(fact_5064_le__minus__one__simps_I4_J,axiom,
% 5.44/5.66 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(4)
% 5.44/5.66 thf(fact_5065_le__minus__one__simps_I2_J,axiom,
% 5.44/5.66 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(2)
% 5.44/5.66 thf(fact_5066_le__minus__one__simps_I2_J,axiom,
% 5.44/5.66 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(2)
% 5.44/5.66 thf(fact_5067_le__minus__one__simps_I2_J,axiom,
% 5.44/5.66 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(2)
% 5.44/5.66 thf(fact_5068_zero__neq__neg__one,axiom,
% 5.44/5.66 ( zero_zero_real
% 5.44/5.66 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_neq_neg_one
% 5.44/5.66 thf(fact_5069_zero__neq__neg__one,axiom,
% 5.44/5.66 ( zero_zero_int
% 5.44/5.66 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_neq_neg_one
% 5.44/5.66 thf(fact_5070_zero__neq__neg__one,axiom,
% 5.44/5.66 ( zero_zero_complex
% 5.44/5.66 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_neq_neg_one
% 5.44/5.66 thf(fact_5071_zero__neq__neg__one,axiom,
% 5.44/5.66 ( zero_z3403309356797280102nteger
% 5.44/5.66 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % zero_neq_neg_one
% 5.44/5.66 thf(fact_5072_numeral__times__minus__swap,axiom,
% 5.44/5.66 ! [W: num,X: real] :
% 5.44/5.66 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 5.44/5.66 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_times_minus_swap
% 5.44/5.66 thf(fact_5073_numeral__times__minus__swap,axiom,
% 5.44/5.66 ! [W: num,X: int] :
% 5.44/5.66 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 5.44/5.66 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_times_minus_swap
% 5.44/5.66 thf(fact_5074_numeral__times__minus__swap,axiom,
% 5.44/5.66 ! [W: num,X: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.44/5.66 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_times_minus_swap
% 5.44/5.66 thf(fact_5075_numeral__times__minus__swap,axiom,
% 5.44/5.66 ! [W: num,X: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.44/5.66 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_times_minus_swap
% 5.44/5.66 thf(fact_5076_less__minus__one__simps_I4_J,axiom,
% 5.44/5.66 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(4)
% 5.44/5.66 thf(fact_5077_less__minus__one__simps_I4_J,axiom,
% 5.44/5.66 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(4)
% 5.44/5.66 thf(fact_5078_less__minus__one__simps_I4_J,axiom,
% 5.44/5.66 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(4)
% 5.44/5.66 thf(fact_5079_less__minus__one__simps_I2_J,axiom,
% 5.44/5.66 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(2)
% 5.44/5.66 thf(fact_5080_less__minus__one__simps_I2_J,axiom,
% 5.44/5.66 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(2)
% 5.44/5.66 thf(fact_5081_less__minus__one__simps_I2_J,axiom,
% 5.44/5.66 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(2)
% 5.44/5.66 thf(fact_5082_nonzero__minus__divide__divide,axiom,
% 5.44/5.66 ! [B: real,A: real] :
% 5.44/5.66 ( ( B != zero_zero_real )
% 5.44/5.66 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % nonzero_minus_divide_divide
% 5.44/5.66 thf(fact_5083_nonzero__minus__divide__divide,axiom,
% 5.44/5.66 ! [B: complex,A: complex] :
% 5.44/5.66 ( ( B != zero_zero_complex )
% 5.44/5.66 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.44/5.66 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % nonzero_minus_divide_divide
% 5.44/5.66 thf(fact_5084_nonzero__minus__divide__right,axiom,
% 5.44/5.66 ! [B: real,A: real] :
% 5.44/5.66 ( ( B != zero_zero_real )
% 5.44/5.66 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.66 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % nonzero_minus_divide_right
% 5.44/5.66 thf(fact_5085_nonzero__minus__divide__right,axiom,
% 5.44/5.66 ! [B: complex,A: complex] :
% 5.44/5.66 ( ( B != zero_zero_complex )
% 5.44/5.66 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.66 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % nonzero_minus_divide_right
% 5.44/5.66 thf(fact_5086_numeral__neq__neg__one,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( numeral_numeral_real @ N2 )
% 5.44/5.66 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_neq_neg_one
% 5.44/5.66 thf(fact_5087_numeral__neq__neg__one,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( numeral_numeral_int @ N2 )
% 5.44/5.66 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_neq_neg_one
% 5.44/5.66 thf(fact_5088_numeral__neq__neg__one,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( numera6690914467698888265omplex @ N2 )
% 5.44/5.66 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_neq_neg_one
% 5.44/5.66 thf(fact_5089_numeral__neq__neg__one,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( ( numera6620942414471956472nteger @ N2 )
% 5.44/5.66 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % numeral_neq_neg_one
% 5.44/5.66 thf(fact_5090_one__neq__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( one_one_real
% 5.44/5.66 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_neq_neg_numeral
% 5.44/5.66 thf(fact_5091_one__neq__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( one_one_int
% 5.44/5.66 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_neq_neg_numeral
% 5.44/5.66 thf(fact_5092_one__neq__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( one_one_complex
% 5.44/5.66 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_neq_neg_numeral
% 5.44/5.66 thf(fact_5093_one__neq__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ( one_one_Code_integer
% 5.44/5.66 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % one_neq_neg_numeral
% 5.44/5.66 thf(fact_5094_square__eq__1__iff,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ( times_times_real @ X @ X )
% 5.44/5.66 = one_one_real )
% 5.44/5.66 = ( ( X = one_one_real )
% 5.44/5.66 | ( X
% 5.44/5.66 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % square_eq_1_iff
% 5.44/5.66 thf(fact_5095_square__eq__1__iff,axiom,
% 5.44/5.66 ! [X: int] :
% 5.44/5.66 ( ( ( times_times_int @ X @ X )
% 5.44/5.66 = one_one_int )
% 5.44/5.66 = ( ( X = one_one_int )
% 5.44/5.66 | ( X
% 5.44/5.66 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % square_eq_1_iff
% 5.44/5.66 thf(fact_5096_square__eq__1__iff,axiom,
% 5.44/5.66 ! [X: complex] :
% 5.44/5.66 ( ( ( times_times_complex @ X @ X )
% 5.44/5.66 = one_one_complex )
% 5.44/5.66 = ( ( X = one_one_complex )
% 5.44/5.66 | ( X
% 5.44/5.66 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % square_eq_1_iff
% 5.44/5.66 thf(fact_5097_square__eq__1__iff,axiom,
% 5.44/5.66 ! [X: code_integer] :
% 5.44/5.66 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.44/5.66 = one_one_Code_integer )
% 5.44/5.66 = ( ( X = one_one_Code_integer )
% 5.44/5.66 | ( X
% 5.44/5.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % square_eq_1_iff
% 5.44/5.66 thf(fact_5098_group__cancel_Osub2,axiom,
% 5.44/5.66 ! [B2: real,K: real,B: real,A: real] :
% 5.44/5.66 ( ( B2
% 5.44/5.66 = ( plus_plus_real @ K @ B ) )
% 5.44/5.66 => ( ( minus_minus_real @ A @ B2 )
% 5.44/5.66 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % group_cancel.sub2
% 5.44/5.66 thf(fact_5099_group__cancel_Osub2,axiom,
% 5.44/5.66 ! [B2: int,K: int,B: int,A: int] :
% 5.44/5.66 ( ( B2
% 5.44/5.66 = ( plus_plus_int @ K @ B ) )
% 5.44/5.66 => ( ( minus_minus_int @ A @ B2 )
% 5.44/5.66 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % group_cancel.sub2
% 5.44/5.66 thf(fact_5100_group__cancel_Osub2,axiom,
% 5.44/5.66 ! [B2: complex,K: complex,B: complex,A: complex] :
% 5.44/5.66 ( ( B2
% 5.44/5.66 = ( plus_plus_complex @ K @ B ) )
% 5.44/5.66 => ( ( minus_minus_complex @ A @ B2 )
% 5.44/5.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % group_cancel.sub2
% 5.44/5.66 thf(fact_5101_group__cancel_Osub2,axiom,
% 5.44/5.66 ! [B2: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.44/5.66 ( ( B2
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.44/5.66 => ( ( minus_8373710615458151222nteger @ A @ B2 )
% 5.44/5.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % group_cancel.sub2
% 5.44/5.66 thf(fact_5102_diff__conv__add__uminus,axiom,
% 5.44/5.66 ( minus_minus_real
% 5.44/5.66 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_conv_add_uminus
% 5.44/5.66 thf(fact_5103_diff__conv__add__uminus,axiom,
% 5.44/5.66 ( minus_minus_int
% 5.44/5.66 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_conv_add_uminus
% 5.44/5.66 thf(fact_5104_diff__conv__add__uminus,axiom,
% 5.44/5.66 ( minus_minus_complex
% 5.44/5.66 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_conv_add_uminus
% 5.44/5.66 thf(fact_5105_diff__conv__add__uminus,axiom,
% 5.44/5.66 ( minus_8373710615458151222nteger
% 5.44/5.66 = ( ^ [A4: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % diff_conv_add_uminus
% 5.44/5.66 thf(fact_5106_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.44/5.66 ( minus_minus_real
% 5.44/5.66 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.44/5.66 thf(fact_5107_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.44/5.66 ( minus_minus_int
% 5.44/5.66 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.44/5.66 thf(fact_5108_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.44/5.66 ( minus_minus_complex
% 5.44/5.66 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.44/5.66 thf(fact_5109_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.44/5.66 ( minus_8373710615458151222nteger
% 5.44/5.66 = ( ^ [A4: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.44/5.66 thf(fact_5110_take__bit__unset__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,M: nat,A: int] :
% 5.44/5.66 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.44/5.66 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_unset_bit_eq
% 5.44/5.66 thf(fact_5111_take__bit__unset__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,M: nat,A: nat] :
% 5.44/5.66 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.44/5.66 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.44/5.66 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_unset_bit_eq
% 5.44/5.66 thf(fact_5112_take__bit__set__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,M: nat,A: int] :
% 5.44/5.66 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.44/5.66 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_set_bit_eq
% 5.44/5.66 thf(fact_5113_take__bit__set__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,M: nat,A: nat] :
% 5.44/5.66 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.44/5.66 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.44/5.66 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_set_bit_eq
% 5.44/5.66 thf(fact_5114_take__bit__flip__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,M: nat,A: int] :
% 5.44/5.66 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.44/5.66 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_flip_bit_eq
% 5.44/5.66 thf(fact_5115_take__bit__flip__bit__eq,axiom,
% 5.44/5.66 ! [N2: nat,M: nat,A: nat] :
% 5.44/5.66 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.44/5.66 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.44/5.66 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.66 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.44/5.66 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_flip_bit_eq
% 5.44/5.66 thf(fact_5116_dvd__div__neg,axiom,
% 5.44/5.66 ! [B: real,A: real] :
% 5.44/5.66 ( ( dvd_dvd_real @ B @ A )
% 5.44/5.66 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.44/5.66 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_div_neg
% 5.44/5.66 thf(fact_5117_dvd__div__neg,axiom,
% 5.44/5.66 ! [B: int,A: int] :
% 5.44/5.66 ( ( dvd_dvd_int @ B @ A )
% 5.44/5.66 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.44/5.66 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_div_neg
% 5.44/5.66 thf(fact_5118_dvd__div__neg,axiom,
% 5.44/5.66 ! [B: complex,A: complex] :
% 5.44/5.66 ( ( dvd_dvd_complex @ B @ A )
% 5.44/5.66 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_div_neg
% 5.44/5.66 thf(fact_5119_dvd__div__neg,axiom,
% 5.44/5.66 ! [B: code_integer,A: code_integer] :
% 5.44/5.66 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.66 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_div_neg
% 5.44/5.66 thf(fact_5120_dvd__neg__div,axiom,
% 5.44/5.66 ! [B: real,A: real] :
% 5.44/5.66 ( ( dvd_dvd_real @ B @ A )
% 5.44/5.66 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.44/5.66 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_neg_div
% 5.44/5.66 thf(fact_5121_dvd__neg__div,axiom,
% 5.44/5.66 ! [B: int,A: int] :
% 5.44/5.66 ( ( dvd_dvd_int @ B @ A )
% 5.44/5.66 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.44/5.66 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_neg_div
% 5.44/5.66 thf(fact_5122_dvd__neg__div,axiom,
% 5.44/5.66 ! [B: complex,A: complex] :
% 5.44/5.66 ( ( dvd_dvd_complex @ B @ A )
% 5.44/5.66 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_neg_div
% 5.44/5.66 thf(fact_5123_dvd__neg__div,axiom,
% 5.44/5.66 ! [B: code_integer,A: code_integer] :
% 5.44/5.66 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.44/5.66 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % dvd_neg_div
% 5.44/5.66 thf(fact_5124_subset__Compl__self__eq,axiom,
% 5.44/5.66 ! [A2: set_int] :
% 5.44/5.66 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.44/5.66 = ( A2 = bot_bot_set_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % subset_Compl_self_eq
% 5.44/5.66 thf(fact_5125_subset__Compl__self__eq,axiom,
% 5.44/5.66 ! [A2: set_real] :
% 5.44/5.66 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 5.44/5.66 = ( A2 = bot_bot_set_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % subset_Compl_self_eq
% 5.44/5.66 thf(fact_5126_subset__Compl__self__eq,axiom,
% 5.44/5.66 ! [A2: set_nat] :
% 5.44/5.66 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.44/5.66 = ( A2 = bot_bot_set_nat ) ) ).
% 5.44/5.66
% 5.44/5.66 % subset_Compl_self_eq
% 5.44/5.66 thf(fact_5127_real__minus__mult__self__le,axiom,
% 5.44/5.66 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % real_minus_mult_self_le
% 5.44/5.66 thf(fact_5128_minus__real__def,axiom,
% 5.44/5.66 ( minus_minus_real
% 5.44/5.66 = ( ^ [X2: real,Y3: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y3 ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_real_def
% 5.44/5.66 thf(fact_5129_take__bit__Suc__minus__bit0,axiom,
% 5.44/5.66 ! [N2: nat,K: num] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.44/5.66 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_minus_bit0
% 5.44/5.66 thf(fact_5130_ln__one__minus__pos__upper__bound,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.66 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_one_minus_pos_upper_bound
% 5.44/5.66 thf(fact_5131_pow_Osimps_I1_J,axiom,
% 5.44/5.66 ! [X: num] :
% 5.44/5.66 ( ( pow @ X @ one )
% 5.44/5.66 = X ) ).
% 5.44/5.66
% 5.44/5.66 % pow.simps(1)
% 5.44/5.66 thf(fact_5132_ln__bound,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_bound
% 5.44/5.66 thf(fact_5133_ln__gt__zero__imp__gt__one,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_gt_zero_imp_gt_one
% 5.44/5.66 thf(fact_5134_ln__less__zero,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.66 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_less_zero
% 5.44/5.66 thf(fact_5135_ln__gt__zero,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.66 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_gt_zero
% 5.44/5.66 thf(fact_5136_ln__ge__zero,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.44/5.66 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_ge_zero
% 5.44/5.66 thf(fact_5137_take__bit__signed__take__bit,axiom,
% 5.44/5.66 ! [M: nat,N2: nat,A: int] :
% 5.44/5.66 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 5.44/5.66 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_signed_take_bit
% 5.44/5.66 thf(fact_5138_neg__numeral__le__zero,axiom,
% 5.44/5.66 ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_zero
% 5.44/5.66 thf(fact_5139_neg__numeral__le__zero,axiom,
% 5.44/5.66 ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_zero
% 5.44/5.66 thf(fact_5140_neg__numeral__le__zero,axiom,
% 5.44/5.66 ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_zero
% 5.44/5.66 thf(fact_5141_not__zero__le__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_zero_le_neg_numeral
% 5.44/5.66 thf(fact_5142_not__zero__le__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_zero_le_neg_numeral
% 5.44/5.66 thf(fact_5143_not__zero__le__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_zero_le_neg_numeral
% 5.44/5.66 thf(fact_5144_not__zero__less__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_zero_less_neg_numeral
% 5.44/5.66 thf(fact_5145_not__zero__less__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_zero_less_neg_numeral
% 5.44/5.66 thf(fact_5146_not__zero__less__neg__numeral,axiom,
% 5.44/5.66 ! [N2: num] :
% 5.44/5.66 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_zero_less_neg_numeral
% 5.44/5.66 thf(fact_5147_neg__numeral__less__zero,axiom,
% 5.44/5.66 ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_zero
% 5.44/5.66 thf(fact_5148_neg__numeral__less__zero,axiom,
% 5.44/5.66 ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_zero
% 5.44/5.66 thf(fact_5149_neg__numeral__less__zero,axiom,
% 5.44/5.66 ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_zero
% 5.44/5.66 thf(fact_5150_le__minus__one__simps_I1_J,axiom,
% 5.44/5.66 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(1)
% 5.44/5.66 thf(fact_5151_le__minus__one__simps_I1_J,axiom,
% 5.44/5.66 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(1)
% 5.44/5.66 thf(fact_5152_le__minus__one__simps_I1_J,axiom,
% 5.44/5.66 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(1)
% 5.44/5.66 thf(fact_5153_le__minus__one__simps_I3_J,axiom,
% 5.44/5.66 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(3)
% 5.44/5.66 thf(fact_5154_le__minus__one__simps_I3_J,axiom,
% 5.44/5.66 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(3)
% 5.44/5.66 thf(fact_5155_le__minus__one__simps_I3_J,axiom,
% 5.44/5.66 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_one_simps(3)
% 5.44/5.66 thf(fact_5156_less__minus__one__simps_I1_J,axiom,
% 5.44/5.66 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(1)
% 5.44/5.66 thf(fact_5157_less__minus__one__simps_I1_J,axiom,
% 5.44/5.66 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(1)
% 5.44/5.66 thf(fact_5158_less__minus__one__simps_I1_J,axiom,
% 5.44/5.66 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(1)
% 5.44/5.66 thf(fact_5159_less__minus__one__simps_I3_J,axiom,
% 5.44/5.66 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(3)
% 5.44/5.66 thf(fact_5160_less__minus__one__simps_I3_J,axiom,
% 5.44/5.66 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(3)
% 5.44/5.66 thf(fact_5161_less__minus__one__simps_I3_J,axiom,
% 5.44/5.66 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_one_simps(3)
% 5.44/5.66 thf(fact_5162_take__bit__decr__eq,axiom,
% 5.44/5.66 ! [N2: nat,K: int] :
% 5.44/5.66 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.44/5.66 != zero_zero_int )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ one_one_int ) )
% 5.44/5.66 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ one_one_int ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_decr_eq
% 5.44/5.66 thf(fact_5163_neg__numeral__le__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_one
% 5.44/5.66 thf(fact_5164_neg__numeral__le__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_one
% 5.44/5.66 thf(fact_5165_neg__numeral__le__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_one
% 5.44/5.66 thf(fact_5166_neg__one__le__numeral,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_le_numeral
% 5.44/5.66 thf(fact_5167_neg__one__le__numeral,axiom,
% 5.44/5.66 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_le_numeral
% 5.44/5.66 thf(fact_5168_neg__one__le__numeral,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_le_numeral
% 5.44/5.66 thf(fact_5169_neg__numeral__le__neg__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_neg_one
% 5.44/5.66 thf(fact_5170_neg__numeral__le__neg__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_neg_one
% 5.44/5.66 thf(fact_5171_neg__numeral__le__neg__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_le_neg_one
% 5.44/5.66 thf(fact_5172_not__numeral__le__neg__one,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_le_neg_one
% 5.44/5.66 thf(fact_5173_not__numeral__le__neg__one,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_le_neg_one
% 5.44/5.66 thf(fact_5174_not__numeral__le__neg__one,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_le_neg_one
% 5.44/5.66 thf(fact_5175_not__one__le__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_one_le_neg_numeral
% 5.44/5.66 thf(fact_5176_not__one__le__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_one_le_neg_numeral
% 5.44/5.66 thf(fact_5177_not__one__le__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_one_le_neg_numeral
% 5.44/5.66 thf(fact_5178_not__neg__one__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_neg_one_less_neg_numeral
% 5.44/5.66 thf(fact_5179_not__neg__one__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_neg_one_less_neg_numeral
% 5.44/5.66 thf(fact_5180_not__neg__one__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_neg_one_less_neg_numeral
% 5.44/5.66 thf(fact_5181_not__one__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_one_less_neg_numeral
% 5.44/5.66 thf(fact_5182_not__one__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_one_less_neg_numeral
% 5.44/5.66 thf(fact_5183_not__one__less__neg__numeral,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_one_less_neg_numeral
% 5.44/5.66 thf(fact_5184_not__numeral__less__neg__one,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_less_neg_one
% 5.44/5.66 thf(fact_5185_not__numeral__less__neg__one,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_less_neg_one
% 5.44/5.66 thf(fact_5186_not__numeral__less__neg__one,axiom,
% 5.44/5.66 ! [M: num] :
% 5.44/5.66 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % not_numeral_less_neg_one
% 5.44/5.66 thf(fact_5187_neg__one__less__numeral,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_less_numeral
% 5.44/5.66 thf(fact_5188_neg__one__less__numeral,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_less_numeral
% 5.44/5.66 thf(fact_5189_neg__one__less__numeral,axiom,
% 5.44/5.66 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_less_numeral
% 5.44/5.66 thf(fact_5190_neg__numeral__less__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_one
% 5.44/5.66 thf(fact_5191_neg__numeral__less__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_one
% 5.44/5.66 thf(fact_5192_neg__numeral__less__one,axiom,
% 5.44/5.66 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.44/5.66
% 5.44/5.66 % neg_numeral_less_one
% 5.44/5.66 thf(fact_5193_nonzero__neg__divide__eq__eq2,axiom,
% 5.44/5.66 ! [B: real,C: real,A: real] :
% 5.44/5.66 ( ( B != zero_zero_real )
% 5.44/5.66 => ( ( C
% 5.44/5.66 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.44/5.66 = ( ( times_times_real @ C @ B )
% 5.44/5.66 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % nonzero_neg_divide_eq_eq2
% 5.44/5.66 thf(fact_5194_nonzero__neg__divide__eq__eq2,axiom,
% 5.44/5.66 ! [B: complex,C: complex,A: complex] :
% 5.44/5.66 ( ( B != zero_zero_complex )
% 5.44/5.66 => ( ( C
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.44/5.66 = ( ( times_times_complex @ C @ B )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % nonzero_neg_divide_eq_eq2
% 5.44/5.66 thf(fact_5195_nonzero__neg__divide__eq__eq,axiom,
% 5.44/5.66 ! [B: real,A: real,C: real] :
% 5.44/5.66 ( ( B != zero_zero_real )
% 5.44/5.66 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.66 = C )
% 5.44/5.66 = ( ( uminus_uminus_real @ A )
% 5.44/5.66 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % nonzero_neg_divide_eq_eq
% 5.44/5.66 thf(fact_5196_nonzero__neg__divide__eq__eq,axiom,
% 5.44/5.66 ! [B: complex,A: complex,C: complex] :
% 5.44/5.66 ( ( B != zero_zero_complex )
% 5.44/5.66 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.66 = C )
% 5.44/5.66 = ( ( uminus1482373934393186551omplex @ A )
% 5.44/5.66 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % nonzero_neg_divide_eq_eq
% 5.44/5.66 thf(fact_5197_minus__divide__eq__eq,axiom,
% 5.44/5.66 ! [B: real,C: real,A: real] :
% 5.44/5.66 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.44/5.66 = A )
% 5.44/5.66 = ( ( ( C != zero_zero_real )
% 5.44/5.66 => ( ( uminus_uminus_real @ B )
% 5.44/5.66 = ( times_times_real @ A @ C ) ) )
% 5.44/5.66 & ( ( C = zero_zero_real )
% 5.44/5.66 => ( A = zero_zero_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_eq_eq
% 5.44/5.66 thf(fact_5198_minus__divide__eq__eq,axiom,
% 5.44/5.66 ! [B: complex,C: complex,A: complex] :
% 5.44/5.66 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.66 = A )
% 5.44/5.66 = ( ( ( C != zero_zero_complex )
% 5.44/5.66 => ( ( uminus1482373934393186551omplex @ B )
% 5.44/5.66 = ( times_times_complex @ A @ C ) ) )
% 5.44/5.66 & ( ( C = zero_zero_complex )
% 5.44/5.66 => ( A = zero_zero_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_eq_eq
% 5.44/5.66 thf(fact_5199_eq__minus__divide__eq,axiom,
% 5.44/5.66 ! [A: real,B: real,C: real] :
% 5.44/5.66 ( ( A
% 5.44/5.66 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.44/5.66 = ( ( ( C != zero_zero_real )
% 5.44/5.66 => ( ( times_times_real @ A @ C )
% 5.44/5.66 = ( uminus_uminus_real @ B ) ) )
% 5.44/5.66 & ( ( C = zero_zero_real )
% 5.44/5.66 => ( A = zero_zero_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_minus_divide_eq
% 5.44/5.66 thf(fact_5200_eq__minus__divide__eq,axiom,
% 5.44/5.66 ! [A: complex,B: complex,C: complex] :
% 5.44/5.66 ( ( A
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.44/5.66 = ( ( ( C != zero_zero_complex )
% 5.44/5.66 => ( ( times_times_complex @ A @ C )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.44/5.66 & ( ( C = zero_zero_complex )
% 5.44/5.66 => ( A = zero_zero_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_minus_divide_eq
% 5.44/5.66 thf(fact_5201_mult__1s__ring__1_I1_J,axiom,
% 5.44/5.66 ! [B: real] :
% 5.44/5.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.44/5.66 = ( uminus_uminus_real @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_1s_ring_1(1)
% 5.44/5.66 thf(fact_5202_mult__1s__ring__1_I1_J,axiom,
% 5.44/5.66 ! [B: int] :
% 5.44/5.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.44/5.66 = ( uminus_uminus_int @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_1s_ring_1(1)
% 5.44/5.66 thf(fact_5203_mult__1s__ring__1_I1_J,axiom,
% 5.44/5.66 ! [B: complex] :
% 5.44/5.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_1s_ring_1(1)
% 5.44/5.66 thf(fact_5204_mult__1s__ring__1_I1_J,axiom,
% 5.44/5.66 ! [B: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_1s_ring_1(1)
% 5.44/5.66 thf(fact_5205_mult__1s__ring__1_I2_J,axiom,
% 5.44/5.66 ! [B: real] :
% 5.44/5.66 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.44/5.66 = ( uminus_uminus_real @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_1s_ring_1(2)
% 5.44/5.66 thf(fact_5206_mult__1s__ring__1_I2_J,axiom,
% 5.44/5.66 ! [B: int] :
% 5.44/5.66 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.44/5.66 = ( uminus_uminus_int @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_1s_ring_1(2)
% 5.44/5.66 thf(fact_5207_mult__1s__ring__1_I2_J,axiom,
% 5.44/5.66 ! [B: complex] :
% 5.44/5.66 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_1s_ring_1(2)
% 5.44/5.66 thf(fact_5208_mult__1s__ring__1_I2_J,axiom,
% 5.44/5.66 ! [B: code_integer] :
% 5.44/5.66 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.44/5.66
% 5.44/5.66 % mult_1s_ring_1(2)
% 5.44/5.66 thf(fact_5209_divide__eq__minus__1__iff,axiom,
% 5.44/5.66 ! [A: real,B: real] :
% 5.44/5.66 ( ( ( divide_divide_real @ A @ B )
% 5.44/5.66 = ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.66 = ( ( B != zero_zero_real )
% 5.44/5.66 & ( A
% 5.44/5.66 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_eq_minus_1_iff
% 5.44/5.66 thf(fact_5210_divide__eq__minus__1__iff,axiom,
% 5.44/5.66 ! [A: complex,B: complex] :
% 5.44/5.66 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.66 = ( ( B != zero_zero_complex )
% 5.44/5.66 & ( A
% 5.44/5.66 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_eq_minus_1_iff
% 5.44/5.66 thf(fact_5211_uminus__numeral__One,axiom,
% 5.44/5.66 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.44/5.66 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_numeral_One
% 5.44/5.66 thf(fact_5212_uminus__numeral__One,axiom,
% 5.44/5.66 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.44/5.66 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_numeral_One
% 5.44/5.66 thf(fact_5213_uminus__numeral__One,axiom,
% 5.44/5.66 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_numeral_One
% 5.44/5.66 thf(fact_5214_uminus__numeral__One,axiom,
% 5.44/5.66 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_numeral_One
% 5.44/5.66 thf(fact_5215_power__minus,axiom,
% 5.44/5.66 ! [A: real,N2: nat] :
% 5.44/5.66 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.44/5.66 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus
% 5.44/5.66 thf(fact_5216_power__minus,axiom,
% 5.44/5.66 ! [A: int,N2: nat] :
% 5.44/5.66 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.44/5.66 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus
% 5.44/5.66 thf(fact_5217_power__minus,axiom,
% 5.44/5.66 ! [A: complex,N2: nat] :
% 5.44/5.66 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.44/5.66 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus
% 5.44/5.66 thf(fact_5218_power__minus,axiom,
% 5.44/5.66 ! [A: code_integer,N2: nat] :
% 5.44/5.66 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.44/5.66 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus
% 5.44/5.66 thf(fact_5219_power__minus__Bit0,axiom,
% 5.44/5.66 ! [X: real,K: num] :
% 5.44/5.66 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.44/5.66 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus_Bit0
% 5.44/5.66 thf(fact_5220_power__minus__Bit0,axiom,
% 5.44/5.66 ! [X: int,K: num] :
% 5.44/5.66 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.44/5.66 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus_Bit0
% 5.44/5.66 thf(fact_5221_power__minus__Bit0,axiom,
% 5.44/5.66 ! [X: complex,K: num] :
% 5.44/5.66 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.44/5.66 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus_Bit0
% 5.44/5.66 thf(fact_5222_power__minus__Bit0,axiom,
% 5.44/5.66 ! [X: code_integer,K: num] :
% 5.44/5.66 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.44/5.66 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power_minus_Bit0
% 5.44/5.66 thf(fact_5223_take__bit__Suc__minus__1__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_minus_1_eq
% 5.44/5.66 thf(fact_5224_take__bit__Suc__minus__1__eq,axiom,
% 5.44/5.66 ! [N2: nat] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_minus_1_eq
% 5.44/5.66 thf(fact_5225_take__bit__numeral__minus__1__eq,axiom,
% 5.44/5.66 ! [K: num] :
% 5.44/5.66 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.66 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_numeral_minus_1_eq
% 5.44/5.66 thf(fact_5226_take__bit__numeral__minus__1__eq,axiom,
% 5.44/5.66 ! [K: num] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.66 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_numeral_minus_1_eq
% 5.44/5.66 thf(fact_5227_real__0__less__add__iff,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.66 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % real_0_less_add_iff
% 5.44/5.66 thf(fact_5228_real__add__less__0__iff,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.44/5.66 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % real_add_less_0_iff
% 5.44/5.66 thf(fact_5229_real__0__le__add__iff,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.66 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.44/5.66
% 5.44/5.66 % real_0_le_add_iff
% 5.44/5.66 thf(fact_5230_real__add__le__0__iff,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.44/5.66 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % real_add_le_0_iff
% 5.44/5.66 thf(fact_5231_ln__ge__zero__imp__ge__one,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_ge_zero_imp_ge_one
% 5.44/5.66 thf(fact_5232_ln__add__one__self__le__self,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_add_one_self_le_self
% 5.44/5.66 thf(fact_5233_ln__mult,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.66 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 5.44/5.66 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_mult
% 5.44/5.66 thf(fact_5234_ln__eq__minus__one,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ( ln_ln_real @ X )
% 5.44/5.66 = ( minus_minus_real @ X @ one_one_real ) )
% 5.44/5.66 => ( X = one_one_real ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_eq_minus_one
% 5.44/5.66 thf(fact_5235_ln__div,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.66 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.66 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_div
% 5.44/5.66 thf(fact_5236_take__bit__minus__small__eq,axiom,
% 5.44/5.66 ! [K: int,N2: nat] :
% 5.44/5.66 ( ( ord_less_int @ zero_zero_int @ K )
% 5.44/5.66 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 5.44/5.66 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_minus_small_eq
% 5.44/5.66 thf(fact_5237_pos__minus__divide__less__eq,axiom,
% 5.44/5.66 ! [C: real,B: real,A: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.44/5.66 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pos_minus_divide_less_eq
% 5.44/5.66 thf(fact_5238_pos__less__minus__divide__eq,axiom,
% 5.44/5.66 ! [C: real,A: real,B: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.44/5.66 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pos_less_minus_divide_eq
% 5.44/5.66 thf(fact_5239_neg__minus__divide__less__eq,axiom,
% 5.44/5.66 ! [C: real,B: real,A: real] :
% 5.44/5.66 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.44/5.66 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_minus_divide_less_eq
% 5.44/5.66 thf(fact_5240_neg__less__minus__divide__eq,axiom,
% 5.44/5.66 ! [C: real,A: real,B: real] :
% 5.44/5.66 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.44/5.66 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_less_minus_divide_eq
% 5.44/5.66 thf(fact_5241_minus__divide__less__eq,axiom,
% 5.44/5.66 ! [B: real,C: real,A: real] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.44/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_less_eq
% 5.44/5.66 thf(fact_5242_less__minus__divide__eq,axiom,
% 5.44/5.66 ! [A: real,B: real,C: real] :
% 5.44/5.66 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.44/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_minus_divide_eq
% 5.44/5.66 thf(fact_5243_eq__divide__eq__numeral_I2_J,axiom,
% 5.44/5.66 ! [W: num,B: real,C: real] :
% 5.44/5.66 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.66 = ( divide_divide_real @ B @ C ) )
% 5.44/5.66 = ( ( ( C != zero_zero_real )
% 5.44/5.66 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.44/5.66 = B ) )
% 5.44/5.66 & ( ( C = zero_zero_real )
% 5.44/5.66 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.66 = zero_zero_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_divide_eq_numeral(2)
% 5.44/5.66 thf(fact_5244_eq__divide__eq__numeral_I2_J,axiom,
% 5.44/5.66 ! [W: num,B: complex,C: complex] :
% 5.44/5.66 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.66 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.44/5.66 = ( ( ( C != zero_zero_complex )
% 5.44/5.66 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.44/5.66 = B ) )
% 5.44/5.66 & ( ( C = zero_zero_complex )
% 5.44/5.66 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.66 = zero_zero_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % eq_divide_eq_numeral(2)
% 5.44/5.66 thf(fact_5245_divide__eq__eq__numeral_I2_J,axiom,
% 5.44/5.66 ! [B: real,C: real,W: num] :
% 5.44/5.66 ( ( ( divide_divide_real @ B @ C )
% 5.44/5.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.66 = ( ( ( C != zero_zero_real )
% 5.44/5.66 => ( B
% 5.44/5.66 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.44/5.66 & ( ( C = zero_zero_real )
% 5.44/5.66 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.66 = zero_zero_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_eq_eq_numeral(2)
% 5.44/5.66 thf(fact_5246_divide__eq__eq__numeral_I2_J,axiom,
% 5.44/5.66 ! [B: complex,C: complex,W: num] :
% 5.44/5.66 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.66 = ( ( ( C != zero_zero_complex )
% 5.44/5.66 => ( B
% 5.44/5.66 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.44/5.66 & ( ( C = zero_zero_complex )
% 5.44/5.66 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.66 = zero_zero_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_eq_eq_numeral(2)
% 5.44/5.66 thf(fact_5247_minus__divide__add__eq__iff,axiom,
% 5.44/5.66 ! [Z: real,X: real,Y: real] :
% 5.44/5.66 ( ( Z != zero_zero_real )
% 5.44/5.66 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 5.44/5.66 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_add_eq_iff
% 5.44/5.66 thf(fact_5248_minus__divide__add__eq__iff,axiom,
% 5.44/5.66 ! [Z: complex,X: complex,Y: complex] :
% 5.44/5.66 ( ( Z != zero_zero_complex )
% 5.44/5.66 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 5.44/5.66 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_add_eq_iff
% 5.44/5.66 thf(fact_5249_add__divide__eq__if__simps_I3_J,axiom,
% 5.44/5.66 ! [Z: real,A: real,B: real] :
% 5.44/5.66 ( ( ( Z = zero_zero_real )
% 5.44/5.66 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.44/5.66 = B ) )
% 5.44/5.66 & ( ( Z != zero_zero_real )
% 5.44/5.66 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.44/5.66 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_divide_eq_if_simps(3)
% 5.44/5.66 thf(fact_5250_add__divide__eq__if__simps_I3_J,axiom,
% 5.44/5.66 ! [Z: complex,A: complex,B: complex] :
% 5.44/5.66 ( ( ( Z = zero_zero_complex )
% 5.44/5.66 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.44/5.66 = B ) )
% 5.44/5.66 & ( ( Z != zero_zero_complex )
% 5.44/5.66 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.44/5.66 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_divide_eq_if_simps(3)
% 5.44/5.66 thf(fact_5251_minus__divide__diff__eq__iff,axiom,
% 5.44/5.66 ! [Z: real,X: real,Y: real] :
% 5.44/5.66 ( ( Z != zero_zero_real )
% 5.44/5.66 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 5.44/5.66 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_diff_eq_iff
% 5.44/5.66 thf(fact_5252_minus__divide__diff__eq__iff,axiom,
% 5.44/5.66 ! [Z: complex,X: complex,Y: complex] :
% 5.44/5.66 ( ( Z != zero_zero_complex )
% 5.44/5.66 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 5.44/5.66 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_diff_eq_iff
% 5.44/5.66 thf(fact_5253_add__divide__eq__if__simps_I5_J,axiom,
% 5.44/5.66 ! [Z: real,A: real,B: real] :
% 5.44/5.66 ( ( ( Z = zero_zero_real )
% 5.44/5.66 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.44/5.66 = ( uminus_uminus_real @ B ) ) )
% 5.44/5.66 & ( ( Z != zero_zero_real )
% 5.44/5.66 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.44/5.66 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_divide_eq_if_simps(5)
% 5.44/5.66 thf(fact_5254_add__divide__eq__if__simps_I5_J,axiom,
% 5.44/5.66 ! [Z: complex,A: complex,B: complex] :
% 5.44/5.66 ( ( ( Z = zero_zero_complex )
% 5.44/5.66 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.44/5.66 & ( ( Z != zero_zero_complex )
% 5.44/5.66 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.44/5.66 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_divide_eq_if_simps(5)
% 5.44/5.66 thf(fact_5255_add__divide__eq__if__simps_I6_J,axiom,
% 5.44/5.66 ! [Z: real,A: real,B: real] :
% 5.44/5.66 ( ( ( Z = zero_zero_real )
% 5.44/5.66 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.44/5.66 = ( uminus_uminus_real @ B ) ) )
% 5.44/5.66 & ( ( Z != zero_zero_real )
% 5.44/5.66 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.44/5.66 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_divide_eq_if_simps(6)
% 5.44/5.66 thf(fact_5256_add__divide__eq__if__simps_I6_J,axiom,
% 5.44/5.66 ! [Z: complex,A: complex,B: complex] :
% 5.44/5.66 ( ( ( Z = zero_zero_complex )
% 5.44/5.66 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.44/5.66 & ( ( Z != zero_zero_complex )
% 5.44/5.66 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.44/5.66 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % add_divide_eq_if_simps(6)
% 5.44/5.66 thf(fact_5257_even__minus,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.44/5.66 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % even_minus
% 5.44/5.66 thf(fact_5258_even__minus,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.44/5.66 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.44/5.66
% 5.44/5.66 % even_minus
% 5.44/5.66 thf(fact_5259_power2__eq__iff,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 | ( X
% 5.44/5.66 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_eq_iff
% 5.44/5.66 thf(fact_5260_power2__eq__iff,axiom,
% 5.44/5.66 ! [X: int,Y: int] :
% 5.44/5.66 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 | ( X
% 5.44/5.66 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_eq_iff
% 5.44/5.66 thf(fact_5261_power2__eq__iff,axiom,
% 5.44/5.66 ! [X: complex,Y: complex] :
% 5.44/5.66 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 | ( X
% 5.44/5.66 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_eq_iff
% 5.44/5.66 thf(fact_5262_power2__eq__iff,axiom,
% 5.44/5.66 ! [X: code_integer,Y: code_integer] :
% 5.44/5.66 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.66 = ( ( X = Y )
% 5.44/5.66 | ( X
% 5.44/5.66 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_eq_iff
% 5.44/5.66 thf(fact_5263_take__bit__Suc__bit0,axiom,
% 5.44/5.66 ! [N2: nat,K: num] :
% 5.44/5.66 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.44/5.66 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_bit0
% 5.44/5.66 thf(fact_5264_take__bit__Suc__bit0,axiom,
% 5.44/5.66 ! [N2: nat,K: num] :
% 5.44/5.66 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.44/5.66 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_Suc_bit0
% 5.44/5.66 thf(fact_5265_take__bit__eq__mod,axiom,
% 5.44/5.66 ( bit_se2923211474154528505it_int
% 5.44/5.66 = ( ^ [N: nat,A4: int] : ( modulo_modulo_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_eq_mod
% 5.44/5.66 thf(fact_5266_take__bit__eq__mod,axiom,
% 5.44/5.66 ( bit_se2925701944663578781it_nat
% 5.44/5.66 = ( ^ [N: nat,A4: nat] : ( modulo_modulo_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_eq_mod
% 5.44/5.66 thf(fact_5267_take__bit__nat__eq__self__iff,axiom,
% 5.44/5.66 ! [N2: nat,M: nat] :
% 5.44/5.66 ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.44/5.66 = M )
% 5.44/5.66 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_nat_eq_self_iff
% 5.44/5.66 thf(fact_5268_take__bit__nat__less__exp,axiom,
% 5.44/5.66 ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_nat_less_exp
% 5.44/5.66 thf(fact_5269_take__bit__nat__eq__self,axiom,
% 5.44/5.66 ! [M: nat,N2: nat] :
% 5.44/5.66 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.66 => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.44/5.66 = M ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_nat_eq_self
% 5.44/5.66 thf(fact_5270_ln__le__minus__one,axiom,
% 5.44/5.66 ! [X: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_le_minus_one
% 5.44/5.66 thf(fact_5271_take__bit__nat__def,axiom,
% 5.44/5.66 ( bit_se2925701944663578781it_nat
% 5.44/5.66 = ( ^ [N: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_nat_def
% 5.44/5.66 thf(fact_5272_ln__diff__le,axiom,
% 5.44/5.66 ! [X: real,Y: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.66 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.66 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % ln_diff_le
% 5.44/5.66 thf(fact_5273_take__bit__int__less__exp,axiom,
% 5.44/5.66 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_int_less_exp
% 5.44/5.66 thf(fact_5274_pos__minus__divide__le__eq,axiom,
% 5.44/5.66 ! [C: real,B: real,A: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.44/5.66 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pos_minus_divide_le_eq
% 5.44/5.66 thf(fact_5275_pos__le__minus__divide__eq,axiom,
% 5.44/5.66 ! [C: real,A: real,B: real] :
% 5.44/5.66 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.44/5.66 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % pos_le_minus_divide_eq
% 5.44/5.66 thf(fact_5276_neg__minus__divide__le__eq,axiom,
% 5.44/5.66 ! [C: real,B: real,A: real] :
% 5.44/5.66 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.44/5.66 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_minus_divide_le_eq
% 5.44/5.66 thf(fact_5277_neg__le__minus__divide__eq,axiom,
% 5.44/5.66 ! [C: real,A: real,B: real] :
% 5.44/5.66 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.44/5.66 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_le_minus_divide_eq
% 5.44/5.66 thf(fact_5278_minus__divide__le__eq,axiom,
% 5.44/5.66 ! [B: real,C: real,A: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.44/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % minus_divide_le_eq
% 5.44/5.66 thf(fact_5279_le__minus__divide__eq,axiom,
% 5.44/5.66 ! [A: real,B: real,C: real] :
% 5.44/5.66 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.44/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % le_minus_divide_eq
% 5.44/5.66 thf(fact_5280_less__divide__eq__numeral_I2_J,axiom,
% 5.44/5.66 ! [W: num,B: real,C: real] :
% 5.44/5.66 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.44/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % less_divide_eq_numeral(2)
% 5.44/5.66 thf(fact_5281_divide__less__eq__numeral_I2_J,axiom,
% 5.44/5.66 ! [B: real,C: real,W: num] :
% 5.44/5.66 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.44/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.66 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % divide_less_eq_numeral(2)
% 5.44/5.66 thf(fact_5282_take__bit__int__def,axiom,
% 5.44/5.66 ( bit_se2923211474154528505it_int
% 5.44/5.66 = ( ^ [N: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % take_bit_int_def
% 5.44/5.66 thf(fact_5283_power2__eq__1__iff,axiom,
% 5.44/5.66 ! [A: real] :
% 5.44/5.66 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = one_one_real )
% 5.44/5.66 = ( ( A = one_one_real )
% 5.44/5.66 | ( A
% 5.44/5.66 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_eq_1_iff
% 5.44/5.66 thf(fact_5284_power2__eq__1__iff,axiom,
% 5.44/5.66 ! [A: int] :
% 5.44/5.66 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = one_one_int )
% 5.44/5.66 = ( ( A = one_one_int )
% 5.44/5.66 | ( A
% 5.44/5.66 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_eq_1_iff
% 5.44/5.66 thf(fact_5285_power2__eq__1__iff,axiom,
% 5.44/5.66 ! [A: complex] :
% 5.44/5.66 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = one_one_complex )
% 5.44/5.66 = ( ( A = one_one_complex )
% 5.44/5.66 | ( A
% 5.44/5.66 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_eq_1_iff
% 5.44/5.66 thf(fact_5286_power2__eq__1__iff,axiom,
% 5.44/5.66 ! [A: code_integer] :
% 5.44/5.66 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.66 = one_one_Code_integer )
% 5.44/5.66 = ( ( A = one_one_Code_integer )
% 5.44/5.66 | ( A
% 5.44/5.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % power2_eq_1_iff
% 5.44/5.66 thf(fact_5287_uminus__power__if,axiom,
% 5.44/5.66 ! [N2: nat,A: real] :
% 5.44/5.66 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.44/5.66 = ( power_power_real @ A @ N2 ) ) )
% 5.44/5.66 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.44/5.66 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_power_if
% 5.44/5.66 thf(fact_5288_uminus__power__if,axiom,
% 5.44/5.66 ! [N2: nat,A: int] :
% 5.44/5.66 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.44/5.66 = ( power_power_int @ A @ N2 ) ) )
% 5.44/5.66 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.44/5.66 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_power_if
% 5.44/5.66 thf(fact_5289_uminus__power__if,axiom,
% 5.44/5.66 ! [N2: nat,A: complex] :
% 5.44/5.66 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.44/5.66 = ( power_power_complex @ A @ N2 ) ) )
% 5.44/5.66 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.44/5.66 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_power_if
% 5.44/5.66 thf(fact_5290_uminus__power__if,axiom,
% 5.44/5.66 ! [N2: nat,A: code_integer] :
% 5.44/5.66 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.44/5.66 = ( power_8256067586552552935nteger @ A @ N2 ) ) )
% 5.44/5.66 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.66 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.44/5.66 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % uminus_power_if
% 5.44/5.66 thf(fact_5291_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.44/5.66 ! [K: nat,N2: nat] :
% 5.44/5.66 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.66 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.44/5.66 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_power_add_eq_neg_one_power_diff
% 5.44/5.66 thf(fact_5292_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.44/5.66 ! [K: nat,N2: nat] :
% 5.44/5.66 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.66 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.44/5.66 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_power_add_eq_neg_one_power_diff
% 5.44/5.66 thf(fact_5293_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.44/5.66 ! [K: nat,N2: nat] :
% 5.44/5.66 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.66 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.44/5.66 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.44/5.66
% 5.44/5.66 % neg_one_power_add_eq_neg_one_power_diff
% 5.44/5.66 thf(fact_5294_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.44/5.66 ! [K: nat,N2: nat] :
% 5.44/5.66 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.66 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.44/5.67 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_one_power_add_eq_neg_one_power_diff
% 5.44/5.67 thf(fact_5295_realpow__square__minus__le,axiom,
% 5.44/5.67 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % realpow_square_minus_le
% 5.44/5.67 thf(fact_5296_num_Osize__gen_I1_J,axiom,
% 5.44/5.67 ( ( size_num @ one )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % num.size_gen(1)
% 5.44/5.67 thf(fact_5297_ln__one__minus__pos__lower__bound,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.67 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % ln_one_minus_pos_lower_bound
% 5.44/5.67 thf(fact_5298_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.44/5.67 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_int_greater_eq_minus_exp
% 5.44/5.67 thf(fact_5299_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.44/5.67 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_int_less_eq_self_iff
% 5.44/5.67 thf(fact_5300_signed__take__bit__int__greater__self__iff,axiom,
% 5.44/5.67 ! [K: int,N2: nat] :
% 5.44/5.67 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.44/5.67 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_int_greater_self_iff
% 5.44/5.67 thf(fact_5301_take__bit__eq__0__iff,axiom,
% 5.44/5.67 ! [N2: nat,A: code_integer] :
% 5.44/5.67 ( ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.44/5.67 = zero_z3403309356797280102nteger )
% 5.44/5.67 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_eq_0_iff
% 5.44/5.67 thf(fact_5302_take__bit__eq__0__iff,axiom,
% 5.44/5.67 ! [N2: nat,A: int] :
% 5.44/5.67 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_eq_0_iff
% 5.44/5.67 thf(fact_5303_take__bit__eq__0__iff,axiom,
% 5.44/5.67 ! [N2: nat,A: nat] :
% 5.44/5.67 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.44/5.67 = zero_zero_nat )
% 5.44/5.67 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_eq_0_iff
% 5.44/5.67 thf(fact_5304_take__bit__nat__less__self__iff,axiom,
% 5.44/5.67 ! [N2: nat,M: nat] :
% 5.44/5.67 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 5.44/5.67 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_nat_less_self_iff
% 5.44/5.67 thf(fact_5305_take__bit__int__less__self__iff,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_int_less_self_iff
% 5.44/5.67 thf(fact_5306_take__bit__int__greater__eq__self__iff,axiom,
% 5.44/5.67 ! [K: int,N2: nat] :
% 5.44/5.67 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.44/5.67 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_int_greater_eq_self_iff
% 5.44/5.67 thf(fact_5307_le__divide__eq__numeral_I2_J,axiom,
% 5.44/5.67 ! [W: num,B: real,C: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.44/5.67 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.67 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.44/5.67 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.67 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.67 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.44/5.67 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.67 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % le_divide_eq_numeral(2)
% 5.44/5.67 thf(fact_5308_divide__le__eq__numeral_I2_J,axiom,
% 5.44/5.67 ! [B: real,C: real,W: num] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.67 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.67 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.44/5.67 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.67 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.67 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.44/5.67 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.67 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divide_le_eq_numeral(2)
% 5.44/5.67 thf(fact_5309_square__le__1,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.67 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % square_le_1
% 5.44/5.67 thf(fact_5310_square__le__1,axiom,
% 5.44/5.67 ! [X: code_integer] :
% 5.44/5.67 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.44/5.67 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.44/5.67 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % square_le_1
% 5.44/5.67 thf(fact_5311_square__le__1,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.44/5.67 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.44/5.67 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % square_le_1
% 5.44/5.67 thf(fact_5312_minus__power__mult__self,axiom,
% 5.44/5.67 ! [A: real,N2: nat] :
% 5.44/5.67 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.44/5.67 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_power_mult_self
% 5.44/5.67 thf(fact_5313_minus__power__mult__self,axiom,
% 5.44/5.67 ! [A: int,N2: nat] :
% 5.44/5.67 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.44/5.67 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_power_mult_self
% 5.44/5.67 thf(fact_5314_minus__power__mult__self,axiom,
% 5.44/5.67 ! [A: complex,N2: nat] :
% 5.44/5.67 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) )
% 5.44/5.67 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_power_mult_self
% 5.44/5.67 thf(fact_5315_minus__power__mult__self,axiom,
% 5.44/5.67 ! [A: code_integer,N2: nat] :
% 5.44/5.67 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.44/5.67 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_power_mult_self
% 5.44/5.67 thf(fact_5316_minus__one__power__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.44/5.67 = one_one_real ) )
% 5.44/5.67 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.44/5.67 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_one_power_iff
% 5.44/5.67 thf(fact_5317_minus__one__power__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.44/5.67 = one_one_int ) )
% 5.44/5.67 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_one_power_iff
% 5.44/5.67 thf(fact_5318_minus__one__power__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.44/5.67 = one_one_complex ) )
% 5.44/5.67 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_one_power_iff
% 5.44/5.67 thf(fact_5319_minus__one__power__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.44/5.67 = one_one_Code_integer ) )
% 5.44/5.67 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_one_power_iff
% 5.44/5.67 thf(fact_5320_signed__take__bit__int__eq__self__iff,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.44/5.67 = K )
% 5.44/5.67 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.44/5.67 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_int_eq_self_iff
% 5.44/5.67 thf(fact_5321_signed__take__bit__int__eq__self,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.44/5.67 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.67 => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.44/5.67 = K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_int_eq_self
% 5.44/5.67 thf(fact_5322_minus__1__div__exp__eq__int,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_1_div_exp_eq_int
% 5.44/5.67 thf(fact_5323_div__pos__neg__trivial,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( ord_less_int @ zero_zero_int @ K )
% 5.44/5.67 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.44/5.67 => ( ( divide_divide_int @ K @ L2 )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % div_pos_neg_trivial
% 5.44/5.67 thf(fact_5324_take__bit__int__eq__self__iff,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.44/5.67 = K )
% 5.44/5.67 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.67 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_int_eq_self_iff
% 5.44/5.67 thf(fact_5325_take__bit__int__eq__self,axiom,
% 5.44/5.67 ! [K: int,N2: nat] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.67 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.67 => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.44/5.67 = K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_int_eq_self
% 5.44/5.67 thf(fact_5326_signed__take__bit__eq__take__bit__shift,axiom,
% 5.44/5.67 ( bit_ri631733984087533419it_int
% 5.44/5.67 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_eq_take_bit_shift
% 5.44/5.67 thf(fact_5327_take__bit__incr__eq,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.44/5.67 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.44/5.67 => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.44/5.67 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_incr_eq
% 5.44/5.67 thf(fact_5328_power__minus1__odd,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.67 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_minus1_odd
% 5.44/5.67 thf(fact_5329_power__minus1__odd,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_minus1_odd
% 5.44/5.67 thf(fact_5330_power__minus1__odd,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_minus1_odd
% 5.44/5.67 thf(fact_5331_power__minus1__odd,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_minus1_odd
% 5.44/5.67 thf(fact_5332_take__bit__Suc,axiom,
% 5.44/5.67 ! [N2: nat,A: code_integer] :
% 5.44/5.67 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 5.44/5.67 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_Suc
% 5.44/5.67 thf(fact_5333_take__bit__Suc,axiom,
% 5.44/5.67 ! [N2: nat,A: int] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_Suc
% 5.44/5.67 thf(fact_5334_take__bit__Suc,axiom,
% 5.44/5.67 ! [N2: nat,A: nat] :
% 5.44/5.67 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 5.44/5.67 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_Suc
% 5.44/5.67 thf(fact_5335_int__bit__induct,axiom,
% 5.44/5.67 ! [P: int > $o,K: int] :
% 5.44/5.67 ( ( P @ zero_zero_int )
% 5.44/5.67 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 => ( ! [K2: int] :
% 5.44/5.67 ( ( P @ K2 )
% 5.44/5.67 => ( ( K2 != zero_zero_int )
% 5.44/5.67 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.67 => ( ! [K2: int] :
% 5.44/5.67 ( ( P @ K2 )
% 5.44/5.67 => ( ( K2
% 5.44/5.67 != ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.44/5.67 => ( P @ K ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % int_bit_induct
% 5.44/5.67 thf(fact_5336_take__bit__int__less__eq,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.44/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.67 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_int_less_eq
% 5.44/5.67 thf(fact_5337_take__bit__int__greater__eq,axiom,
% 5.44/5.67 ! [K: int,N2: nat] :
% 5.44/5.67 ( ( ord_less_int @ K @ zero_zero_int )
% 5.44/5.67 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_int_greater_eq
% 5.44/5.67 thf(fact_5338_stable__imp__take__bit__eq,axiom,
% 5.44/5.67 ! [A: code_integer,N2: nat] :
% 5.44/5.67 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.67 = A )
% 5.44/5.67 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.44/5.67 = zero_z3403309356797280102nteger ) )
% 5.44/5.67 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.44/5.67 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % stable_imp_take_bit_eq
% 5.44/5.67 thf(fact_5339_stable__imp__take__bit__eq,axiom,
% 5.44/5.67 ! [A: int,N2: nat] :
% 5.44/5.67 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.67 = A )
% 5.44/5.67 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.44/5.67 = zero_zero_int ) )
% 5.44/5.67 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.44/5.67 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % stable_imp_take_bit_eq
% 5.44/5.67 thf(fact_5340_stable__imp__take__bit__eq,axiom,
% 5.44/5.67 ! [A: nat,N2: nat] :
% 5.44/5.67 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.67 = A )
% 5.44/5.67 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.44/5.67 = zero_zero_nat ) )
% 5.44/5.67 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.44/5.67 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % stable_imp_take_bit_eq
% 5.44/5.67 thf(fact_5341_divmod__step__nat__def,axiom,
% 5.44/5.67 ( unique5026877609467782581ep_nat
% 5.44/5.67 = ( ^ [L: num] :
% 5.44/5.67 ( produc2626176000494625587at_nat
% 5.44/5.67 @ ^ [Q4: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R4 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_step_nat_def
% 5.44/5.67 thf(fact_5342_ln__one__plus__pos__lower__bound,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.67 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % ln_one_plus_pos_lower_bound
% 5.44/5.67 thf(fact_5343_signed__take__bit__int__greater__eq,axiom,
% 5.44/5.67 ! [K: int,N2: nat] :
% 5.44/5.67 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.67 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_int_greater_eq
% 5.44/5.67 thf(fact_5344_divmod__step__int__def,axiom,
% 5.44/5.67 ( unique5024387138958732305ep_int
% 5.44/5.67 = ( ^ [L: num] :
% 5.44/5.67 ( produc4245557441103728435nt_int
% 5.44/5.67 @ ^ [Q4: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R4 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_step_int_def
% 5.44/5.67 thf(fact_5345_ln__2__less__1,axiom,
% 5.44/5.67 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.44/5.67
% 5.44/5.67 % ln_2_less_1
% 5.44/5.67 thf(fact_5346_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.44/5.67 thf(fact_5347_tanh__ln__real,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 5.44/5.67 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_ln_real
% 5.44/5.67 thf(fact_5348_divmod__algorithm__code_I5_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( produc2626176000494625587at_nat
% 5.44/5.67 @ ^ [Q4: nat,R4: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) )
% 5.44/5.67 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(5)
% 5.44/5.67 thf(fact_5349_divmod__algorithm__code_I5_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( produc4245557441103728435nt_int
% 5.44/5.67 @ ^ [Q4: int,R4: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) )
% 5.44/5.67 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(5)
% 5.44/5.67 thf(fact_5350_divmod__nat__if,axiom,
% 5.44/5.67 ( divmod_nat
% 5.44/5.67 = ( ^ [M6: nat,N: nat] :
% 5.44/5.67 ( if_Pro6206227464963214023at_nat
% 5.44/5.67 @ ( ( N = zero_zero_nat )
% 5.44/5.67 | ( ord_less_nat @ M6 @ N ) )
% 5.44/5.67 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.44/5.67 @ ( produc2626176000494625587at_nat
% 5.44/5.67 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.44/5.67 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_nat_if
% 5.44/5.67 thf(fact_5351_signed__take__bit__Suc__minus__bit1,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_Suc_minus_bit1
% 5.44/5.67 thf(fact_5352_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ln_one_plus_x_minus_x_bound
% 5.44/5.67 thf(fact_5353_semiring__norm_I90_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ( bit1 @ M )
% 5.44/5.67 = ( bit1 @ N2 ) )
% 5.44/5.67 = ( M = N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(90)
% 5.44/5.67 thf(fact_5354_case__prodI,axiom,
% 5.44/5.67 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.44/5.67 ( ( F @ A @ B )
% 5.44/5.67 => ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI
% 5.44/5.67 thf(fact_5355_case__prodI,axiom,
% 5.44/5.67 ! [F: num > num > $o,A: num,B: num] :
% 5.44/5.67 ( ( F @ A @ B )
% 5.44/5.67 => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI
% 5.44/5.67 thf(fact_5356_case__prodI,axiom,
% 5.44/5.67 ! [F: nat > num > $o,A: nat,B: num] :
% 5.44/5.67 ( ( F @ A @ B )
% 5.44/5.67 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI
% 5.44/5.67 thf(fact_5357_case__prodI,axiom,
% 5.44/5.67 ! [F: int > int > $o,A: int,B: int] :
% 5.44/5.67 ( ( F @ A @ B )
% 5.44/5.67 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI
% 5.44/5.67 thf(fact_5358_case__prodI,axiom,
% 5.44/5.67 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.44/5.67 ( ( F @ A @ B )
% 5.44/5.67 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI
% 5.44/5.67 thf(fact_5359_case__prodI2,axiom,
% 5.44/5.67 ! [P5: produc6271795597528267376eger_o,C: code_integer > $o > $o] :
% 5.44/5.67 ( ! [A3: code_integer,B3: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ A3 @ B3 ) )
% 5.44/5.67 => ( C @ A3 @ B3 ) )
% 5.44/5.67 => ( produc7828578312038201481er_o_o @ C @ P5 ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI2
% 5.44/5.67 thf(fact_5360_case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_num_num,C: num > num > $o] :
% 5.44/5.67 ( ! [A3: num,B3: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ A3 @ B3 ) )
% 5.44/5.67 => ( C @ A3 @ B3 ) )
% 5.44/5.67 => ( produc5703948589228662326_num_o @ C @ P5 ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI2
% 5.44/5.67 thf(fact_5361_case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_nat_num,C: nat > num > $o] :
% 5.44/5.67 ( ! [A3: nat,B3: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 5.44/5.67 => ( C @ A3 @ B3 ) )
% 5.44/5.67 => ( produc4927758841916487424_num_o @ C @ P5 ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI2
% 5.44/5.67 thf(fact_5362_case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_int_int,C: int > int > $o] :
% 5.44/5.67 ( ! [A3: int,B3: int] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_int_int @ A3 @ B3 ) )
% 5.44/5.67 => ( C @ A3 @ B3 ) )
% 5.44/5.67 => ( produc4947309494688390418_int_o @ C @ P5 ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI2
% 5.44/5.67 thf(fact_5363_case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_nat_nat,C: nat > nat > $o] :
% 5.44/5.67 ( ! [A3: nat,B3: nat] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_nat @ A3 @ B3 ) )
% 5.44/5.67 => ( C @ A3 @ B3 ) )
% 5.44/5.67 => ( produc6081775807080527818_nat_o @ C @ P5 ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI2
% 5.44/5.67 thf(fact_5364_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: nat,C: code_integer > $o > set_nat,A: code_integer,B: $o] :
% 5.44/5.67 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5365_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: real,C: code_integer > $o > set_real,A: code_integer,B: $o] :
% 5.44/5.67 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5366_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: int,C: code_integer > $o > set_int,A: code_integer,B: $o] :
% 5.44/5.67 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5367_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: complex,C: code_integer > $o > set_complex,A: code_integer,B: $o] :
% 5.44/5.67 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5368_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 5.44/5.67 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5369_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 5.44/5.67 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5370_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 5.44/5.67 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5371_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: complex,C: num > num > set_complex,A: num,B: num] :
% 5.44/5.67 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5372_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: nat,C: nat > num > set_nat,A: nat,B: num] :
% 5.44/5.67 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5373_mem__case__prodI,axiom,
% 5.44/5.67 ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 5.44/5.67 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.44/5.67 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI
% 5.44/5.67 thf(fact_5374_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: produc6271795597528267376eger_o,Z: nat,C: code_integer > $o > set_nat] :
% 5.44/5.67 ( ! [A3: code_integer,B3: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ A3 @ B3 ) )
% 5.44/5.67 => ( member_nat @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5375_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: produc6271795597528267376eger_o,Z: real,C: code_integer > $o > set_real] :
% 5.44/5.67 ( ! [A3: code_integer,B3: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ A3 @ B3 ) )
% 5.44/5.67 => ( member_real @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5376_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: produc6271795597528267376eger_o,Z: int,C: code_integer > $o > set_int] :
% 5.44/5.67 ( ! [A3: code_integer,B3: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ A3 @ B3 ) )
% 5.44/5.67 => ( member_int @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5377_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: produc6271795597528267376eger_o,Z: complex,C: code_integer > $o > set_complex] :
% 5.44/5.67 ( ! [A3: code_integer,B3: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ A3 @ B3 ) )
% 5.44/5.67 => ( member_complex @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5378_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 5.44/5.67 ( ! [A3: num,B3: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ A3 @ B3 ) )
% 5.44/5.67 => ( member_nat @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5379_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_num_num,Z: real,C: num > num > set_real] :
% 5.44/5.67 ( ! [A3: num,B3: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ A3 @ B3 ) )
% 5.44/5.67 => ( member_real @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5380_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_num_num,Z: int,C: num > num > set_int] :
% 5.44/5.67 ( ! [A3: num,B3: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ A3 @ B3 ) )
% 5.44/5.67 => ( member_int @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5381_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_num_num,Z: complex,C: num > num > set_complex] :
% 5.44/5.67 ( ! [A3: num,B3: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ A3 @ B3 ) )
% 5.44/5.67 => ( member_complex @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5382_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_nat_num,Z: nat,C: nat > num > set_nat] :
% 5.44/5.67 ( ! [A3: nat,B3: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 5.44/5.67 => ( member_nat @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5383_mem__case__prodI2,axiom,
% 5.44/5.67 ! [P5: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 5.44/5.67 ( ! [A3: nat,B3: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_num @ A3 @ B3 ) )
% 5.44/5.67 => ( member_real @ Z @ ( C @ A3 @ B3 ) ) )
% 5.44/5.67 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodI2
% 5.44/5.67 thf(fact_5384_case__prodI2_H,axiom,
% 5.44/5.67 ! [P5: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.44/5.67 ( ! [A3: nat,B3: nat] :
% 5.44/5.67 ( ( ( product_Pair_nat_nat @ A3 @ B3 )
% 5.44/5.67 = P5 )
% 5.44/5.67 => ( C @ A3 @ B3 @ X ) )
% 5.44/5.67 => ( produc8739625826339149834_nat_o @ C @ P5 @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodI2'
% 5.44/5.67 thf(fact_5385_semiring__norm_I89_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( bit1 @ M )
% 5.44/5.67 != ( bit0 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(89)
% 5.44/5.67 thf(fact_5386_semiring__norm_I88_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( bit0 @ M )
% 5.44/5.67 != ( bit1 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(88)
% 5.44/5.67 thf(fact_5387_semiring__norm_I86_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( bit1 @ M )
% 5.44/5.67 != one ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(86)
% 5.44/5.67 thf(fact_5388_semiring__norm_I84_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( one
% 5.44/5.67 != ( bit1 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(84)
% 5.44/5.67 thf(fact_5389_abs__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.67 = ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_numeral
% 5.44/5.67 thf(fact_5390_abs__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.67 = ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_numeral
% 5.44/5.67 thf(fact_5391_abs__mult__self__eq,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.44/5.67 = ( times_times_real @ A @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult_self_eq
% 5.44/5.67 thf(fact_5392_abs__mult__self__eq,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.44/5.67 = ( times_times_int @ A @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult_self_eq
% 5.44/5.67 thf(fact_5393_abs__add__abs,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.44/5.67 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_add_abs
% 5.44/5.67 thf(fact_5394_abs__add__abs,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_add_abs
% 5.44/5.67 thf(fact_5395_abs__1,axiom,
% 5.44/5.67 ( ( abs_abs_complex @ one_one_complex )
% 5.44/5.67 = one_one_complex ) ).
% 5.44/5.67
% 5.44/5.67 % abs_1
% 5.44/5.67 thf(fact_5396_abs__1,axiom,
% 5.44/5.67 ( ( abs_abs_real @ one_one_real )
% 5.44/5.67 = one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % abs_1
% 5.44/5.67 thf(fact_5397_abs__1,axiom,
% 5.44/5.67 ( ( abs_abs_int @ one_one_int )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % abs_1
% 5.44/5.67 thf(fact_5398_abs__divide,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.67 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_divide
% 5.44/5.67 thf(fact_5399_abs__divide,axiom,
% 5.44/5.67 ! [A: complex,B: complex] :
% 5.44/5.67 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.67 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_divide
% 5.44/5.67 thf(fact_5400_tanh__real__less__iff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 5.44/5.67 = ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_less_iff
% 5.44/5.67 thf(fact_5401_tanh__real__le__iff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 5.44/5.67 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_le_iff
% 5.44/5.67 thf(fact_5402_semiring__norm_I80_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(80)
% 5.44/5.67 thf(fact_5403_semiring__norm_I73_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(73)
% 5.44/5.67 thf(fact_5404_abs__le__zero__iff,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.44/5.67 = ( A = zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_zero_iff
% 5.44/5.67 thf(fact_5405_abs__le__zero__iff,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.44/5.67 = ( A = zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_zero_iff
% 5.44/5.67 thf(fact_5406_abs__le__self__iff,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.44/5.67 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_self_iff
% 5.44/5.67 thf(fact_5407_abs__le__self__iff,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.44/5.67 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_self_iff
% 5.44/5.67 thf(fact_5408_abs__of__nonneg,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.67 => ( ( abs_abs_real @ A )
% 5.44/5.67 = A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_nonneg
% 5.44/5.67 thf(fact_5409_abs__of__nonneg,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.67 => ( ( abs_abs_int @ A )
% 5.44/5.67 = A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_nonneg
% 5.44/5.67 thf(fact_5410_zero__less__abs__iff,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.44/5.67 = ( A != zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_less_abs_iff
% 5.44/5.67 thf(fact_5411_zero__less__abs__iff,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.44/5.67 = ( A != zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_less_abs_iff
% 5.44/5.67 thf(fact_5412_abs__neg__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.67 = ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_neg_numeral
% 5.44/5.67 thf(fact_5413_abs__neg__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.67 = ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_neg_numeral
% 5.44/5.67 thf(fact_5414_abs__neg__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.67 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_neg_numeral
% 5.44/5.67 thf(fact_5415_abs__neg__one,axiom,
% 5.44/5.67 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.67 = one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % abs_neg_one
% 5.44/5.67 thf(fact_5416_abs__neg__one,axiom,
% 5.44/5.67 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % abs_neg_one
% 5.44/5.67 thf(fact_5417_abs__neg__one,axiom,
% 5.44/5.67 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = one_one_Code_integer ) ).
% 5.44/5.67
% 5.44/5.67 % abs_neg_one
% 5.44/5.67 thf(fact_5418_abs__power__minus,axiom,
% 5.44/5.67 ! [A: real,N2: nat] :
% 5.44/5.67 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.44/5.67 = ( abs_abs_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_power_minus
% 5.44/5.67 thf(fact_5419_abs__power__minus,axiom,
% 5.44/5.67 ! [A: int,N2: nat] :
% 5.44/5.67 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.44/5.67 = ( abs_abs_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_power_minus
% 5.44/5.67 thf(fact_5420_abs__power__minus,axiom,
% 5.44/5.67 ! [A: code_integer,N2: nat] :
% 5.44/5.67 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.44/5.67 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_power_minus
% 5.44/5.67 thf(fact_5421_semiring__norm_I7_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(7)
% 5.44/5.67 thf(fact_5422_semiring__norm_I9_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(9)
% 5.44/5.67 thf(fact_5423_semiring__norm_I14_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(14)
% 5.44/5.67 thf(fact_5424_semiring__norm_I15_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(15)
% 5.44/5.67 thf(fact_5425_semiring__norm_I72_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(72)
% 5.44/5.67 thf(fact_5426_semiring__norm_I81_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(81)
% 5.44/5.67 thf(fact_5427_semiring__norm_I70_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(70)
% 5.44/5.67 thf(fact_5428_semiring__norm_I77_J,axiom,
% 5.44/5.67 ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(77)
% 5.44/5.67 thf(fact_5429_tanh__real__pos__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.44/5.67 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_pos_iff
% 5.44/5.67 thf(fact_5430_tanh__real__neg__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.44/5.67 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_neg_iff
% 5.44/5.67 thf(fact_5431_tanh__real__nonneg__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.44/5.67 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_nonneg_iff
% 5.44/5.67 thf(fact_5432_tanh__real__nonpos__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.44/5.67 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_nonpos_iff
% 5.44/5.67 thf(fact_5433_zero__le__divide__abs__iff,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.44/5.67 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.67 | ( B = zero_zero_real ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_le_divide_abs_iff
% 5.44/5.67 thf(fact_5434_divide__le__0__abs__iff,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.44/5.67 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.67 | ( B = zero_zero_real ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divide_le_0_abs_iff
% 5.44/5.67 thf(fact_5435_abs__of__nonpos,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.67 => ( ( abs_abs_real @ A )
% 5.44/5.67 = ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_nonpos
% 5.44/5.67 thf(fact_5436_abs__of__nonpos,axiom,
% 5.44/5.67 ! [A: code_integer] :
% 5.44/5.67 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.44/5.67 => ( ( abs_abs_Code_integer @ A )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_nonpos
% 5.44/5.67 thf(fact_5437_abs__of__nonpos,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.44/5.67 => ( ( abs_abs_int @ A )
% 5.44/5.67 = ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_nonpos
% 5.44/5.67 thf(fact_5438_zdiv__numeral__Bit1,axiom,
% 5.44/5.67 ! [V: num,W: num] :
% 5.44/5.67 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.44/5.67 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % zdiv_numeral_Bit1
% 5.44/5.67 thf(fact_5439_semiring__norm_I10_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(10)
% 5.44/5.67 thf(fact_5440_semiring__norm_I8_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.44/5.67 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(8)
% 5.44/5.67 thf(fact_5441_semiring__norm_I5_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.44/5.67 = ( bit1 @ M ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(5)
% 5.44/5.67 thf(fact_5442_semiring__norm_I4_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(4)
% 5.44/5.67 thf(fact_5443_semiring__norm_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( bit1 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(3)
% 5.44/5.67 thf(fact_5444_artanh__minus__real,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.67 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % artanh_minus_real
% 5.44/5.67 thf(fact_5445_semiring__norm_I16_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(16)
% 5.44/5.67 thf(fact_5446_semiring__norm_I79_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(79)
% 5.44/5.67 thf(fact_5447_semiring__norm_I74_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(74)
% 5.44/5.67 thf(fact_5448_zero__less__power__abs__iff,axiom,
% 5.44/5.67 ! [A: real,N2: nat] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.44/5.67 = ( ( A != zero_zero_real )
% 5.44/5.67 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_less_power_abs_iff
% 5.44/5.67 thf(fact_5449_zero__less__power__abs__iff,axiom,
% 5.44/5.67 ! [A: int,N2: nat] :
% 5.44/5.67 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 5.44/5.67 = ( ( A != zero_zero_int )
% 5.44/5.67 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_less_power_abs_iff
% 5.44/5.67 thf(fact_5450_abs__power2,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_power2
% 5.44/5.67 thf(fact_5451_abs__power2,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_power2
% 5.44/5.67 thf(fact_5452_power2__abs,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.67 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power2_abs
% 5.44/5.67 thf(fact_5453_power2__abs,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.67 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power2_abs
% 5.44/5.67 thf(fact_5454_dvd__numeral__simp,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.44/5.67 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N2 @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dvd_numeral_simp
% 5.44/5.67 thf(fact_5455_dvd__numeral__simp,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.67 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N2 @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dvd_numeral_simp
% 5.44/5.67 thf(fact_5456_dvd__numeral__simp,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.67 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N2 @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dvd_numeral_simp
% 5.44/5.67 thf(fact_5457_divmod__algorithm__code_I2_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.44/5.67 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(2)
% 5.44/5.67 thf(fact_5458_divmod__algorithm__code_I2_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( unique5052692396658037445od_int @ M @ one )
% 5.44/5.67 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(2)
% 5.44/5.67 thf(fact_5459_power__even__abs__numeral,axiom,
% 5.44/5.67 ! [W: num,A: real] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.67 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.67 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_even_abs_numeral
% 5.44/5.67 thf(fact_5460_power__even__abs__numeral,axiom,
% 5.44/5.67 ! [W: num,A: int] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.67 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.44/5.67 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_even_abs_numeral
% 5.44/5.67 thf(fact_5461_div__Suc__eq__div__add3,axiom,
% 5.44/5.67 ! [M: nat,N2: nat] :
% 5.44/5.67 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.44/5.67 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % div_Suc_eq_div_add3
% 5.44/5.67 thf(fact_5462_Suc__div__eq__add3__div__numeral,axiom,
% 5.44/5.67 ! [M: nat,V: num] :
% 5.44/5.67 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.44/5.67 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % Suc_div_eq_add3_div_numeral
% 5.44/5.67 thf(fact_5463_divmod__algorithm__code_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(3)
% 5.44/5.67 thf(fact_5464_divmod__algorithm__code_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(3)
% 5.44/5.67 thf(fact_5465_mod__Suc__eq__mod__add3,axiom,
% 5.44/5.67 ! [M: nat,N2: nat] :
% 5.44/5.67 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.44/5.67 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mod_Suc_eq_mod_add3
% 5.44/5.67 thf(fact_5466_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.44/5.67 ! [M: nat,V: num] :
% 5.44/5.67 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.44/5.67 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % Suc_mod_eq_add3_mod_numeral
% 5.44/5.67 thf(fact_5467_divmod__algorithm__code_I4_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(4)
% 5.44/5.67 thf(fact_5468_divmod__algorithm__code_I4_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(4)
% 5.44/5.67 thf(fact_5469_zmod__numeral__Bit1,axiom,
% 5.44/5.67 ! [V: num,W: num] :
% 5.44/5.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.44/5.67 = ( 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 ) ) ).
% 5.44/5.67
% 5.44/5.67 % zmod_numeral_Bit1
% 5.44/5.67 thf(fact_5470_divmod__algorithm__code_I8_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ( ord_less_num @ M @ N2 )
% 5.44/5.67 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.44/5.67 & ( ~ ( ord_less_num @ M @ N2 )
% 5.44/5.67 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(8)
% 5.44/5.67 thf(fact_5471_divmod__algorithm__code_I8_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ( ord_less_num @ M @ N2 )
% 5.44/5.67 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.44/5.67 & ( ~ ( ord_less_num @ M @ N2 )
% 5.44/5.67 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(8)
% 5.44/5.67 thf(fact_5472_divmod__algorithm__code_I8_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ( ord_less_num @ M @ N2 )
% 5.44/5.67 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.44/5.67 & ( ~ ( ord_less_num @ M @ N2 )
% 5.44/5.67 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(8)
% 5.44/5.67 thf(fact_5473_divmod__algorithm__code_I7_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.44/5.67 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.44/5.67 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.44/5.67 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(7)
% 5.44/5.67 thf(fact_5474_divmod__algorithm__code_I7_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.44/5.67 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.44/5.67 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.44/5.67 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(7)
% 5.44/5.67 thf(fact_5475_divmod__algorithm__code_I7_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.44/5.67 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.44/5.67 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.44/5.67 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(7)
% 5.44/5.67 thf(fact_5476_signed__take__bit__Suc__bit1,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_Suc_bit1
% 5.44/5.67 thf(fact_5477_divmod__algorithm__code_I6_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( produc2626176000494625587at_nat
% 5.44/5.67 @ ^ [Q4: nat,R4: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) @ one_one_nat ) )
% 5.44/5.67 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(6)
% 5.44/5.67 thf(fact_5478_divmod__algorithm__code_I6_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( produc4245557441103728435nt_int
% 5.44/5.67 @ ^ [Q4: int,R4: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) @ one_one_int ) )
% 5.44/5.67 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_algorithm_code(6)
% 5.44/5.67 thf(fact_5479_take__bit__minus,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 5.44/5.67 = ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_minus
% 5.44/5.67 thf(fact_5480_abs__ge__self,axiom,
% 5.44/5.67 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ge_self
% 5.44/5.67 thf(fact_5481_abs__ge__self,axiom,
% 5.44/5.67 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ge_self
% 5.44/5.67 thf(fact_5482_abs__le__D1,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.44/5.67 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_D1
% 5.44/5.67 thf(fact_5483_abs__le__D1,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.44/5.67 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_D1
% 5.44/5.67 thf(fact_5484_abs__mult,axiom,
% 5.44/5.67 ! [A: complex,B: complex] :
% 5.44/5.67 ( ( abs_abs_complex @ ( times_times_complex @ A @ B ) )
% 5.44/5.67 = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult
% 5.44/5.67 thf(fact_5485_abs__mult,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.44/5.67 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult
% 5.44/5.67 thf(fact_5486_abs__mult,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.44/5.67 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult
% 5.44/5.67 thf(fact_5487_abs__one,axiom,
% 5.44/5.67 ( ( abs_abs_real @ one_one_real )
% 5.44/5.67 = one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % abs_one
% 5.44/5.67 thf(fact_5488_abs__one,axiom,
% 5.44/5.67 ( ( abs_abs_int @ one_one_int )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % abs_one
% 5.44/5.67 thf(fact_5489_power__abs,axiom,
% 5.44/5.67 ! [A: real,N2: nat] :
% 5.44/5.67 ( ( abs_abs_real @ ( power_power_real @ A @ N2 ) )
% 5.44/5.67 = ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_abs
% 5.44/5.67 thf(fact_5490_power__abs,axiom,
% 5.44/5.67 ! [A: int,N2: nat] :
% 5.44/5.67 ( ( abs_abs_int @ ( power_power_int @ A @ N2 ) )
% 5.44/5.67 = ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_abs
% 5.44/5.67 thf(fact_5491_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: nat,C: code_integer > $o > set_nat,P5: produc6271795597528267376eger_o] :
% 5.44/5.67 ( ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: code_integer,Y5: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_nat @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5492_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: real,C: code_integer > $o > set_real,P5: produc6271795597528267376eger_o] :
% 5.44/5.67 ( ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: code_integer,Y5: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_real @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5493_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: int,C: code_integer > $o > set_int,P5: produc6271795597528267376eger_o] :
% 5.44/5.67 ( ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: code_integer,Y5: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_int @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5494_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: complex,C: code_integer > $o > set_complex,P5: produc6271795597528267376eger_o] :
% 5.44/5.67 ( ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: code_integer,Y5: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_complex @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5495_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: nat,C: num > num > set_nat,P5: product_prod_num_num] :
% 5.44/5.67 ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: num,Y5: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_nat @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5496_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: real,C: num > num > set_real,P5: product_prod_num_num] :
% 5.44/5.67 ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: num,Y5: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_real @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5497_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: int,C: num > num > set_int,P5: product_prod_num_num] :
% 5.44/5.67 ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: num,Y5: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_int @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5498_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: complex,C: num > num > set_complex,P5: product_prod_num_num] :
% 5.44/5.67 ( ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: num,Y5: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_complex @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5499_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: nat,C: nat > num > set_nat,P5: product_prod_nat_num] :
% 5.44/5.67 ( ( member_nat @ Z @ ( produc4130284055270567454et_nat @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: nat,Y5: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_num @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_nat @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5500_mem__case__prodE,axiom,
% 5.44/5.67 ! [Z: real,C: nat > num > set_real,P5: product_prod_nat_num] :
% 5.44/5.67 ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P5 ) )
% 5.44/5.67 => ~ ! [X5: nat,Y5: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_num @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( member_real @ Z @ ( C @ X5 @ Y5 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mem_case_prodE
% 5.44/5.67 thf(fact_5501_verit__eq__simplify_I14_J,axiom,
% 5.44/5.67 ! [X22: num,X32: num] :
% 5.44/5.67 ( ( bit0 @ X22 )
% 5.44/5.67 != ( bit1 @ X32 ) ) ).
% 5.44/5.67
% 5.44/5.67 % verit_eq_simplify(14)
% 5.44/5.67 thf(fact_5502_verit__eq__simplify_I12_J,axiom,
% 5.44/5.67 ! [X32: num] :
% 5.44/5.67 ( one
% 5.44/5.67 != ( bit1 @ X32 ) ) ).
% 5.44/5.67
% 5.44/5.67 % verit_eq_simplify(12)
% 5.44/5.67 thf(fact_5503_case__prodD,axiom,
% 5.44/5.67 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.44/5.67 ( ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) )
% 5.44/5.67 => ( F @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodD
% 5.44/5.67 thf(fact_5504_case__prodD,axiom,
% 5.44/5.67 ! [F: num > num > $o,A: num,B: num] :
% 5.44/5.67 ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 5.44/5.67 => ( F @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodD
% 5.44/5.67 thf(fact_5505_case__prodD,axiom,
% 5.44/5.67 ! [F: nat > num > $o,A: nat,B: num] :
% 5.44/5.67 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 5.44/5.67 => ( F @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodD
% 5.44/5.67 thf(fact_5506_case__prodD,axiom,
% 5.44/5.67 ! [F: int > int > $o,A: int,B: int] :
% 5.44/5.67 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.44/5.67 => ( F @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodD
% 5.44/5.67 thf(fact_5507_case__prodD,axiom,
% 5.44/5.67 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.44/5.67 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.44/5.67 => ( F @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodD
% 5.44/5.67 thf(fact_5508_case__prodE,axiom,
% 5.44/5.67 ! [C: code_integer > $o > $o,P5: produc6271795597528267376eger_o] :
% 5.44/5.67 ( ( produc7828578312038201481er_o_o @ C @ P5 )
% 5.44/5.67 => ~ ! [X5: code_integer,Y5: $o] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( produc6677183202524767010eger_o @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( C @ X5 @ Y5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodE
% 5.44/5.67 thf(fact_5509_case__prodE,axiom,
% 5.44/5.67 ! [C: num > num > $o,P5: product_prod_num_num] :
% 5.44/5.67 ( ( produc5703948589228662326_num_o @ C @ P5 )
% 5.44/5.67 => ~ ! [X5: num,Y5: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_num_num @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( C @ X5 @ Y5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodE
% 5.44/5.67 thf(fact_5510_case__prodE,axiom,
% 5.44/5.67 ! [C: nat > num > $o,P5: product_prod_nat_num] :
% 5.44/5.67 ( ( produc4927758841916487424_num_o @ C @ P5 )
% 5.44/5.67 => ~ ! [X5: nat,Y5: num] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_num @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( C @ X5 @ Y5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodE
% 5.44/5.67 thf(fact_5511_case__prodE,axiom,
% 5.44/5.67 ! [C: int > int > $o,P5: product_prod_int_int] :
% 5.44/5.67 ( ( produc4947309494688390418_int_o @ C @ P5 )
% 5.44/5.67 => ~ ! [X5: int,Y5: int] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_int_int @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( C @ X5 @ Y5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodE
% 5.44/5.67 thf(fact_5512_case__prodE,axiom,
% 5.44/5.67 ! [C: nat > nat > $o,P5: product_prod_nat_nat] :
% 5.44/5.67 ( ( produc6081775807080527818_nat_o @ C @ P5 )
% 5.44/5.67 => ~ ! [X5: nat,Y5: nat] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_nat @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( C @ X5 @ Y5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodE
% 5.44/5.67 thf(fact_5513_case__prodD_H,axiom,
% 5.44/5.67 ! [R2: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.44/5.67 ( ( produc8739625826339149834_nat_o @ R2 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.44/5.67 => ( R2 @ A @ B @ C ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodD'
% 5.44/5.67 thf(fact_5514_case__prodE_H,axiom,
% 5.44/5.67 ! [C: nat > nat > product_prod_nat_nat > $o,P5: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.44/5.67 ( ( produc8739625826339149834_nat_o @ C @ P5 @ Z )
% 5.44/5.67 => ~ ! [X5: nat,Y5: nat] :
% 5.44/5.67 ( ( P5
% 5.44/5.67 = ( product_Pair_nat_nat @ X5 @ Y5 ) )
% 5.44/5.67 => ~ ( C @ X5 @ Y5 @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % case_prodE'
% 5.44/5.67 thf(fact_5515_abs__ge__zero,axiom,
% 5.44/5.67 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ge_zero
% 5.44/5.67 thf(fact_5516_abs__ge__zero,axiom,
% 5.44/5.67 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ge_zero
% 5.44/5.67 thf(fact_5517_abs__not__less__zero,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.44/5.67
% 5.44/5.67 % abs_not_less_zero
% 5.44/5.67 thf(fact_5518_abs__not__less__zero,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % abs_not_less_zero
% 5.44/5.67 thf(fact_5519_abs__of__pos,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.67 => ( ( abs_abs_real @ A )
% 5.44/5.67 = A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_pos
% 5.44/5.67 thf(fact_5520_abs__of__pos,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( ord_less_int @ zero_zero_int @ A )
% 5.44/5.67 => ( ( abs_abs_int @ A )
% 5.44/5.67 = A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_pos
% 5.44/5.67 thf(fact_5521_abs__triangle__ineq,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq
% 5.44/5.67 thf(fact_5522_abs__triangle__ineq,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq
% 5.44/5.67 thf(fact_5523_abs__mult__less,axiom,
% 5.44/5.67 ! [A: real,C: real,B: real,D: real] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.44/5.67 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.44/5.67 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult_less
% 5.44/5.67 thf(fact_5524_abs__mult__less,axiom,
% 5.44/5.67 ! [A: int,C: int,B: int,D: int] :
% 5.44/5.67 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.44/5.67 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.44/5.67 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult_less
% 5.44/5.67 thf(fact_5525_abs__triangle__ineq2__sym,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq2_sym
% 5.44/5.67 thf(fact_5526_abs__triangle__ineq2__sym,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq2_sym
% 5.44/5.67 thf(fact_5527_abs__triangle__ineq3,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq3
% 5.44/5.67 thf(fact_5528_abs__triangle__ineq3,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq3
% 5.44/5.67 thf(fact_5529_abs__triangle__ineq2,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq2
% 5.44/5.67 thf(fact_5530_abs__triangle__ineq2,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq2
% 5.44/5.67 thf(fact_5531_nonzero__abs__divide,axiom,
% 5.44/5.67 ! [B: real,A: real] :
% 5.44/5.67 ( ( B != zero_zero_real )
% 5.44/5.67 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.67 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % nonzero_abs_divide
% 5.44/5.67 thf(fact_5532_abs__leI,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.67 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.44/5.67 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_leI
% 5.44/5.67 thf(fact_5533_abs__leI,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.44/5.67 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.44/5.67 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_leI
% 5.44/5.67 thf(fact_5534_abs__leI,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ A @ B )
% 5.44/5.67 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.44/5.67 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_leI
% 5.44/5.67 thf(fact_5535_abs__le__D2,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.44/5.67 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_D2
% 5.44/5.67 thf(fact_5536_abs__le__D2,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.44/5.67 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_D2
% 5.44/5.67 thf(fact_5537_abs__le__D2,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.44/5.67 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_D2
% 5.44/5.67 thf(fact_5538_abs__le__iff,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.44/5.67 = ( ( ord_less_eq_real @ A @ B )
% 5.44/5.67 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_iff
% 5.44/5.67 thf(fact_5539_abs__le__iff,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.44/5.67 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.44/5.67 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_iff
% 5.44/5.67 thf(fact_5540_abs__le__iff,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.44/5.67 = ( ( ord_less_eq_int @ A @ B )
% 5.44/5.67 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_iff
% 5.44/5.67 thf(fact_5541_abs__ge__minus__self,axiom,
% 5.44/5.67 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ge_minus_self
% 5.44/5.67 thf(fact_5542_abs__ge__minus__self,axiom,
% 5.44/5.67 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ge_minus_self
% 5.44/5.67 thf(fact_5543_abs__ge__minus__self,axiom,
% 5.44/5.67 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ge_minus_self
% 5.44/5.67 thf(fact_5544_abs__less__iff,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.44/5.67 = ( ( ord_less_real @ A @ B )
% 5.44/5.67 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_less_iff
% 5.44/5.67 thf(fact_5545_abs__less__iff,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.44/5.67 = ( ( ord_less_int @ A @ B )
% 5.44/5.67 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_less_iff
% 5.44/5.67 thf(fact_5546_abs__less__iff,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.44/5.67 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.44/5.67 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_less_iff
% 5.44/5.67 thf(fact_5547_abs__real__def,axiom,
% 5.44/5.67 ( abs_abs_real
% 5.44/5.67 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_real_def
% 5.44/5.67 thf(fact_5548_xor__num_Ocases,axiom,
% 5.44/5.67 ! [X: product_prod_num_num] :
% 5.44/5.67 ( ( X
% 5.44/5.67 != ( product_Pair_num_num @ one @ one ) )
% 5.44/5.67 => ( ! [N4: num] :
% 5.44/5.67 ( X
% 5.44/5.67 != ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) )
% 5.44/5.67 => ( ! [N4: num] :
% 5.44/5.67 ( X
% 5.44/5.67 != ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) )
% 5.44/5.67 => ( ! [M5: num] :
% 5.44/5.67 ( X
% 5.44/5.67 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 5.44/5.67 => ( ! [M5: num,N4: num] :
% 5.44/5.67 ( X
% 5.44/5.67 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N4 ) ) )
% 5.44/5.67 => ( ! [M5: num,N4: num] :
% 5.44/5.67 ( X
% 5.44/5.67 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N4 ) ) )
% 5.44/5.67 => ( ! [M5: num] :
% 5.44/5.67 ( X
% 5.44/5.67 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 5.44/5.67 => ( ! [M5: num,N4: num] :
% 5.44/5.67 ( X
% 5.44/5.67 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N4 ) ) )
% 5.44/5.67 => ~ ! [M5: num,N4: num] :
% 5.44/5.67 ( X
% 5.44/5.67 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % xor_num.cases
% 5.44/5.67 thf(fact_5549_num_Oexhaust,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( Y != one )
% 5.44/5.67 => ( ! [X23: num] :
% 5.44/5.67 ( Y
% 5.44/5.67 != ( bit0 @ X23 ) )
% 5.44/5.67 => ~ ! [X33: num] :
% 5.44/5.67 ( Y
% 5.44/5.67 != ( bit1 @ X33 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % num.exhaust
% 5.44/5.67 thf(fact_5550_sin__bound__lemma,axiom,
% 5.44/5.67 ! [X: real,Y: real,U: real,V: real] :
% 5.44/5.67 ( ( X = Y )
% 5.44/5.67 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.44/5.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % sin_bound_lemma
% 5.44/5.67 thf(fact_5551_tanh__real__lt__1,axiom,
% 5.44/5.67 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_lt_1
% 5.44/5.67 thf(fact_5552_tanh__real__gt__neg1,axiom,
% 5.44/5.67 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_gt_neg1
% 5.44/5.67 thf(fact_5553_dense__eq0__I,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ! [E2: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.44/5.67 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 5.44/5.67 => ( X = zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % dense_eq0_I
% 5.44/5.67 thf(fact_5554_abs__eq__mult,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.67 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.44/5.67 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.67 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.44/5.67 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.44/5.67 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_eq_mult
% 5.44/5.67 thf(fact_5555_abs__eq__mult,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.67 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.44/5.67 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.67 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.44/5.67 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.44/5.67 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_eq_mult
% 5.44/5.67 thf(fact_5556_abs__mult__pos,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 5.44/5.67 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult_pos
% 5.44/5.67 thf(fact_5557_abs__mult__pos,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.67 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 5.44/5.67 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mult_pos
% 5.44/5.67 thf(fact_5558_abs__eq__iff_H,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( ( abs_abs_real @ A )
% 5.44/5.67 = B )
% 5.44/5.67 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.67 & ( ( A = B )
% 5.44/5.67 | ( A
% 5.44/5.67 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_eq_iff'
% 5.44/5.67 thf(fact_5559_abs__eq__iff_H,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( ( abs_abs_Code_integer @ A )
% 5.44/5.67 = B )
% 5.44/5.67 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.44/5.67 & ( ( A = B )
% 5.44/5.67 | ( A
% 5.44/5.67 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_eq_iff'
% 5.44/5.67 thf(fact_5560_abs__eq__iff_H,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ( abs_abs_int @ A )
% 5.44/5.67 = B )
% 5.44/5.67 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.67 & ( ( A = B )
% 5.44/5.67 | ( A
% 5.44/5.67 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_eq_iff'
% 5.44/5.67 thf(fact_5561_eq__abs__iff_H,axiom,
% 5.44/5.67 ! [A: real,B: real] :
% 5.44/5.67 ( ( A
% 5.44/5.67 = ( abs_abs_real @ B ) )
% 5.44/5.67 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.67 & ( ( B = A )
% 5.44/5.67 | ( B
% 5.44/5.67 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % eq_abs_iff'
% 5.44/5.67 thf(fact_5562_eq__abs__iff_H,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( A
% 5.44/5.67 = ( abs_abs_Code_integer @ B ) )
% 5.44/5.67 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.44/5.67 & ( ( B = A )
% 5.44/5.67 | ( B
% 5.44/5.67 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % eq_abs_iff'
% 5.44/5.67 thf(fact_5563_eq__abs__iff_H,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( A
% 5.44/5.67 = ( abs_abs_int @ B ) )
% 5.44/5.67 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.44/5.67 & ( ( B = A )
% 5.44/5.67 | ( B
% 5.44/5.67 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % eq_abs_iff'
% 5.44/5.67 thf(fact_5564_abs__minus__le__zero,axiom,
% 5.44/5.67 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.44/5.67
% 5.44/5.67 % abs_minus_le_zero
% 5.44/5.67 thf(fact_5565_abs__minus__le__zero,axiom,
% 5.44/5.67 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.44/5.67
% 5.44/5.67 % abs_minus_le_zero
% 5.44/5.67 thf(fact_5566_abs__minus__le__zero,axiom,
% 5.44/5.67 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % abs_minus_le_zero
% 5.44/5.67 thf(fact_5567_zero__le__power__abs,axiom,
% 5.44/5.67 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_le_power_abs
% 5.44/5.67 thf(fact_5568_zero__le__power__abs,axiom,
% 5.44/5.67 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_le_power_abs
% 5.44/5.67 thf(fact_5569_abs__div__pos,axiom,
% 5.44/5.67 ! [Y: real,X: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.67 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 5.44/5.67 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_div_pos
% 5.44/5.67 thf(fact_5570_abs__if__raw,axiom,
% 5.44/5.67 ( abs_abs_real
% 5.44/5.67 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_if_raw
% 5.44/5.67 thf(fact_5571_abs__if__raw,axiom,
% 5.44/5.67 ( abs_abs_int
% 5.44/5.67 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_if_raw
% 5.44/5.67 thf(fact_5572_abs__if__raw,axiom,
% 5.44/5.67 ( abs_abs_Code_integer
% 5.44/5.67 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_if_raw
% 5.44/5.67 thf(fact_5573_abs__of__neg,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.67 => ( ( abs_abs_real @ A )
% 5.44/5.67 = ( uminus_uminus_real @ A ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_neg
% 5.44/5.67 thf(fact_5574_abs__of__neg,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( ord_less_int @ A @ zero_zero_int )
% 5.44/5.67 => ( ( abs_abs_int @ A )
% 5.44/5.67 = ( uminus_uminus_int @ A ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_neg
% 5.44/5.67 thf(fact_5575_abs__of__neg,axiom,
% 5.44/5.67 ! [A: code_integer] :
% 5.44/5.67 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.44/5.67 => ( ( abs_abs_Code_integer @ A )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_of_neg
% 5.44/5.67 thf(fact_5576_abs__if,axiom,
% 5.44/5.67 ( abs_abs_real
% 5.44/5.67 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_if
% 5.44/5.67 thf(fact_5577_abs__if,axiom,
% 5.44/5.67 ( abs_abs_int
% 5.44/5.67 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_if
% 5.44/5.67 thf(fact_5578_abs__if,axiom,
% 5.44/5.67 ( abs_abs_Code_integer
% 5.44/5.67 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_if
% 5.44/5.67 thf(fact_5579_abs__diff__triangle__ineq,axiom,
% 5.44/5.67 ! [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 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_diff_triangle_ineq
% 5.44/5.67 thf(fact_5580_abs__diff__triangle__ineq,axiom,
% 5.44/5.67 ! [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 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_diff_triangle_ineq
% 5.44/5.67 thf(fact_5581_abs__triangle__ineq4,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq4
% 5.44/5.67 thf(fact_5582_abs__triangle__ineq4,axiom,
% 5.44/5.67 ! [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 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_triangle_ineq4
% 5.44/5.67 thf(fact_5583_abs__diff__le__iff,axiom,
% 5.44/5.67 ! [X: real,A: real,R: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 5.44/5.67 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X )
% 5.44/5.67 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_diff_le_iff
% 5.44/5.67 thf(fact_5584_abs__diff__le__iff,axiom,
% 5.44/5.67 ! [X: int,A: int,R: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 5.44/5.67 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X )
% 5.44/5.67 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_diff_le_iff
% 5.44/5.67 thf(fact_5585_abs__diff__less__iff,axiom,
% 5.44/5.67 ! [X: real,A: real,R: real] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 5.44/5.67 = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X )
% 5.44/5.67 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_diff_less_iff
% 5.44/5.67 thf(fact_5586_abs__diff__less__iff,axiom,
% 5.44/5.67 ! [X: int,A: int,R: int] :
% 5.44/5.67 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 5.44/5.67 = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X )
% 5.44/5.67 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_diff_less_iff
% 5.44/5.67 thf(fact_5587_numeral__Bit1,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_Bit1
% 5.44/5.67 thf(fact_5588_numeral__Bit1,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_Bit1
% 5.44/5.67 thf(fact_5589_numeral__Bit1,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_Bit1
% 5.44/5.67 thf(fact_5590_numeral__Bit1,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_Bit1
% 5.44/5.67 thf(fact_5591_numeral__Bit1,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_Bit1
% 5.44/5.67 thf(fact_5592_eval__nat__numeral_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % eval_nat_numeral(3)
% 5.44/5.67 thf(fact_5593_power__minus__Bit1,axiom,
% 5.44/5.67 ! [X: real,K: num] :
% 5.44/5.67 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_minus_Bit1
% 5.44/5.67 thf(fact_5594_power__minus__Bit1,axiom,
% 5.44/5.67 ! [X: int,K: num] :
% 5.44/5.67 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_minus_Bit1
% 5.44/5.67 thf(fact_5595_power__minus__Bit1,axiom,
% 5.44/5.67 ! [X: complex,K: num] :
% 5.44/5.67 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_minus_Bit1
% 5.44/5.67 thf(fact_5596_power__minus__Bit1,axiom,
% 5.44/5.67 ! [X: code_integer,K: num] :
% 5.44/5.67 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_minus_Bit1
% 5.44/5.67 thf(fact_5597_cong__exp__iff__simps_I13_J,axiom,
% 5.44/5.67 ! [M: num,Q2: num,N2: num] :
% 5.44/5.67 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.44/5.67 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.44/5.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(13)
% 5.44/5.67 thf(fact_5598_cong__exp__iff__simps_I13_J,axiom,
% 5.44/5.67 ! [M: num,Q2: num,N2: num] :
% 5.44/5.67 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.44/5.67 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.44/5.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(13)
% 5.44/5.67 thf(fact_5599_cong__exp__iff__simps_I12_J,axiom,
% 5.44/5.67 ! [M: num,Q2: num,N2: num] :
% 5.44/5.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(12)
% 5.44/5.67 thf(fact_5600_cong__exp__iff__simps_I12_J,axiom,
% 5.44/5.67 ! [M: num,Q2: num,N2: num] :
% 5.44/5.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(12)
% 5.44/5.67 thf(fact_5601_cong__exp__iff__simps_I10_J,axiom,
% 5.44/5.67 ! [M: num,Q2: num,N2: num] :
% 5.44/5.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(10)
% 5.44/5.67 thf(fact_5602_cong__exp__iff__simps_I10_J,axiom,
% 5.44/5.67 ! [M: num,Q2: num,N2: num] :
% 5.44/5.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(10)
% 5.44/5.67 thf(fact_5603_lemma__interval__lt,axiom,
% 5.44/5.67 ! [A: real,X: real,B: real] :
% 5.44/5.67 ( ( ord_less_real @ A @ X )
% 5.44/5.67 => ( ( ord_less_real @ X @ B )
% 5.44/5.67 => ? [D3: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.67 & ! [Y2: real] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y2 ) ) @ D3 )
% 5.44/5.67 => ( ( ord_less_real @ A @ Y2 )
% 5.44/5.67 & ( ord_less_real @ Y2 @ B ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % lemma_interval_lt
% 5.44/5.67 thf(fact_5604_numeral__code_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_code(3)
% 5.44/5.67 thf(fact_5605_numeral__code_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_code(3)
% 5.44/5.67 thf(fact_5606_numeral__code_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_code(3)
% 5.44/5.67 thf(fact_5607_numeral__code_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_code(3)
% 5.44/5.67 thf(fact_5608_numeral__code_I3_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_code(3)
% 5.44/5.67 thf(fact_5609_power__numeral__odd,axiom,
% 5.44/5.67 ! [Z: complex,W: num] :
% 5.44/5.67 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.44/5.67 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_numeral_odd
% 5.44/5.67 thf(fact_5610_power__numeral__odd,axiom,
% 5.44/5.67 ! [Z: real,W: num] :
% 5.44/5.67 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.44/5.67 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_numeral_odd
% 5.44/5.67 thf(fact_5611_power__numeral__odd,axiom,
% 5.44/5.67 ! [Z: nat,W: num] :
% 5.44/5.67 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.44/5.67 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_numeral_odd
% 5.44/5.67 thf(fact_5612_power__numeral__odd,axiom,
% 5.44/5.67 ! [Z: int,W: num] :
% 5.44/5.67 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.44/5.67 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_numeral_odd
% 5.44/5.67 thf(fact_5613_abs__add__one__gt__zero,axiom,
% 5.44/5.67 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_add_one_gt_zero
% 5.44/5.67 thf(fact_5614_abs__add__one__gt__zero,axiom,
% 5.44/5.67 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_add_one_gt_zero
% 5.44/5.67 thf(fact_5615_numeral__Bit1__div__2,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.67 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_Bit1_div_2
% 5.44/5.67 thf(fact_5616_numeral__Bit1__div__2,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.67 = ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_Bit1_div_2
% 5.44/5.67 thf(fact_5617_numeral__Bit1__div__2,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.67 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_Bit1_div_2
% 5.44/5.67 thf(fact_5618_odd__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % odd_numeral
% 5.44/5.67 thf(fact_5619_odd__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % odd_numeral
% 5.44/5.67 thf(fact_5620_odd__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % odd_numeral
% 5.44/5.67 thf(fact_5621_cong__exp__iff__simps_I3_J,axiom,
% 5.44/5.67 ! [N2: num,Q2: num] :
% 5.44/5.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 != zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(3)
% 5.44/5.67 thf(fact_5622_cong__exp__iff__simps_I3_J,axiom,
% 5.44/5.67 ! [N2: num,Q2: num] :
% 5.44/5.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 != zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(3)
% 5.44/5.67 thf(fact_5623_power3__eq__cube,axiom,
% 5.44/5.67 ! [A: complex] :
% 5.44/5.67 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.44/5.67 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % power3_eq_cube
% 5.44/5.67 thf(fact_5624_power3__eq__cube,axiom,
% 5.44/5.67 ! [A: real] :
% 5.44/5.67 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.44/5.67 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % power3_eq_cube
% 5.44/5.67 thf(fact_5625_power3__eq__cube,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.44/5.67 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % power3_eq_cube
% 5.44/5.67 thf(fact_5626_power3__eq__cube,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.44/5.67 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % power3_eq_cube
% 5.44/5.67 thf(fact_5627_numeral__3__eq__3,axiom,
% 5.44/5.67 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.44/5.67 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_3_eq_3
% 5.44/5.67 thf(fact_5628_Suc3__eq__add__3,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 5.44/5.67 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % Suc3_eq_add_3
% 5.44/5.67 thf(fact_5629_lemma__interval,axiom,
% 5.44/5.67 ! [A: real,X: real,B: real] :
% 5.44/5.67 ( ( ord_less_real @ A @ X )
% 5.44/5.67 => ( ( ord_less_real @ X @ B )
% 5.44/5.67 => ? [D3: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.67 & ! [Y2: real] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y2 ) ) @ D3 )
% 5.44/5.67 => ( ( ord_less_eq_real @ A @ Y2 )
% 5.44/5.67 & ( ord_less_eq_real @ Y2 @ B ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % lemma_interval
% 5.44/5.67 thf(fact_5630_mod__exhaust__less__4,axiom,
% 5.44/5.67 ! [M: nat] :
% 5.44/5.67 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = zero_zero_nat )
% 5.44/5.67 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = one_one_nat )
% 5.44/5.67 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.67 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mod_exhaust_less_4
% 5.44/5.67 thf(fact_5631_abs__le__square__iff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 5.44/5.67 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_square_iff
% 5.44/5.67 thf(fact_5632_abs__le__square__iff,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_le_square_iff
% 5.44/5.67 thf(fact_5633_abs__square__eq__1,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.67 = one_one_real )
% 5.44/5.67 = ( ( abs_abs_real @ X )
% 5.44/5.67 = one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_square_eq_1
% 5.44/5.67 thf(fact_5634_abs__square__eq__1,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.67 = one_one_int )
% 5.44/5.67 = ( ( abs_abs_int @ X )
% 5.44/5.67 = one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_square_eq_1
% 5.44/5.67 thf(fact_5635_num_Osize_I6_J,axiom,
% 5.44/5.67 ! [X32: num] :
% 5.44/5.67 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.44/5.67 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % num.size(6)
% 5.44/5.67 thf(fact_5636_num_Osize__gen_I3_J,axiom,
% 5.44/5.67 ! [X32: num] :
% 5.44/5.67 ( ( size_num @ ( bit1 @ X32 ) )
% 5.44/5.67 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % num.size_gen(3)
% 5.44/5.67 thf(fact_5637_power__even__abs,axiom,
% 5.44/5.67 ! [N2: nat,A: real] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N2 )
% 5.44/5.67 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_even_abs
% 5.44/5.67 thf(fact_5638_power__even__abs,axiom,
% 5.44/5.67 ! [N2: nat,A: int] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N2 )
% 5.44/5.67 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_even_abs
% 5.44/5.67 thf(fact_5639_cong__exp__iff__simps_I11_J,axiom,
% 5.44/5.67 ! [M: num,Q2: num] :
% 5.44/5.67 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.44/5.67 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.44/5.67 = zero_zero_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(11)
% 5.44/5.67 thf(fact_5640_cong__exp__iff__simps_I11_J,axiom,
% 5.44/5.67 ! [M: num,Q2: num] :
% 5.44/5.67 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.44/5.67 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.44/5.67 = zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(11)
% 5.44/5.67 thf(fact_5641_cong__exp__iff__simps_I7_J,axiom,
% 5.44/5.67 ! [Q2: num,N2: num] :
% 5.44/5.67 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.44/5.67 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.44/5.67 = zero_zero_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(7)
% 5.44/5.67 thf(fact_5642_cong__exp__iff__simps_I7_J,axiom,
% 5.44/5.67 ! [Q2: num,N2: num] :
% 5.44/5.67 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.44/5.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.44/5.67 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 5.44/5.67 = zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % cong_exp_iff_simps(7)
% 5.44/5.67 thf(fact_5643_Suc__div__eq__add3__div,axiom,
% 5.44/5.67 ! [M: nat,N2: nat] :
% 5.44/5.67 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.44/5.67 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % Suc_div_eq_add3_div
% 5.44/5.67 thf(fact_5644_Suc__mod__eq__add3__mod,axiom,
% 5.44/5.67 ! [M: nat,N2: nat] :
% 5.44/5.67 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.44/5.67 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % Suc_mod_eq_add3_mod
% 5.44/5.67 thf(fact_5645_abs__sqrt__wlog,axiom,
% 5.44/5.67 ! [P: real > real > $o,X: real] :
% 5.44/5.67 ( ! [X5: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.44/5.67 => ( P @ X5 @ ( power_power_real @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.67 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_sqrt_wlog
% 5.44/5.67 thf(fact_5646_abs__sqrt__wlog,axiom,
% 5.44/5.67 ! [P: int > int > $o,X: int] :
% 5.44/5.67 ( ! [X5: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.44/5.67 => ( P @ X5 @ ( power_power_int @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.67 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_sqrt_wlog
% 5.44/5.67 thf(fact_5647_power2__le__iff__abs__le,axiom,
% 5.44/5.67 ! [Y: real,X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.67 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power2_le_iff_abs_le
% 5.44/5.67 thf(fact_5648_power2__le__iff__abs__le,axiom,
% 5.44/5.67 ! [Y: int,X: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.67 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power2_le_iff_abs_le
% 5.44/5.67 thf(fact_5649_abs__square__le__1,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.44/5.67 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_square_le_1
% 5.44/5.67 thf(fact_5650_abs__square__le__1,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.44/5.67 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_square_le_1
% 5.44/5.67 thf(fact_5651_abs__square__less__1,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.44/5.67 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_square_less_1
% 5.44/5.67 thf(fact_5652_abs__square__less__1,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.44/5.67 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_square_less_1
% 5.44/5.67 thf(fact_5653_divmod__def,axiom,
% 5.44/5.67 ( unique3479559517661332726nteger
% 5.44/5.67 = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_def
% 5.44/5.67 thf(fact_5654_divmod__def,axiom,
% 5.44/5.67 ( unique5055182867167087721od_nat
% 5.44/5.67 = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_def
% 5.44/5.67 thf(fact_5655_divmod__def,axiom,
% 5.44/5.67 ( unique5052692396658037445od_int
% 5.44/5.67 = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_def
% 5.44/5.67 thf(fact_5656_divmod_H__nat__def,axiom,
% 5.44/5.67 ( unique5055182867167087721od_nat
% 5.44/5.67 = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod'_nat_def
% 5.44/5.67 thf(fact_5657_power__mono__even,axiom,
% 5.44/5.67 ! [N2: nat,A: real,B: real] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.44/5.67 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_mono_even
% 5.44/5.67 thf(fact_5658_power__mono__even,axiom,
% 5.44/5.67 ! [N2: nat,A: int,B: int] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.67 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.44/5.67 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % power_mono_even
% 5.44/5.67 thf(fact_5659_divmod__nat__def,axiom,
% 5.44/5.67 ( divmod_nat
% 5.44/5.67 = ( ^ [M6: nat,N: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N ) @ ( modulo_modulo_nat @ M6 @ N ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_nat_def
% 5.44/5.67 thf(fact_5660_eq__diff__eq_H,axiom,
% 5.44/5.67 ! [X: real,Y: real,Z: real] :
% 5.44/5.67 ( ( X
% 5.44/5.67 = ( minus_minus_real @ Y @ Z ) )
% 5.44/5.67 = ( Y
% 5.44/5.67 = ( plus_plus_real @ X @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % eq_diff_eq'
% 5.44/5.67 thf(fact_5661_take__bit__Suc__bit1,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_Suc_bit1
% 5.44/5.67 thf(fact_5662_take__bit__Suc__bit1,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_Suc_bit1
% 5.44/5.67 thf(fact_5663_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.44/5.67 thf(fact_5664_odd__mod__4__div__2,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.44/5.67 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % odd_mod_4_div_2
% 5.44/5.67 thf(fact_5665_divmod__divmod__step,axiom,
% 5.44/5.67 ( unique5055182867167087721od_nat
% 5.44/5.67 = ( ^ [M6: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_divmod_step
% 5.44/5.67 thf(fact_5666_divmod__divmod__step,axiom,
% 5.44/5.67 ( unique5052692396658037445od_int
% 5.44/5.67 = ( ^ [M6: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_divmod_step
% 5.44/5.67 thf(fact_5667_divmod__divmod__step,axiom,
% 5.44/5.67 ( unique3479559517661332726nteger
% 5.44/5.67 = ( ^ [M6: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_divmod_step
% 5.44/5.67 thf(fact_5668_minus__one__div__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % minus_one_div_numeral
% 5.44/5.67 thf(fact_5669_one__div__minus__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_div_minus_numeral
% 5.44/5.67 thf(fact_5670_signed__take__bit__numeral__minus__bit1,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_numeral_minus_bit1
% 5.44/5.67 thf(fact_5671_dbl__dec__simps_I4_J,axiom,
% 5.44/5.67 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(4)
% 5.44/5.67 thf(fact_5672_dbl__dec__simps_I4_J,axiom,
% 5.44/5.67 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(4)
% 5.44/5.67 thf(fact_5673_dbl__dec__simps_I4_J,axiom,
% 5.44/5.67 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(4)
% 5.44/5.67 thf(fact_5674_dbl__dec__simps_I4_J,axiom,
% 5.44/5.67 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(4)
% 5.44/5.67 thf(fact_5675_take__bit__Suc__minus__bit1,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_Suc_minus_bit1
% 5.44/5.67 thf(fact_5676_signed__take__bit__numeral__bit1,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_numeral_bit1
% 5.44/5.67 thf(fact_5677_dbl__dec__simps_I3_J,axiom,
% 5.44/5.67 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.44/5.67 = one_one_complex ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(3)
% 5.44/5.67 thf(fact_5678_dbl__dec__simps_I3_J,axiom,
% 5.44/5.67 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.44/5.67 = one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(3)
% 5.44/5.67 thf(fact_5679_dbl__dec__simps_I3_J,axiom,
% 5.44/5.67 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(3)
% 5.44/5.67 thf(fact_5680_pred__numeral__simps_I1_J,axiom,
% 5.44/5.67 ( ( pred_numeral @ one )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % pred_numeral_simps(1)
% 5.44/5.67 thf(fact_5681_Suc__eq__numeral,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( ( suc @ N2 )
% 5.44/5.67 = ( numeral_numeral_nat @ K ) )
% 5.44/5.67 = ( N2
% 5.44/5.67 = ( pred_numeral @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % Suc_eq_numeral
% 5.44/5.67 thf(fact_5682_eq__numeral__Suc,axiom,
% 5.44/5.67 ! [K: num,N2: nat] :
% 5.44/5.67 ( ( ( numeral_numeral_nat @ K )
% 5.44/5.67 = ( suc @ N2 ) )
% 5.44/5.67 = ( ( pred_numeral @ K )
% 5.44/5.67 = N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % eq_numeral_Suc
% 5.44/5.67 thf(fact_5683_pred__numeral__inc,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( pred_numeral @ ( inc @ K ) )
% 5.44/5.67 = ( numeral_numeral_nat @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % pred_numeral_inc
% 5.44/5.67 thf(fact_5684_less__numeral__Suc,axiom,
% 5.44/5.67 ! [K: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.44/5.67 = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % less_numeral_Suc
% 5.44/5.67 thf(fact_5685_less__Suc__numeral,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.44/5.67 = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % less_Suc_numeral
% 5.44/5.67 thf(fact_5686_pred__numeral__simps_I3_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % pred_numeral_simps(3)
% 5.44/5.67 thf(fact_5687_le__Suc__numeral,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.44/5.67 = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % le_Suc_numeral
% 5.44/5.67 thf(fact_5688_le__numeral__Suc,axiom,
% 5.44/5.67 ! [K: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % le_numeral_Suc
% 5.44/5.67 thf(fact_5689_diff__Suc__numeral,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.44/5.67 = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_Suc_numeral
% 5.44/5.67 thf(fact_5690_diff__numeral__Suc,axiom,
% 5.44/5.67 ! [K: num,N2: nat] :
% 5.44/5.67 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.44/5.67 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_Suc
% 5.44/5.67 thf(fact_5691_max__Suc__numeral,axiom,
% 5.44/5.67 ! [N2: nat,K: num] :
% 5.44/5.67 ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.44/5.67 = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % max_Suc_numeral
% 5.44/5.67 thf(fact_5692_max__numeral__Suc,axiom,
% 5.44/5.67 ! [K: num,N2: nat] :
% 5.44/5.67 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.44/5.67 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % max_numeral_Suc
% 5.44/5.67 thf(fact_5693_dbl__dec__simps_I2_J,axiom,
% 5.44/5.67 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.44/5.67 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(2)
% 5.44/5.67 thf(fact_5694_dbl__dec__simps_I2_J,axiom,
% 5.44/5.67 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(2)
% 5.44/5.67 thf(fact_5695_dbl__dec__simps_I2_J,axiom,
% 5.44/5.67 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(2)
% 5.44/5.67 thf(fact_5696_dbl__dec__simps_I2_J,axiom,
% 5.44/5.67 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(2)
% 5.44/5.67 thf(fact_5697_add__neg__numeral__special_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_neg_numeral_special(5)
% 5.44/5.67 thf(fact_5698_add__neg__numeral__special_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_neg_numeral_special(5)
% 5.44/5.67 thf(fact_5699_add__neg__numeral__special_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_neg_numeral_special(5)
% 5.44/5.67 thf(fact_5700_add__neg__numeral__special_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_neg_numeral_special(5)
% 5.44/5.67 thf(fact_5701_add__neg__numeral__special_I6_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_neg_numeral_special(6)
% 5.44/5.67 thf(fact_5702_add__neg__numeral__special_I6_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_neg_numeral_special(6)
% 5.44/5.67 thf(fact_5703_add__neg__numeral__special_I6_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_neg_numeral_special(6)
% 5.44/5.67 thf(fact_5704_add__neg__numeral__special_I6_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_neg_numeral_special(6)
% 5.44/5.67 thf(fact_5705_diff__numeral__special_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_special(5)
% 5.44/5.67 thf(fact_5706_diff__numeral__special_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_special(5)
% 5.44/5.67 thf(fact_5707_diff__numeral__special_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_special(5)
% 5.44/5.67 thf(fact_5708_diff__numeral__special_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_special(5)
% 5.44/5.67 thf(fact_5709_diff__numeral__special_I6_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.67 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_special(6)
% 5.44/5.67 thf(fact_5710_diff__numeral__special_I6_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_special(6)
% 5.44/5.67 thf(fact_5711_diff__numeral__special_I6_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.67 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_special(6)
% 5.44/5.67 thf(fact_5712_diff__numeral__special_I6_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % diff_numeral_special(6)
% 5.44/5.67 thf(fact_5713_signed__take__bit__numeral__bit0,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.44/5.67 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_numeral_bit0
% 5.44/5.67 thf(fact_5714_signed__take__bit__numeral__minus__bit0,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.44/5.67 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % signed_take_bit_numeral_minus_bit0
% 5.44/5.67 thf(fact_5715_num__induct,axiom,
% 5.44/5.67 ! [P: num > $o,X: num] :
% 5.44/5.67 ( ( P @ one )
% 5.44/5.67 => ( ! [X5: num] :
% 5.44/5.67 ( ( P @ X5 )
% 5.44/5.67 => ( P @ ( inc @ X5 ) ) )
% 5.44/5.67 => ( P @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % num_induct
% 5.44/5.67 thf(fact_5716_add__inc,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 5.44/5.67 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_inc
% 5.44/5.67 thf(fact_5717_numeral__eq__Suc,axiom,
% 5.44/5.67 ( numeral_numeral_nat
% 5.44/5.67 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_eq_Suc
% 5.44/5.67 thf(fact_5718_inc_Osimps_I1_J,axiom,
% 5.44/5.67 ( ( inc @ one )
% 5.44/5.67 = ( bit0 @ one ) ) ).
% 5.44/5.67
% 5.44/5.67 % inc.simps(1)
% 5.44/5.67 thf(fact_5719_inc_Osimps_I2_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( inc @ ( bit0 @ X ) )
% 5.44/5.67 = ( bit1 @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % inc.simps(2)
% 5.44/5.67 thf(fact_5720_inc_Osimps_I3_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( inc @ ( bit1 @ X ) )
% 5.44/5.67 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % inc.simps(3)
% 5.44/5.67 thf(fact_5721_add__One,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( plus_plus_num @ X @ one )
% 5.44/5.67 = ( inc @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % add_One
% 5.44/5.67 thf(fact_5722_abs__mod__less,axiom,
% 5.44/5.67 ! [L2: int,K: int] :
% 5.44/5.67 ( ( L2 != zero_zero_int )
% 5.44/5.67 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % abs_mod_less
% 5.44/5.67 thf(fact_5723_mult__inc,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( times_times_num @ X @ ( inc @ Y ) )
% 5.44/5.67 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % mult_inc
% 5.44/5.67 thf(fact_5724_pred__numeral__def,axiom,
% 5.44/5.67 ( pred_numeral
% 5.44/5.67 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % pred_numeral_def
% 5.44/5.67 thf(fact_5725_numeral__inc,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( numera1916890842035813515d_enat @ ( inc @ X ) )
% 5.44/5.67 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_inc
% 5.44/5.67 thf(fact_5726_numeral__inc,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 5.44/5.67 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_inc
% 5.44/5.67 thf(fact_5727_numeral__inc,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( numeral_numeral_real @ ( inc @ X ) )
% 5.44/5.67 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_inc
% 5.44/5.67 thf(fact_5728_numeral__inc,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 5.44/5.67 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_inc
% 5.44/5.67 thf(fact_5729_numeral__inc,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( numeral_numeral_int @ ( inc @ X ) )
% 5.44/5.67 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_inc
% 5.44/5.67 thf(fact_5730_even__abs__add__iff,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 5.44/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_abs_add_iff
% 5.44/5.67 thf(fact_5731_even__add__abs__iff,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 5.44/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_add_abs_iff
% 5.44/5.67 thf(fact_5732_take__bit__numeral__minus__bit1,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_numeral_minus_bit1
% 5.44/5.67 thf(fact_5733_nat__intermed__int__val,axiom,
% 5.44/5.67 ! [M: nat,N2: nat,F: nat > int,K: int] :
% 5.44/5.67 ( ! [I4: nat] :
% 5.44/5.67 ( ( ( ord_less_eq_nat @ M @ I4 )
% 5.44/5.67 & ( ord_less_nat @ I4 @ N2 ) )
% 5.44/5.67 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.44/5.67 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.67 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.44/5.67 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.44/5.67 => ? [I4: nat] :
% 5.44/5.67 ( ( ord_less_eq_nat @ M @ I4 )
% 5.44/5.67 & ( ord_less_eq_nat @ I4 @ N2 )
% 5.44/5.67 & ( ( F @ I4 )
% 5.44/5.67 = K ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % nat_intermed_int_val
% 5.44/5.67 thf(fact_5734_dbl__dec__def,axiom,
% 5.44/5.67 ( neg_nu6511756317524482435omplex
% 5.44/5.67 = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_def
% 5.44/5.67 thf(fact_5735_dbl__dec__def,axiom,
% 5.44/5.67 ( neg_nu6075765906172075777c_real
% 5.44/5.67 = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_def
% 5.44/5.67 thf(fact_5736_dbl__dec__def,axiom,
% 5.44/5.67 ( neg_nu3811975205180677377ec_int
% 5.44/5.67 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_def
% 5.44/5.67 thf(fact_5737_take__bit__numeral__bit0,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.44/5.67 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_numeral_bit0
% 5.44/5.67 thf(fact_5738_take__bit__numeral__bit0,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.44/5.67 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_numeral_bit0
% 5.44/5.67 thf(fact_5739_nat__ivt__aux,axiom,
% 5.44/5.67 ! [N2: nat,F: nat > int,K: int] :
% 5.44/5.67 ( ! [I4: nat] :
% 5.44/5.67 ( ( ord_less_nat @ I4 @ N2 )
% 5.44/5.67 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.44/5.67 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.44/5.67 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.44/5.67 => ? [I4: nat] :
% 5.44/5.67 ( ( ord_less_eq_nat @ I4 @ N2 )
% 5.44/5.67 & ( ( F @ I4 )
% 5.44/5.67 = K ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % nat_ivt_aux
% 5.44/5.67 thf(fact_5740_take__bit__numeral__minus__bit0,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.44/5.67 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_numeral_minus_bit0
% 5.44/5.67 thf(fact_5741_nat0__intermed__int__val,axiom,
% 5.44/5.67 ! [N2: nat,F: nat > int,K: int] :
% 5.44/5.67 ( ! [I4: nat] :
% 5.44/5.67 ( ( ord_less_nat @ I4 @ N2 )
% 5.44/5.67 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.44/5.67 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.44/5.67 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.44/5.67 => ? [I4: nat] :
% 5.44/5.67 ( ( ord_less_eq_nat @ I4 @ N2 )
% 5.44/5.67 & ( ( F @ I4 )
% 5.44/5.67 = K ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % nat0_intermed_int_val
% 5.44/5.67 thf(fact_5742_take__bit__numeral__bit1,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_numeral_bit1
% 5.44/5.67 thf(fact_5743_take__bit__numeral__bit1,axiom,
% 5.44/5.67 ! [L2: num,K: num] :
% 5.44/5.67 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.44/5.67 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_numeral_bit1
% 5.44/5.67 thf(fact_5744_arctan__double,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.67 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.44/5.67 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % arctan_double
% 5.44/5.67 thf(fact_5745_dbl__inc__simps_I3_J,axiom,
% 5.44/5.67 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.44/5.67 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(3)
% 5.44/5.67 thf(fact_5746_dbl__inc__simps_I3_J,axiom,
% 5.44/5.67 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.44/5.67 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(3)
% 5.44/5.67 thf(fact_5747_dbl__inc__simps_I3_J,axiom,
% 5.44/5.67 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.44/5.67 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(3)
% 5.44/5.67 thf(fact_5748_divmod__BitM__2__eq,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.44/5.67 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % divmod_BitM_2_eq
% 5.44/5.67 thf(fact_5749_of__int__code__if,axiom,
% 5.44/5.67 ( ring_1_of_int_real
% 5.44/5.67 = ( ^ [K3: int] :
% 5.44/5.67 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.44/5.67 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.44/5.67 @ ( if_real
% 5.44/5.67 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.44/5.67 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_code_if
% 5.44/5.67 thf(fact_5750_of__int__code__if,axiom,
% 5.44/5.67 ( ring_1_of_int_int
% 5.44/5.67 = ( ^ [K3: int] :
% 5.44/5.67 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.44/5.67 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.44/5.67 @ ( if_int
% 5.44/5.67 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.44/5.67 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_code_if
% 5.44/5.67 thf(fact_5751_of__int__code__if,axiom,
% 5.44/5.67 ( ring_17405671764205052669omplex
% 5.44/5.67 = ( ^ [K3: int] :
% 5.44/5.67 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.44/5.67 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.44/5.67 @ ( if_complex
% 5.44/5.67 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.44/5.67 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_code_if
% 5.44/5.67 thf(fact_5752_of__int__code__if,axiom,
% 5.44/5.67 ( ring_18347121197199848620nteger
% 5.44/5.67 = ( ^ [K3: int] :
% 5.44/5.67 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.44/5.67 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.44/5.67 @ ( if_Code_integer
% 5.44/5.67 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.44/5.67 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_code_if
% 5.44/5.67 thf(fact_5753_dbl__inc__simps_I1_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(1)
% 5.44/5.67 thf(fact_5754_dbl__inc__simps_I1_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(1)
% 5.44/5.67 thf(fact_5755_dbl__inc__simps_I1_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(1)
% 5.44/5.67 thf(fact_5756_dbl__inc__simps_I1_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(1)
% 5.44/5.67 thf(fact_5757_dbl__dec__simps_I1_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(1)
% 5.44/5.67 thf(fact_5758_dbl__dec__simps_I1_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(1)
% 5.44/5.67 thf(fact_5759_dbl__dec__simps_I1_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(1)
% 5.44/5.67 thf(fact_5760_dbl__dec__simps_I1_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(1)
% 5.44/5.67 thf(fact_5761_of__int__numeral,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.44/5.67 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_numeral
% 5.44/5.67 thf(fact_5762_of__int__numeral,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.44/5.67 = ( numeral_numeral_real @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_numeral
% 5.44/5.67 thf(fact_5763_of__int__numeral,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.44/5.67 = ( numeral_numeral_int @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_numeral
% 5.44/5.67 thf(fact_5764_of__int__eq__numeral__iff,axiom,
% 5.44/5.67 ! [Z: int,N2: num] :
% 5.44/5.67 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.44/5.67 = ( numera6690914467698888265omplex @ N2 ) )
% 5.44/5.67 = ( Z
% 5.44/5.67 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_numeral_iff
% 5.44/5.67 thf(fact_5765_of__int__eq__numeral__iff,axiom,
% 5.44/5.67 ! [Z: int,N2: num] :
% 5.44/5.67 ( ( ( ring_1_of_int_real @ Z )
% 5.44/5.67 = ( numeral_numeral_real @ N2 ) )
% 5.44/5.67 = ( Z
% 5.44/5.67 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_numeral_iff
% 5.44/5.67 thf(fact_5766_of__int__eq__numeral__iff,axiom,
% 5.44/5.67 ! [Z: int,N2: num] :
% 5.44/5.67 ( ( ( ring_1_of_int_int @ Z )
% 5.44/5.67 = ( numeral_numeral_int @ N2 ) )
% 5.44/5.67 = ( Z
% 5.44/5.67 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_numeral_iff
% 5.44/5.67 thf(fact_5767_of__int__le__iff,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.67 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_iff
% 5.44/5.67 thf(fact_5768_of__int__le__iff,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.44/5.67 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_iff
% 5.44/5.67 thf(fact_5769_of__int__less__iff,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.67 = ( ord_less_int @ W @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_iff
% 5.44/5.67 thf(fact_5770_of__int__less__iff,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.44/5.67 = ( ord_less_int @ W @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_iff
% 5.44/5.67 thf(fact_5771_of__int__1,axiom,
% 5.44/5.67 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.44/5.67 = one_one_complex ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_1
% 5.44/5.67 thf(fact_5772_of__int__1,axiom,
% 5.44/5.67 ( ( ring_1_of_int_int @ one_one_int )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_1
% 5.44/5.67 thf(fact_5773_of__int__1,axiom,
% 5.44/5.67 ( ( ring_1_of_int_real @ one_one_int )
% 5.44/5.67 = one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_1
% 5.44/5.67 thf(fact_5774_of__int__eq__1__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.44/5.67 = one_one_complex )
% 5.44/5.67 = ( Z = one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_1_iff
% 5.44/5.67 thf(fact_5775_of__int__eq__1__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ( ring_1_of_int_int @ Z )
% 5.44/5.67 = one_one_int )
% 5.44/5.67 = ( Z = one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_1_iff
% 5.44/5.67 thf(fact_5776_of__int__eq__1__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ( ring_1_of_int_real @ Z )
% 5.44/5.67 = one_one_real )
% 5.44/5.67 = ( Z = one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_1_iff
% 5.44/5.67 thf(fact_5777_of__int__mult,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 5.44/5.67 = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_mult
% 5.44/5.67 thf(fact_5778_of__int__mult,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.44/5.67 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_mult
% 5.44/5.67 thf(fact_5779_of__int__mult,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.44/5.67 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_mult
% 5.44/5.67 thf(fact_5780_of__int__add,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 5.44/5.67 = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_add
% 5.44/5.67 thf(fact_5781_of__int__add,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.44/5.67 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_add
% 5.44/5.67 thf(fact_5782_of__int__add,axiom,
% 5.44/5.67 ! [W: int,Z: int] :
% 5.44/5.67 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.44/5.67 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_add
% 5.44/5.67 thf(fact_5783_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: int,B: int,W: nat] :
% 5.44/5.67 ( ( ( ring_1_of_int_real @ X )
% 5.44/5.67 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.44/5.67 = ( X
% 5.44/5.67 = ( power_power_int @ B @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5784_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: int,B: int,W: nat] :
% 5.44/5.67 ( ( ( ring_1_of_int_int @ X )
% 5.44/5.67 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.44/5.67 = ( X
% 5.44/5.67 = ( power_power_int @ B @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5785_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: int,B: int,W: nat] :
% 5.44/5.67 ( ( ( ring_17405671764205052669omplex @ X )
% 5.44/5.67 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.44/5.67 = ( X
% 5.44/5.67 = ( power_power_int @ B @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5786_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.44/5.67 ! [B: int,W: nat,X: int] :
% 5.44/5.67 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.44/5.67 = ( ring_1_of_int_real @ X ) )
% 5.44/5.67 = ( ( power_power_int @ B @ W )
% 5.44/5.67 = X ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_of_int_power_cancel_iff
% 5.44/5.67 thf(fact_5787_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.44/5.67 ! [B: int,W: nat,X: int] :
% 5.44/5.67 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.44/5.67 = ( ring_1_of_int_int @ X ) )
% 5.44/5.67 = ( ( power_power_int @ B @ W )
% 5.44/5.67 = X ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_of_int_power_cancel_iff
% 5.44/5.67 thf(fact_5788_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.44/5.67 ! [B: int,W: nat,X: int] :
% 5.44/5.67 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.44/5.67 = ( ring_17405671764205052669omplex @ X ) )
% 5.44/5.67 = ( ( power_power_int @ B @ W )
% 5.44/5.67 = X ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_of_int_power_cancel_iff
% 5.44/5.67 thf(fact_5789_of__int__power,axiom,
% 5.44/5.67 ! [Z: int,N2: nat] :
% 5.44/5.67 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N2 ) )
% 5.44/5.67 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power
% 5.44/5.67 thf(fact_5790_of__int__power,axiom,
% 5.44/5.67 ! [Z: int,N2: nat] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N2 ) )
% 5.44/5.67 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power
% 5.44/5.67 thf(fact_5791_of__int__power,axiom,
% 5.44/5.67 ! [Z: int,N2: nat] :
% 5.44/5.67 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N2 ) )
% 5.44/5.67 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power
% 5.44/5.67 thf(fact_5792_zero__less__arctan__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 5.44/5.67 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_less_arctan_iff
% 5.44/5.67 thf(fact_5793_arctan__less__zero__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 5.44/5.67 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % arctan_less_zero_iff
% 5.44/5.67 thf(fact_5794_arctan__le__zero__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 5.44/5.67 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % arctan_le_zero_iff
% 5.44/5.67 thf(fact_5795_zero__le__arctan__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 5.44/5.67 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % zero_le_arctan_iff
% 5.44/5.67 thf(fact_5796_dbl__inc__simps_I2_J,axiom,
% 5.44/5.67 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.44/5.67 = one_one_complex ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(2)
% 5.44/5.67 thf(fact_5797_dbl__inc__simps_I2_J,axiom,
% 5.44/5.67 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.44/5.67 = one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(2)
% 5.44/5.67 thf(fact_5798_dbl__inc__simps_I2_J,axiom,
% 5.44/5.67 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(2)
% 5.44/5.67 thf(fact_5799_dbl__inc__simps_I4_J,axiom,
% 5.44/5.67 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.67 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(4)
% 5.44/5.67 thf(fact_5800_dbl__inc__simps_I4_J,axiom,
% 5.44/5.67 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(4)
% 5.44/5.67 thf(fact_5801_dbl__inc__simps_I4_J,axiom,
% 5.44/5.67 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(4)
% 5.44/5.67 thf(fact_5802_dbl__inc__simps_I4_J,axiom,
% 5.44/5.67 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(4)
% 5.44/5.67 thf(fact_5803_dbl__inc__simps_I5_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.44/5.67 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(5)
% 5.44/5.67 thf(fact_5804_dbl__inc__simps_I5_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.44/5.67 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(5)
% 5.44/5.67 thf(fact_5805_dbl__inc__simps_I5_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.44/5.67 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_simps(5)
% 5.44/5.67 thf(fact_5806_dbl__dec__simps_I5_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.44/5.67 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(5)
% 5.44/5.67 thf(fact_5807_dbl__dec__simps_I5_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.44/5.67 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(5)
% 5.44/5.67 thf(fact_5808_dbl__dec__simps_I5_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.44/5.67 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_dec_simps(5)
% 5.44/5.67 thf(fact_5809_pred__numeral__simps_I2_J,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % pred_numeral_simps(2)
% 5.44/5.67 thf(fact_5810_of__int__le__0__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.44/5.67 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_0_iff
% 5.44/5.67 thf(fact_5811_of__int__le__0__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.44/5.67 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_0_iff
% 5.44/5.67 thf(fact_5812_of__int__0__le__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.67 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_0_le_iff
% 5.44/5.67 thf(fact_5813_of__int__0__le__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.44/5.67 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_0_le_iff
% 5.44/5.67 thf(fact_5814_of__int__0__less__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.67 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_0_less_iff
% 5.44/5.67 thf(fact_5815_of__int__0__less__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.44/5.67 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_0_less_iff
% 5.44/5.67 thf(fact_5816_of__int__less__0__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.44/5.67 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_0_iff
% 5.44/5.67 thf(fact_5817_of__int__less__0__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.44/5.67 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_0_iff
% 5.44/5.67 thf(fact_5818_of__int__numeral__le__iff,axiom,
% 5.44/5.67 ! [N2: num,Z: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_numeral_le_iff
% 5.44/5.67 thf(fact_5819_of__int__numeral__le__iff,axiom,
% 5.44/5.67 ! [N2: num,Z: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_numeral_le_iff
% 5.44/5.67 thf(fact_5820_of__int__le__numeral__iff,axiom,
% 5.44/5.67 ! [Z: int,N2: num] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_numeral_iff
% 5.44/5.67 thf(fact_5821_of__int__le__numeral__iff,axiom,
% 5.44/5.67 ! [Z: int,N2: num] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_numeral_iff
% 5.44/5.67 thf(fact_5822_of__int__less__numeral__iff,axiom,
% 5.44/5.67 ! [Z: int,N2: num] :
% 5.44/5.67 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.67 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_numeral_iff
% 5.44/5.67 thf(fact_5823_of__int__less__numeral__iff,axiom,
% 5.44/5.67 ! [Z: int,N2: num] :
% 5.44/5.67 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.67 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_numeral_iff
% 5.44/5.67 thf(fact_5824_of__int__numeral__less__iff,axiom,
% 5.44/5.67 ! [N2: num,Z: int] :
% 5.44/5.67 ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.67 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_numeral_less_iff
% 5.44/5.67 thf(fact_5825_of__int__numeral__less__iff,axiom,
% 5.44/5.67 ! [N2: num,Z: int] :
% 5.44/5.67 ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.44/5.67 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_numeral_less_iff
% 5.44/5.67 thf(fact_5826_of__int__1__le__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.67 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_1_le_iff
% 5.44/5.67 thf(fact_5827_of__int__1__le__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.44/5.67 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_1_le_iff
% 5.44/5.67 thf(fact_5828_of__int__le__1__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.44/5.67 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_1_iff
% 5.44/5.67 thf(fact_5829_of__int__le__1__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.44/5.67 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_1_iff
% 5.44/5.67 thf(fact_5830_of__int__1__less__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.67 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_1_less_iff
% 5.44/5.67 thf(fact_5831_of__int__1__less__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.44/5.67 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_1_less_iff
% 5.44/5.67 thf(fact_5832_of__int__less__1__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.44/5.67 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_1_iff
% 5.44/5.67 thf(fact_5833_of__int__less__1__iff,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.44/5.67 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_1_iff
% 5.44/5.67 thf(fact_5834_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,Y: int] :
% 5.44/5.67 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 )
% 5.44/5.67 = ( ring_17405671764205052669omplex @ Y ) )
% 5.44/5.67 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.44/5.67 = Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5835_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,Y: int] :
% 5.44/5.67 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 )
% 5.44/5.67 = ( ring_1_of_int_real @ Y ) )
% 5.44/5.67 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.44/5.67 = Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5836_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,Y: int] :
% 5.44/5.67 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.44/5.67 = ( ring_1_of_int_int @ Y ) )
% 5.44/5.67 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.44/5.67 = Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5837_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [Y: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.44/5.67 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 ) )
% 5.44/5.67 = ( Y
% 5.44/5.67 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5838_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [Y: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ( ring_1_of_int_real @ Y )
% 5.44/5.67 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.44/5.67 = ( Y
% 5.44/5.67 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5839_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [Y: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ( ring_1_of_int_int @ Y )
% 5.44/5.67 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.44/5.67 = ( Y
% 5.44/5.67 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5840_of__int__power__le__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: int,B: int,W: nat] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.44/5.67 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power_le_of_int_cancel_iff
% 5.44/5.67 thf(fact_5841_of__int__power__le__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: int,B: int,W: nat] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.44/5.67 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power_le_of_int_cancel_iff
% 5.44/5.67 thf(fact_5842_of__int__le__of__int__power__cancel__iff,axiom,
% 5.44/5.67 ! [B: int,W: nat,X: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_of_int_power_cancel_iff
% 5.44/5.67 thf(fact_5843_of__int__le__of__int__power__cancel__iff,axiom,
% 5.44/5.67 ! [B: int,W: nat,X: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_of_int_power_cancel_iff
% 5.44/5.67 thf(fact_5844_of__int__less__of__int__power__cancel__iff,axiom,
% 5.44/5.67 ! [B: int,W: nat,X: int] :
% 5.44/5.67 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.44/5.67 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_of_int_power_cancel_iff
% 5.44/5.67 thf(fact_5845_of__int__less__of__int__power__cancel__iff,axiom,
% 5.44/5.67 ! [B: int,W: nat,X: int] :
% 5.44/5.67 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.44/5.67 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_of_int_power_cancel_iff
% 5.44/5.67 thf(fact_5846_of__int__power__less__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: int,B: int,W: nat] :
% 5.44/5.67 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.44/5.67 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power_less_of_int_cancel_iff
% 5.44/5.67 thf(fact_5847_of__int__power__less__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: int,B: int,W: nat] :
% 5.44/5.67 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.44/5.67 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_power_less_of_int_cancel_iff
% 5.44/5.67 thf(fact_5848_numeral__power__le__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_power_le_of_int_cancel_iff
% 5.44/5.67 thf(fact_5849_numeral__power__le__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_power_le_of_int_cancel_iff
% 5.44/5.67 thf(fact_5850_of__int__le__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5851_of__int__le__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5852_numeral__power__less__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.44/5.67 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_power_less_of_int_cancel_iff
% 5.44/5.67 thf(fact_5853_numeral__power__less__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.44/5.67 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_power_less_of_int_cancel_iff
% 5.44/5.67 thf(fact_5854_of__int__less__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.44/5.67 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5855_of__int__less__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.44/5.67 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5856_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [Y: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ( ring_1_of_int_real @ Y )
% 5.44/5.67 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 5.44/5.67 = ( Y
% 5.44/5.67 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5857_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [Y: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ( ring_1_of_int_int @ Y )
% 5.44/5.67 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 5.44/5.67 = ( Y
% 5.44/5.67 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5858_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [Y: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.44/5.67 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N2 ) )
% 5.44/5.67 = ( Y
% 5.44/5.67 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5859_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [Y: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ( ring_18347121197199848620nteger @ Y )
% 5.44/5.67 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 5.44/5.67 = ( Y
% 5.44/5.67 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_eq_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5860_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,Y: int] :
% 5.44/5.67 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 )
% 5.44/5.67 = ( ring_1_of_int_real @ Y ) )
% 5.44/5.67 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.44/5.67 = Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5861_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,Y: int] :
% 5.44/5.67 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.44/5.67 = ( ring_1_of_int_int @ Y ) )
% 5.44/5.67 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.44/5.67 = Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5862_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,Y: int] :
% 5.44/5.67 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N2 )
% 5.44/5.67 = ( ring_17405671764205052669omplex @ Y ) )
% 5.44/5.67 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.44/5.67 = Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5863_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,Y: int] :
% 5.44/5.67 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 )
% 5.44/5.67 = ( ring_18347121197199848620nteger @ Y ) )
% 5.44/5.67 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.44/5.67 = Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_eq_of_int_cancel_iff
% 5.44/5.67 thf(fact_5864_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5865_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5866_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 5.44/5.67 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_le_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5867_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_le_of_int_cancel_iff
% 5.44/5.67 thf(fact_5868_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_le_of_int_cancel_iff
% 5.44/5.67 thf(fact_5869_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.44/5.67 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_le_of_int_cancel_iff
% 5.44/5.67 thf(fact_5870_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.44/5.67 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_less_of_int_cancel_iff
% 5.44/5.67 thf(fact_5871_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.44/5.67 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_less_of_int_cancel_iff
% 5.44/5.67 thf(fact_5872_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.44/5.67 ! [X: num,N2: nat,A: int] :
% 5.44/5.67 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.44/5.67 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.44/5.67
% 5.44/5.67 % neg_numeral_power_less_of_int_cancel_iff
% 5.44/5.67 thf(fact_5873_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 5.44/5.67 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5874_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 5.44/5.67 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5875_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.44/5.67 ! [A: int,X: num,N2: nat] :
% 5.44/5.67 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 5.44/5.67 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_less_neg_numeral_power_cancel_iff
% 5.44/5.67 thf(fact_5876_mult__of__int__commute,axiom,
% 5.44/5.67 ! [X: int,Y: complex] :
% 5.44/5.67 ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y )
% 5.44/5.67 = ( times_times_complex @ Y @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mult_of_int_commute
% 5.44/5.67 thf(fact_5877_mult__of__int__commute,axiom,
% 5.44/5.67 ! [X: int,Y: real] :
% 5.44/5.67 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y )
% 5.44/5.67 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mult_of_int_commute
% 5.44/5.67 thf(fact_5878_mult__of__int__commute,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 5.44/5.67 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mult_of_int_commute
% 5.44/5.67 thf(fact_5879_of__int__max,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( ring_1_of_int_real @ ( ord_max_int @ X @ Y ) )
% 5.44/5.67 = ( ord_max_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_max
% 5.44/5.67 thf(fact_5880_of__int__max,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( ord_max_int @ X @ Y ) )
% 5.44/5.67 = ( ord_max_int @ ( ring_1_of_int_int @ X ) @ ( ring_1_of_int_int @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_max
% 5.44/5.67 thf(fact_5881_of__int__max,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( ring_18347121197199848620nteger @ ( ord_max_int @ X @ Y ) )
% 5.44/5.67 = ( ord_max_Code_integer @ ( ring_18347121197199848620nteger @ X ) @ ( ring_18347121197199848620nteger @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_max
% 5.44/5.67 thf(fact_5882_arctan__monotone,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_real @ X @ Y )
% 5.44/5.67 => ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % arctan_monotone
% 5.44/5.67 thf(fact_5883_arctan__less__iff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.44/5.67 = ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % arctan_less_iff
% 5.44/5.67 thf(fact_5884_arctan__monotone_H,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.67 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % arctan_monotone'
% 5.44/5.67 thf(fact_5885_arctan__le__iff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.44/5.67 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % arctan_le_iff
% 5.44/5.67 thf(fact_5886_semiring__norm_I26_J,axiom,
% 5.44/5.67 ( ( bitM @ one )
% 5.44/5.67 = one ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(26)
% 5.44/5.67 thf(fact_5887_take__bit__of__int,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 5.44/5.67 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_of_int
% 5.44/5.67 thf(fact_5888_semiring__norm_I28_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bitM @ ( bit1 @ N2 ) )
% 5.44/5.67 = ( bit1 @ ( bit0 @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(28)
% 5.44/5.67 thf(fact_5889_semiring__norm_I27_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bitM @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( bit1 @ ( bitM @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_norm(27)
% 5.44/5.67 thf(fact_5890_inc__BitM__eq,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( inc @ ( bitM @ N2 ) )
% 5.44/5.67 = ( bit0 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % inc_BitM_eq
% 5.44/5.67 thf(fact_5891_BitM__inc__eq,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bitM @ ( inc @ N2 ) )
% 5.44/5.67 = ( bit1 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % BitM_inc_eq
% 5.44/5.67 thf(fact_5892_real__of__int__div4,axiom,
% 5.44/5.67 ! [N2: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % real_of_int_div4
% 5.44/5.67 thf(fact_5893_real__of__int__div,axiom,
% 5.44/5.67 ! [D: int,N2: int] :
% 5.44/5.67 ( ( dvd_dvd_int @ D @ N2 )
% 5.44/5.67 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ D ) )
% 5.44/5.67 = ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % real_of_int_div
% 5.44/5.67 thf(fact_5894_eval__nat__numeral_I2_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.44/5.67 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % eval_nat_numeral(2)
% 5.44/5.67 thf(fact_5895_BitM__plus__one,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 5.44/5.67 = ( bit0 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % BitM_plus_one
% 5.44/5.67 thf(fact_5896_one__plus__BitM,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 5.44/5.67 = ( bit0 @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_plus_BitM
% 5.44/5.67 thf(fact_5897_of__int__nonneg,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.44/5.67 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_nonneg
% 5.44/5.67 thf(fact_5898_of__int__nonneg,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.44/5.67 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_nonneg
% 5.44/5.67 thf(fact_5899_of__int__leD,axiom,
% 5.44/5.67 ! [N2: int,X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X )
% 5.44/5.67 => ( ( N2 = zero_zero_int )
% 5.44/5.67 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_leD
% 5.44/5.67 thf(fact_5900_of__int__leD,axiom,
% 5.44/5.67 ! [N2: int,X: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 5.44/5.67 => ( ( N2 = zero_zero_int )
% 5.44/5.67 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_leD
% 5.44/5.67 thf(fact_5901_of__int__pos,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.44/5.67 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_pos
% 5.44/5.67 thf(fact_5902_of__int__pos,axiom,
% 5.44/5.67 ! [Z: int] :
% 5.44/5.67 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.44/5.67 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_pos
% 5.44/5.67 thf(fact_5903_of__int__lessD,axiom,
% 5.44/5.67 ! [N2: int,X: real] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X )
% 5.44/5.67 => ( ( N2 = zero_zero_int )
% 5.44/5.67 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_lessD
% 5.44/5.67 thf(fact_5904_of__int__lessD,axiom,
% 5.44/5.67 ! [N2: int,X: int] :
% 5.44/5.67 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 5.44/5.67 => ( ( N2 = zero_zero_int )
% 5.44/5.67 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_lessD
% 5.44/5.67 thf(fact_5905_of__int__neg__numeral,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.44/5.67 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_neg_numeral
% 5.44/5.67 thf(fact_5906_of__int__neg__numeral,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_neg_numeral
% 5.44/5.67 thf(fact_5907_of__int__neg__numeral,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.44/5.67 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_neg_numeral
% 5.44/5.67 thf(fact_5908_of__int__neg__numeral,axiom,
% 5.44/5.67 ! [K: num] :
% 5.44/5.67 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_neg_numeral
% 5.44/5.67 thf(fact_5909_int__le__real__less,axiom,
% 5.44/5.67 ( ord_less_eq_int
% 5.44/5.67 = ( ^ [N: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % int_le_real_less
% 5.44/5.67 thf(fact_5910_int__less__real__le,axiom,
% 5.44/5.67 ( ord_less_int
% 5.44/5.67 = ( ^ [N: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % int_less_real_le
% 5.44/5.67 thf(fact_5911_dbl__inc__def,axiom,
% 5.44/5.67 ( neg_nu8557863876264182079omplex
% 5.44/5.67 = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_def
% 5.44/5.67 thf(fact_5912_dbl__inc__def,axiom,
% 5.44/5.67 ( neg_nu8295874005876285629c_real
% 5.44/5.67 = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_def
% 5.44/5.67 thf(fact_5913_dbl__inc__def,axiom,
% 5.44/5.67 ( neg_nu5851722552734809277nc_int
% 5.44/5.67 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % dbl_inc_def
% 5.44/5.67 thf(fact_5914_real__of__int__div__aux,axiom,
% 5.44/5.67 ! [X: int,D: int] :
% 5.44/5.67 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 5.44/5.67 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % real_of_int_div_aux
% 5.44/5.67 thf(fact_5915_numeral__BitM,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numera6690914467698888265omplex @ ( bitM @ N2 ) )
% 5.44/5.67 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N2 ) ) @ one_one_complex ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_BitM
% 5.44/5.67 thf(fact_5916_numeral__BitM,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_real @ ( bitM @ N2 ) )
% 5.44/5.67 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N2 ) ) @ one_one_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_BitM
% 5.44/5.67 thf(fact_5917_numeral__BitM,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( numeral_numeral_int @ ( bitM @ N2 ) )
% 5.44/5.67 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % numeral_BitM
% 5.44/5.67 thf(fact_5918_odd__numeral__BitM,axiom,
% 5.44/5.67 ! [W: num] :
% 5.44/5.67 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % odd_numeral_BitM
% 5.44/5.67 thf(fact_5919_odd__numeral__BitM,axiom,
% 5.44/5.67 ! [W: num] :
% 5.44/5.67 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % odd_numeral_BitM
% 5.44/5.67 thf(fact_5920_odd__numeral__BitM,axiom,
% 5.44/5.67 ! [W: num] :
% 5.44/5.67 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % odd_numeral_BitM
% 5.44/5.67 thf(fact_5921_real__of__int__div2,axiom,
% 5.44/5.67 ! [N2: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % real_of_int_div2
% 5.44/5.67 thf(fact_5922_real__of__int__div3,axiom,
% 5.44/5.67 ! [N2: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) ) @ one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % real_of_int_div3
% 5.44/5.67 thf(fact_5923_even__of__int__iff,axiom,
% 5.44/5.67 ! [K: int] :
% 5.44/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.44/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_of_int_iff
% 5.44/5.67 thf(fact_5924_even__of__int__iff,axiom,
% 5.44/5.67 ! [K: int] :
% 5.44/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.44/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_of_int_iff
% 5.44/5.67 thf(fact_5925_arctan__add,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.67 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.44/5.67 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.44/5.67 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % arctan_add
% 5.44/5.67 thf(fact_5926_floor__exists1,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ? [X5: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X5 ) @ X )
% 5.44/5.67 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.44/5.67 & ! [Y2: int] :
% 5.44/5.67 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ X )
% 5.44/5.67 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y2 @ one_one_int ) ) ) )
% 5.44/5.67 => ( Y2 = X5 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % floor_exists1
% 5.44/5.67 thf(fact_5927_floor__exists,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ? [Z4: int] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X )
% 5.44/5.67 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % floor_exists
% 5.44/5.67 thf(fact_5928_mask__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.67 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_numeral
% 5.44/5.67 thf(fact_5929_mask__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_numeral
% 5.44/5.67 thf(fact_5930_tanh__real__altdef,axiom,
% 5.44/5.67 ( tanh_real
% 5.44/5.67 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_real_altdef
% 5.44/5.67 thf(fact_5931_and__int__unfold,axiom,
% 5.44/5.67 ( bit_se725231765392027082nd_int
% 5.44/5.67 = ( ^ [K3: int,L: int] :
% 5.44/5.67 ( if_int
% 5.44/5.67 @ ( ( K3 = zero_zero_int )
% 5.44/5.67 | ( L = zero_zero_int ) )
% 5.44/5.67 @ zero_zero_int
% 5.44/5.67 @ ( if_int
% 5.44/5.67 @ ( K3
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 @ L
% 5.44/5.67 @ ( if_int
% 5.44/5.67 @ ( L
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 @ K3
% 5.44/5.67 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_int_unfold
% 5.44/5.67 thf(fact_5932_or__int__unfold,axiom,
% 5.44/5.67 ( bit_se1409905431419307370or_int
% 5.44/5.67 = ( ^ [K3: int,L: int] :
% 5.44/5.67 ( if_int
% 5.44/5.67 @ ( ( K3
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 | ( L
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.44/5.67 @ ( uminus_uminus_int @ one_one_int )
% 5.44/5.67 @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_int_unfold
% 5.44/5.67 thf(fact_5933_and_Oright__idem,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.44/5.67 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.right_idem
% 5.44/5.67 thf(fact_5934_and_Oright__idem,axiom,
% 5.44/5.67 ! [A: nat,B: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.44/5.67 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.right_idem
% 5.44/5.67 thf(fact_5935_and_Oleft__idem,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.44/5.67 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.left_idem
% 5.44/5.67 thf(fact_5936_and_Oleft__idem,axiom,
% 5.44/5.67 ! [A: nat,B: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.44/5.67 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.left_idem
% 5.44/5.67 thf(fact_5937_and_Oidem,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % and.idem
% 5.44/5.67 thf(fact_5938_and_Oidem,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % and.idem
% 5.44/5.67 thf(fact_5939_or_Oright__idem,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ B )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.right_idem
% 5.44/5.67 thf(fact_5940_or_Oright__idem,axiom,
% 5.44/5.67 ! [A: nat,B: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ B )
% 5.44/5.67 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.right_idem
% 5.44/5.67 thf(fact_5941_or_Oleft__idem,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.left_idem
% 5.44/5.67 thf(fact_5942_or_Oleft__idem,axiom,
% 5.44/5.67 ! [A: nat,B: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.44/5.67 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.left_idem
% 5.44/5.67 thf(fact_5943_or_Oidem,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ A @ A )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % or.idem
% 5.44/5.67 thf(fact_5944_or_Oidem,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ A @ A )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % or.idem
% 5.44/5.67 thf(fact_5945_mask__nat__positive__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.44/5.67 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_nat_positive_iff
% 5.44/5.67 thf(fact_5946_bit_Oconj__zero__right,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % bit.conj_zero_right
% 5.44/5.67 thf(fact_5947_bit_Oconj__zero__left,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % bit.conj_zero_left
% 5.44/5.67 thf(fact_5948_zero__and__eq,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % zero_and_eq
% 5.44/5.67 thf(fact_5949_zero__and__eq,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % zero_and_eq
% 5.44/5.67 thf(fact_5950_and__zero__eq,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_zero_eq
% 5.44/5.67 thf(fact_5951_and__zero__eq,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_zero_eq
% 5.44/5.67 thf(fact_5952_or_Oright__neutral,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ A @ zero_zero_int )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % or.right_neutral
% 5.44/5.67 thf(fact_5953_or_Oright__neutral,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ A @ zero_zero_nat )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % or.right_neutral
% 5.44/5.67 thf(fact_5954_or_Oleft__neutral,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ zero_zero_int @ A )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % or.left_neutral
% 5.44/5.67 thf(fact_5955_or_Oleft__neutral,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ zero_zero_nat @ A )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % or.left_neutral
% 5.44/5.67 thf(fact_5956_exp__less__mono,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_real @ X @ Y )
% 5.44/5.67 => ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_less_mono
% 5.44/5.67 thf(fact_5957_exp__less__cancel__iff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.44/5.67 = ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_less_cancel_iff
% 5.44/5.67 thf(fact_5958_take__bit__and,axiom,
% 5.44/5.67 ! [N2: nat,A: int,B: int] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.44/5.67 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_and
% 5.44/5.67 thf(fact_5959_take__bit__and,axiom,
% 5.44/5.67 ! [N2: nat,A: nat,B: nat] :
% 5.44/5.67 ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.44/5.67 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_and
% 5.44/5.67 thf(fact_5960_exp__le__cancel__iff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.44/5.67 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_le_cancel_iff
% 5.44/5.67 thf(fact_5961_take__bit__or,axiom,
% 5.44/5.67 ! [N2: nat,A: int,B: int] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_or
% 5.44/5.67 thf(fact_5962_take__bit__or,axiom,
% 5.44/5.67 ! [N2: nat,A: nat,B: nat] :
% 5.44/5.67 ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.44/5.67 = ( bit_se1412395901928357646or_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_or
% 5.44/5.67 thf(fact_5963_exp__zero,axiom,
% 5.44/5.67 ( ( exp_complex @ zero_zero_complex )
% 5.44/5.67 = one_one_complex ) ).
% 5.44/5.67
% 5.44/5.67 % exp_zero
% 5.44/5.67 thf(fact_5964_exp__zero,axiom,
% 5.44/5.67 ( ( exp_real @ zero_zero_real )
% 5.44/5.67 = one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % exp_zero
% 5.44/5.67 thf(fact_5965_and_Oleft__neutral,axiom,
% 5.44/5.67 ! [A: code_integer] :
% 5.44/5.67 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % and.left_neutral
% 5.44/5.67 thf(fact_5966_and_Oleft__neutral,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % and.left_neutral
% 5.44/5.67 thf(fact_5967_and_Oright__neutral,axiom,
% 5.44/5.67 ! [A: code_integer] :
% 5.44/5.67 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % and.right_neutral
% 5.44/5.67 thf(fact_5968_and_Oright__neutral,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = A ) ).
% 5.44/5.67
% 5.44/5.67 % and.right_neutral
% 5.44/5.67 thf(fact_5969_bit_Oconj__one__right,axiom,
% 5.44/5.67 ! [X: code_integer] :
% 5.44/5.67 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = X ) ).
% 5.44/5.67
% 5.44/5.67 % bit.conj_one_right
% 5.44/5.67 thf(fact_5970_bit_Oconj__one__right,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = X ) ).
% 5.44/5.67
% 5.44/5.67 % bit.conj_one_right
% 5.44/5.67 thf(fact_5971_bit_Odisj__one__left,axiom,
% 5.44/5.67 ! [X: code_integer] :
% 5.44/5.67 ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.disj_one_left
% 5.44/5.67 thf(fact_5972_bit_Odisj__one__left,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.disj_one_left
% 5.44/5.67 thf(fact_5973_bit_Odisj__one__right,axiom,
% 5.44/5.67 ! [X: code_integer] :
% 5.44/5.67 ( ( bit_se1080825931792720795nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.disj_one_right
% 5.44/5.67 thf(fact_5974_bit_Odisj__one__right,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.disj_one_right
% 5.44/5.67 thf(fact_5975_mask__eq__0__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ( bit_se2002935070580805687sk_nat @ N2 )
% 5.44/5.67 = zero_zero_nat )
% 5.44/5.67 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_eq_0_iff
% 5.44/5.67 thf(fact_5976_mask__eq__0__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ( bit_se2000444600071755411sk_int @ N2 )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_eq_0_iff
% 5.44/5.67 thf(fact_5977_mask__0,axiom,
% 5.44/5.67 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % mask_0
% 5.44/5.67 thf(fact_5978_mask__0,axiom,
% 5.44/5.67 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % mask_0
% 5.44/5.67 thf(fact_5979_exp__eq__one__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ( exp_real @ X )
% 5.44/5.67 = one_one_real )
% 5.44/5.67 = ( X = zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_eq_one_iff
% 5.44/5.67 thf(fact_5980_and__nonnegative__int__iff,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.44/5.67 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.67 | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_nonnegative_int_iff
% 5.44/5.67 thf(fact_5981_and__negative__int__iff,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 5.44/5.67 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.44/5.67 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_negative_int_iff
% 5.44/5.67 thf(fact_5982_or__nonnegative__int__iff,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 5.44/5.67 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.67 & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_nonnegative_int_iff
% 5.44/5.67 thf(fact_5983_or__negative__int__iff,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 5.44/5.67 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.44/5.67 | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_negative_int_iff
% 5.44/5.67 thf(fact_5984_and__numerals_I2_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(2)
% 5.44/5.67 thf(fact_5985_and__numerals_I2_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.67 = one_one_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(2)
% 5.44/5.67 thf(fact_5986_and__numerals_I8_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(8)
% 5.44/5.67 thf(fact_5987_and__numerals_I8_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.44/5.67 = one_one_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(8)
% 5.44/5.67 thf(fact_5988_or__numerals_I2_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(2)
% 5.44/5.67 thf(fact_5989_or__numerals_I2_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(2)
% 5.44/5.67 thf(fact_5990_or__numerals_I8_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.44/5.67 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(8)
% 5.44/5.67 thf(fact_5991_or__numerals_I8_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(8)
% 5.44/5.67 thf(fact_5992_mask__Suc__0,axiom,
% 5.44/5.67 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.44/5.67 = one_one_nat ) ).
% 5.44/5.67
% 5.44/5.67 % mask_Suc_0
% 5.44/5.67 thf(fact_5993_mask__Suc__0,axiom,
% 5.44/5.67 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % mask_Suc_0
% 5.44/5.67 thf(fact_5994_one__less__exp__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 5.44/5.67 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_less_exp_iff
% 5.44/5.67 thf(fact_5995_exp__less__one__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 5.44/5.67 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_less_one_iff
% 5.44/5.67 thf(fact_5996_one__le__exp__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 5.44/5.67 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_le_exp_iff
% 5.44/5.67 thf(fact_5997_exp__le__one__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 5.44/5.67 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_le_one_iff
% 5.44/5.67 thf(fact_5998_take__bit__minus__one__eq__mask,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( bit_se1745604003318907178nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_minus_one_eq_mask
% 5.44/5.67 thf(fact_5999_take__bit__minus__one__eq__mask,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_minus_one_eq_mask
% 5.44/5.67 thf(fact_6000_exp__ln,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.44/5.67 = X ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_ln
% 5.44/5.67 thf(fact_6001_exp__ln__iff,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.44/5.67 = X )
% 5.44/5.67 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_ln_iff
% 5.44/5.67 thf(fact_6002_and__numerals_I1_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(1)
% 5.44/5.67 thf(fact_6003_and__numerals_I1_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(1)
% 5.44/5.67 thf(fact_6004_and__numerals_I5_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(5)
% 5.44/5.67 thf(fact_6005_and__numerals_I5_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(5)
% 5.44/5.67 thf(fact_6006_and__numerals_I3_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(3)
% 5.44/5.67 thf(fact_6007_and__numerals_I3_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(3)
% 5.44/5.67 thf(fact_6008_or__numerals_I3_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(3)
% 5.44/5.67 thf(fact_6009_or__numerals_I3_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(3)
% 5.44/5.67 thf(fact_6010_or__numerals_I1_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(1)
% 5.44/5.67 thf(fact_6011_or__numerals_I1_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(1)
% 5.44/5.67 thf(fact_6012_or__numerals_I5_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.44/5.67 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(5)
% 5.44/5.67 thf(fact_6013_or__numerals_I5_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(5)
% 5.44/5.67 thf(fact_6014_and__minus__numerals_I2_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_minus_numerals(2)
% 5.44/5.67 thf(fact_6015_and__minus__numerals_I6_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_minus_numerals(6)
% 5.44/5.67 thf(fact_6016_or__minus__numerals_I2_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_minus_numerals(2)
% 5.44/5.67 thf(fact_6017_or__minus__numerals_I6_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_minus_numerals(6)
% 5.44/5.67 thf(fact_6018_and__numerals_I4_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(4)
% 5.44/5.67 thf(fact_6019_and__numerals_I4_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(4)
% 5.44/5.67 thf(fact_6020_and__numerals_I6_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(6)
% 5.44/5.67 thf(fact_6021_and__numerals_I6_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(6)
% 5.44/5.67 thf(fact_6022_and__minus__numerals_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_minus_numerals(5)
% 5.44/5.67 thf(fact_6023_and__minus__numerals_I1_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.67 = zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % and_minus_numerals(1)
% 5.44/5.67 thf(fact_6024_and__numerals_I7_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(7)
% 5.44/5.67 thf(fact_6025_and__numerals_I7_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_numerals(7)
% 5.44/5.67 thf(fact_6026_or__numerals_I4_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(4)
% 5.44/5.67 thf(fact_6027_or__numerals_I4_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(4)
% 5.44/5.67 thf(fact_6028_or__numerals_I6_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(6)
% 5.44/5.67 thf(fact_6029_or__numerals_I6_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(6)
% 5.44/5.67 thf(fact_6030_or__numerals_I7_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(7)
% 5.44/5.67 thf(fact_6031_or__numerals_I7_J,axiom,
% 5.44/5.67 ! [X: num,Y: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_numerals(7)
% 5.44/5.67 thf(fact_6032_of__int__or__eq,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_or_eq
% 5.44/5.67 thf(fact_6033_of__int__and__eq,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.44/5.67 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_and_eq
% 5.44/5.67 thf(fact_6034_of__int__mask__eq,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.44/5.67 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_mask_eq
% 5.44/5.67 thf(fact_6035_take__bit__eq__mask,axiom,
% 5.44/5.67 ( bit_se2923211474154528505it_int
% 5.44/5.67 = ( ^ [N: nat,A4: int] : ( bit_se725231765392027082nd_int @ A4 @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_eq_mask
% 5.44/5.67 thf(fact_6036_take__bit__eq__mask,axiom,
% 5.44/5.67 ( bit_se2925701944663578781it_nat
% 5.44/5.67 = ( ^ [N: nat,A4: nat] : ( bit_se727722235901077358nd_nat @ A4 @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_eq_mask
% 5.44/5.67 thf(fact_6037_bit_Odisj__conj__distrib2,axiom,
% 5.44/5.67 ! [Y: int,Z: int,X: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y @ Z ) @ X )
% 5.44/5.67 = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y @ X ) @ ( bit_se1409905431419307370or_int @ Z @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.disj_conj_distrib2
% 5.44/5.67 thf(fact_6038_bit_Oconj__disj__distrib2,axiom,
% 5.44/5.67 ! [Y: int,Z: int,X: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y @ Z ) @ X )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y @ X ) @ ( bit_se725231765392027082nd_int @ Z @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.conj_disj_distrib2
% 5.44/5.67 thf(fact_6039_bit_Odisj__conj__distrib,axiom,
% 5.44/5.67 ! [X: int,Y: int,Z: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ X @ ( bit_se725231765392027082nd_int @ Y @ Z ) )
% 5.44/5.67 = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.disj_conj_distrib
% 5.44/5.67 thf(fact_6040_bit_Oconj__disj__distrib,axiom,
% 5.44/5.67 ! [X: int,Y: int,Z: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ X @ ( bit_se1409905431419307370or_int @ Y @ Z ) )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se725231765392027082nd_int @ X @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.conj_disj_distrib
% 5.44/5.67 thf(fact_6041_and_Oleft__commute,axiom,
% 5.44/5.67 ! [B: int,A: int,C: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.44/5.67 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.left_commute
% 5.44/5.67 thf(fact_6042_and_Oleft__commute,axiom,
% 5.44/5.67 ! [B: nat,A: nat,C: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.44/5.67 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.left_commute
% 5.44/5.67 thf(fact_6043_or_Oleft__commute,axiom,
% 5.44/5.67 ! [B: int,A: int,C: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ B @ ( bit_se1409905431419307370or_int @ A @ C ) )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.left_commute
% 5.44/5.67 thf(fact_6044_or_Oleft__commute,axiom,
% 5.44/5.67 ! [B: nat,A: nat,C: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ B @ ( bit_se1412395901928357646or_nat @ A @ C ) )
% 5.44/5.67 = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.left_commute
% 5.44/5.67 thf(fact_6045_and_Ocommute,axiom,
% 5.44/5.67 ( bit_se725231765392027082nd_int
% 5.44/5.67 = ( ^ [A4: int,B4: int] : ( bit_se725231765392027082nd_int @ B4 @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.commute
% 5.44/5.67 thf(fact_6046_and_Ocommute,axiom,
% 5.44/5.67 ( bit_se727722235901077358nd_nat
% 5.44/5.67 = ( ^ [A4: nat,B4: nat] : ( bit_se727722235901077358nd_nat @ B4 @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.commute
% 5.44/5.67 thf(fact_6047_or_Ocommute,axiom,
% 5.44/5.67 ( bit_se1409905431419307370or_int
% 5.44/5.67 = ( ^ [A4: int,B4: int] : ( bit_se1409905431419307370or_int @ B4 @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.commute
% 5.44/5.67 thf(fact_6048_or_Ocommute,axiom,
% 5.44/5.67 ( bit_se1412395901928357646or_nat
% 5.44/5.67 = ( ^ [A4: nat,B4: nat] : ( bit_se1412395901928357646or_nat @ B4 @ A4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.commute
% 5.44/5.67 thf(fact_6049_and_Oassoc,axiom,
% 5.44/5.67 ! [A: int,B: int,C: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.44/5.67 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.assoc
% 5.44/5.67 thf(fact_6050_and_Oassoc,axiom,
% 5.44/5.67 ! [A: nat,B: nat,C: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.44/5.67 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and.assoc
% 5.44/5.67 thf(fact_6051_or_Oassoc,axiom,
% 5.44/5.67 ! [A: int,B: int,C: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ C )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.assoc
% 5.44/5.67 thf(fact_6052_or_Oassoc,axiom,
% 5.44/5.67 ! [A: nat,B: nat,C: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ C )
% 5.44/5.67 = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or.assoc
% 5.44/5.67 thf(fact_6053_plus__and__or,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 5.44/5.67 = ( plus_plus_int @ X @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % plus_and_or
% 5.44/5.67 thf(fact_6054_bit_Odisj__zero__right,axiom,
% 5.44/5.67 ! [X: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ X @ zero_zero_int )
% 5.44/5.67 = X ) ).
% 5.44/5.67
% 5.44/5.67 % bit.disj_zero_right
% 5.44/5.67 thf(fact_6055_or__eq__0__iff,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ( bit_se1409905431419307370or_int @ A @ B )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 = ( ( A = zero_zero_int )
% 5.44/5.67 & ( B = zero_zero_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_eq_0_iff
% 5.44/5.67 thf(fact_6056_or__eq__0__iff,axiom,
% 5.44/5.67 ! [A: nat,B: nat] :
% 5.44/5.67 ( ( ( bit_se1412395901928357646or_nat @ A @ B )
% 5.44/5.67 = zero_zero_nat )
% 5.44/5.67 = ( ( A = zero_zero_nat )
% 5.44/5.67 & ( B = zero_zero_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_eq_0_iff
% 5.44/5.67 thf(fact_6057_exp__less__cancel,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.44/5.67 => ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_less_cancel
% 5.44/5.67 thf(fact_6058_exp__times__arg__commute,axiom,
% 5.44/5.67 ! [A2: complex] :
% 5.44/5.67 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.44/5.67 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_times_arg_commute
% 5.44/5.67 thf(fact_6059_exp__times__arg__commute,axiom,
% 5.44/5.67 ! [A2: real] :
% 5.44/5.67 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.44/5.67 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_times_arg_commute
% 5.44/5.67 thf(fact_6060_bit_Ocomplement__unique,axiom,
% 5.44/5.67 ! [A: code_integer,X: code_integer,Y: code_integer] :
% 5.44/5.67 ( ( ( bit_se3949692690581998587nteger @ A @ X )
% 5.44/5.67 = zero_z3403309356797280102nteger )
% 5.44/5.67 => ( ( ( bit_se1080825931792720795nteger @ A @ X )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 => ( ( ( bit_se3949692690581998587nteger @ A @ Y )
% 5.44/5.67 = zero_z3403309356797280102nteger )
% 5.44/5.67 => ( ( ( bit_se1080825931792720795nteger @ A @ Y )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 => ( X = Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.complement_unique
% 5.44/5.67 thf(fact_6061_bit_Ocomplement__unique,axiom,
% 5.44/5.67 ! [A: int,X: int,Y: int] :
% 5.44/5.67 ( ( ( bit_se725231765392027082nd_int @ A @ X )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 => ( ( ( bit_se1409905431419307370or_int @ A @ X )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 => ( ( ( bit_se725231765392027082nd_int @ A @ Y )
% 5.44/5.67 = zero_zero_int )
% 5.44/5.67 => ( ( ( bit_se1409905431419307370or_int @ A @ Y )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 => ( X = Y ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % bit.complement_unique
% 5.44/5.67 thf(fact_6062_less__eq__mask,axiom,
% 5.44/5.67 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % less_eq_mask
% 5.44/5.67 thf(fact_6063_and__eq__minus__1__iff,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 = ( ( A
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.44/5.67 & ( B
% 5.44/5.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_eq_minus_1_iff
% 5.44/5.67 thf(fact_6064_and__eq__minus__1__iff,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 = ( ( A
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.67 & ( B
% 5.44/5.67 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_eq_minus_1_iff
% 5.44/5.67 thf(fact_6065_not__exp__less__zero,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.44/5.67
% 5.44/5.67 % not_exp_less_zero
% 5.44/5.67 thf(fact_6066_exp__gt__zero,axiom,
% 5.44/5.67 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_gt_zero
% 5.44/5.67 thf(fact_6067_exp__total,axiom,
% 5.44/5.67 ! [Y: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.67 => ? [X5: real] :
% 5.44/5.67 ( ( exp_real @ X5 )
% 5.44/5.67 = Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_total
% 5.44/5.67 thf(fact_6068_exp__ge__zero,axiom,
% 5.44/5.67 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_ge_zero
% 5.44/5.67 thf(fact_6069_not__exp__le__zero,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.44/5.67
% 5.44/5.67 % not_exp_le_zero
% 5.44/5.67 thf(fact_6070_OR__lower,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.67 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % OR_lower
% 5.44/5.67 thf(fact_6071_or__greater__eq,axiom,
% 5.44/5.67 ! [L2: int,K: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.44/5.67 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_greater_eq
% 5.44/5.67 thf(fact_6072_AND__lower,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.67 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % AND_lower
% 5.44/5.67 thf(fact_6073_AND__upper1,axiom,
% 5.44/5.67 ! [X: int,Y: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.67 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % AND_upper1
% 5.44/5.67 thf(fact_6074_AND__upper2,axiom,
% 5.44/5.67 ! [Y: int,X: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.67 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 5.44/5.67
% 5.44/5.67 % AND_upper2
% 5.44/5.67 thf(fact_6075_AND__upper1_H,axiom,
% 5.44/5.67 ! [Y: int,Z: int,Ya: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.67 => ( ( ord_less_eq_int @ Y @ Z )
% 5.44/5.67 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % AND_upper1'
% 5.44/5.67 thf(fact_6076_AND__upper2_H,axiom,
% 5.44/5.67 ! [Y: int,Z: int,X: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.67 => ( ( ord_less_eq_int @ Y @ Z )
% 5.44/5.67 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % AND_upper2'
% 5.44/5.67 thf(fact_6077_exp__add__commuting,axiom,
% 5.44/5.67 ! [X: complex,Y: complex] :
% 5.44/5.67 ( ( ( times_times_complex @ X @ Y )
% 5.44/5.67 = ( times_times_complex @ Y @ X ) )
% 5.44/5.67 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.67 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_add_commuting
% 5.44/5.67 thf(fact_6078_exp__add__commuting,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ( times_times_real @ X @ Y )
% 5.44/5.67 = ( times_times_real @ Y @ X ) )
% 5.44/5.67 => ( ( exp_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.67 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_add_commuting
% 5.44/5.67 thf(fact_6079_mult__exp__exp,axiom,
% 5.44/5.67 ! [X: complex,Y: complex] :
% 5.44/5.67 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) )
% 5.44/5.67 = ( exp_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mult_exp_exp
% 5.44/5.67 thf(fact_6080_mult__exp__exp,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.44/5.67 = ( exp_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mult_exp_exp
% 5.44/5.67 thf(fact_6081_exp__diff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( exp_real @ ( minus_minus_real @ X @ Y ) )
% 5.44/5.67 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_diff
% 5.44/5.67 thf(fact_6082_exp__diff,axiom,
% 5.44/5.67 ! [X: complex,Y: complex] :
% 5.44/5.67 ( ( exp_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.44/5.67 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_diff
% 5.44/5.67 thf(fact_6083_mask__nonnegative__int,axiom,
% 5.44/5.67 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_nonnegative_int
% 5.44/5.67 thf(fact_6084_not__mask__negative__int,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 5.44/5.67
% 5.44/5.67 % not_mask_negative_int
% 5.44/5.67 thf(fact_6085_mask__Suc__exp,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N2 ) )
% 5.44/5.67 = ( bit_se1412395901928357646or_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_Suc_exp
% 5.44/5.67 thf(fact_6086_mask__Suc__exp,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( bit_se2000444600071755411sk_int @ ( suc @ N2 ) )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_Suc_exp
% 5.44/5.67 thf(fact_6087_exp__gt__one,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_gt_one
% 5.44/5.67 thf(fact_6088_exp__ge__add__one__self,axiom,
% 5.44/5.67 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_ge_add_one_self
% 5.44/5.67 thf(fact_6089_and__less__eq,axiom,
% 5.44/5.67 ! [L2: int,K: int] :
% 5.44/5.67 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.44/5.67 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_less_eq
% 5.44/5.67 thf(fact_6090_AND__upper1_H_H,axiom,
% 5.44/5.67 ! [Y: int,Z: int,Ya: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.67 => ( ( ord_less_int @ Y @ Z )
% 5.44/5.67 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % AND_upper1''
% 5.44/5.67 thf(fact_6091_AND__upper2_H_H,axiom,
% 5.44/5.67 ! [Y: int,Z: int,X: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.67 => ( ( ord_less_int @ Y @ Z )
% 5.44/5.67 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % AND_upper2''
% 5.44/5.67 thf(fact_6092_exp__minus__inverse,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 5.44/5.67 = one_one_real ) ).
% 5.44/5.67
% 5.44/5.67 % exp_minus_inverse
% 5.44/5.67 thf(fact_6093_exp__minus__inverse,axiom,
% 5.44/5.67 ! [X: complex] :
% 5.44/5.67 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 5.44/5.67 = one_one_complex ) ).
% 5.44/5.67
% 5.44/5.67 % exp_minus_inverse
% 5.44/5.67 thf(fact_6094_mask__Suc__double,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N2 ) )
% 5.44/5.67 = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_Suc_double
% 5.44/5.67 thf(fact_6095_mask__Suc__double,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( bit_se2000444600071755411sk_int @ ( suc @ N2 ) )
% 5.44/5.67 = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_Suc_double
% 5.44/5.67 thf(fact_6096_less__mask,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.67 => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % less_mask
% 5.44/5.67 thf(fact_6097_even__and__iff,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.44/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_and_iff
% 5.44/5.67 thf(fact_6098_even__and__iff,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.44/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_and_iff
% 5.44/5.67 thf(fact_6099_even__and__iff,axiom,
% 5.44/5.67 ! [A: nat,B: nat] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.44/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_and_iff
% 5.44/5.67 thf(fact_6100_even__or__iff,axiom,
% 5.44/5.67 ! [A: code_integer,B: code_integer] :
% 5.44/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 5.44/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_or_iff
% 5.44/5.67 thf(fact_6101_even__or__iff,axiom,
% 5.44/5.67 ! [A: int,B: int] :
% 5.44/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.44/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_or_iff
% 5.44/5.67 thf(fact_6102_even__or__iff,axiom,
% 5.44/5.67 ! [A: nat,B: nat] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.44/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.67 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_or_iff
% 5.44/5.67 thf(fact_6103_exp__ge__add__one__self__aux,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_ge_add_one_self_aux
% 5.44/5.67 thf(fact_6104_even__and__iff__int,axiom,
% 5.44/5.67 ! [K: int,L2: int] :
% 5.44/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.44/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.44/5.67 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % even_and_iff_int
% 5.44/5.67 thf(fact_6105_lemma__exp__total,axiom,
% 5.44/5.67 ! [Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.44/5.67 => ? [X5: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.44/5.67 & ( ord_less_eq_real @ X5 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.44/5.67 & ( ( exp_real @ X5 )
% 5.44/5.67 = Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % lemma_exp_total
% 5.44/5.67 thf(fact_6106_ln__ge__iff,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 5.44/5.67 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % ln_ge_iff
% 5.44/5.67 thf(fact_6107_ln__x__over__x__mono,axiom,
% 5.44/5.67 ! [X: real,Y: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.67 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % ln_x_over_x_mono
% 5.44/5.67 thf(fact_6108_one__and__eq,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.44/5.67 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_and_eq
% 5.44/5.67 thf(fact_6109_one__and__eq,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.44/5.67 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_and_eq
% 5.44/5.67 thf(fact_6110_and__one__eq,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.44/5.67 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_one_eq
% 5.44/5.67 thf(fact_6111_and__one__eq,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.44/5.67 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_one_eq
% 5.44/5.67 thf(fact_6112_exp__le,axiom,
% 5.44/5.67 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_le
% 5.44/5.67 thf(fact_6113_take__bit__eq__mask__iff,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.44/5.67 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.44/5.67 = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.44/5.67 = zero_zero_int ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_eq_mask_iff
% 5.44/5.67 thf(fact_6114_tanh__altdef,axiom,
% 5.44/5.67 ( tanh_real
% 5.44/5.67 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_altdef
% 5.44/5.67 thf(fact_6115_tanh__altdef,axiom,
% 5.44/5.67 ( tanh_complex
% 5.44/5.67 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % tanh_altdef
% 5.44/5.67 thf(fact_6116_Suc__mask__eq__exp,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.44/5.67 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % Suc_mask_eq_exp
% 5.44/5.67 thf(fact_6117_mask__nat__less__exp,axiom,
% 5.44/5.67 ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_nat_less_exp
% 5.44/5.67 thf(fact_6118_exp__half__le2,axiom,
% 5.44/5.67 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_half_le2
% 5.44/5.67 thf(fact_6119_exp__double,axiom,
% 5.44/5.67 ! [Z: complex] :
% 5.44/5.67 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.44/5.67 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_double
% 5.44/5.67 thf(fact_6120_exp__double,axiom,
% 5.44/5.67 ! [Z: real] :
% 5.44/5.67 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.44/5.67 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_double
% 5.44/5.67 thf(fact_6121_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N2 ) )
% 5.44/5.67 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_bit_operations_class.even_mask_iff
% 5.44/5.67 thf(fact_6122_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.44/5.67 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_bit_operations_class.even_mask_iff
% 5.44/5.67 thf(fact_6123_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.44/5.67 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.67
% 5.44/5.67 % semiring_bit_operations_class.even_mask_iff
% 5.44/5.67 thf(fact_6124_or__one__eq,axiom,
% 5.44/5.67 ! [A: code_integer] :
% 5.44/5.67 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 5.44/5.67 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_one_eq
% 5.44/5.67 thf(fact_6125_or__one__eq,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 5.44/5.67 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_one_eq
% 5.44/5.67 thf(fact_6126_or__one__eq,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 5.44/5.67 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_one_eq
% 5.44/5.67 thf(fact_6127_one__or__eq,axiom,
% 5.44/5.67 ! [A: code_integer] :
% 5.44/5.67 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 5.44/5.67 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_or_eq
% 5.44/5.67 thf(fact_6128_one__or__eq,axiom,
% 5.44/5.67 ! [A: int] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 5.44/5.67 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_or_eq
% 5.44/5.67 thf(fact_6129_one__or__eq,axiom,
% 5.44/5.67 ! [A: nat] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 5.44/5.67 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % one_or_eq
% 5.44/5.67 thf(fact_6130_OR__upper,axiom,
% 5.44/5.67 ! [X: int,N2: nat,Y: int] :
% 5.44/5.67 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.67 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.67 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.67 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % OR_upper
% 5.44/5.67 thf(fact_6131_or__int__rec,axiom,
% 5.44/5.67 ( bit_se1409905431419307370or_int
% 5.44/5.67 = ( ^ [K3: int,L: int] :
% 5.44/5.67 ( plus_plus_int
% 5.44/5.67 @ ( zero_n2684676970156552555ol_int
% 5.44/5.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.44/5.67 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.44/5.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_int_rec
% 5.44/5.67 thf(fact_6132_mask__nat__def,axiom,
% 5.44/5.67 ( bit_se2002935070580805687sk_nat
% 5.44/5.67 = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_nat_def
% 5.44/5.67 thf(fact_6133_and__int__rec,axiom,
% 5.44/5.67 ( bit_se725231765392027082nd_int
% 5.44/5.67 = ( ^ [K3: int,L: int] :
% 5.44/5.67 ( plus_plus_int
% 5.44/5.67 @ ( zero_n2684676970156552555ol_int
% 5.44/5.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.44/5.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.44/5.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_int_rec
% 5.44/5.67 thf(fact_6134_mask__half__int,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.67 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_half_int
% 5.44/5.67 thf(fact_6135_exists__least__lemma,axiom,
% 5.44/5.67 ! [P: nat > $o] :
% 5.44/5.67 ( ~ ( P @ zero_zero_nat )
% 5.44/5.67 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.44/5.67 => ? [N4: nat] :
% 5.44/5.67 ( ~ ( P @ N4 )
% 5.44/5.67 & ( P @ ( suc @ N4 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exists_least_lemma
% 5.44/5.67 thf(fact_6136_mask__int__def,axiom,
% 5.44/5.67 ( bit_se2000444600071755411sk_int
% 5.44/5.67 = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_int_def
% 5.44/5.67 thf(fact_6137_ex__le__of__int,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ? [Z4: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z4 ) ) ).
% 5.44/5.67
% 5.44/5.67 % ex_le_of_int
% 5.44/5.67 thf(fact_6138_ex__of__int__less,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ? [Z4: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z4 ) @ X ) ).
% 5.44/5.67
% 5.44/5.67 % ex_of_int_less
% 5.44/5.67 thf(fact_6139_ex__less__of__int,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ? [Z4: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z4 ) ) ).
% 5.44/5.67
% 5.44/5.67 % ex_less_of_int
% 5.44/5.67 thf(fact_6140_mask__eq__exp__minus__1,axiom,
% 5.44/5.67 ( bit_se2002935070580805687sk_nat
% 5.44/5.67 = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_eq_exp_minus_1
% 5.44/5.67 thf(fact_6141_mask__eq__exp__minus__1,axiom,
% 5.44/5.67 ( bit_se2000444600071755411sk_int
% 5.44/5.67 = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % mask_eq_exp_minus_1
% 5.44/5.67 thf(fact_6142_exp__bound,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.67 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_bound
% 5.44/5.67 thf(fact_6143_real__exp__bound__lemma,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.67 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % real_exp_bound_lemma
% 5.44/5.67 thf(fact_6144_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.44/5.67 ! [N2: nat,K: int] :
% 5.44/5.67 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.44/5.67 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.44/5.67 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % take_bit_eq_mask_iff_exp_dvd
% 5.44/5.67 thf(fact_6145_exp__lower__Taylor__quadratic,axiom,
% 5.44/5.67 ! [X: real] :
% 5.44/5.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.67 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % exp_lower_Taylor_quadratic
% 5.44/5.67 thf(fact_6146_round__unique,axiom,
% 5.44/5.67 ! [X: real,Y: int] :
% 5.44/5.67 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 5.44/5.67 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.44/5.67 => ( ( archim8280529875227126926d_real @ X )
% 5.44/5.67 = Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % round_unique
% 5.44/5.67 thf(fact_6147_round__unique_H,axiom,
% 5.44/5.67 ! [X: real,N2: int] :
% 5.44/5.67 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.67 => ( ( archim8280529875227126926d_real @ X )
% 5.44/5.67 = N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % round_unique'
% 5.44/5.67 thf(fact_6148_of__int__round__abs__le,axiom,
% 5.44/5.67 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % of_int_round_abs_le
% 5.44/5.67 thf(fact_6149_and__int_Osimps,axiom,
% 5.44/5.67 ( bit_se725231765392027082nd_int
% 5.44/5.67 = ( ^ [K3: int,L: int] :
% 5.44/5.67 ( if_int
% 5.44/5.67 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.44/5.67 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.44/5.67 @ ( uminus_uminus_int
% 5.44/5.67 @ ( zero_n2684676970156552555ol_int
% 5.44/5.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.44/5.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.44/5.67 @ ( plus_plus_int
% 5.44/5.67 @ ( zero_n2684676970156552555ol_int
% 5.44/5.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.44/5.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.44/5.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_int.simps
% 5.44/5.67 thf(fact_6150_and__int_Oelims,axiom,
% 5.44/5.67 ! [X: int,Xa2: int,Y: int] :
% 5.44/5.67 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.44/5.67 = Y )
% 5.44/5.67 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.44/5.67 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.44/5.67 => ( Y
% 5.44/5.67 = ( uminus_uminus_int
% 5.44/5.67 @ ( zero_n2684676970156552555ol_int
% 5.44/5.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.44/5.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.44/5.67 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.44/5.67 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.44/5.67 => ( Y
% 5.44/5.67 = ( plus_plus_int
% 5.44/5.67 @ ( zero_n2684676970156552555ol_int
% 5.44/5.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.44/5.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.44/5.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_int.elims
% 5.44/5.67 thf(fact_6151_or__minus__numerals_I1_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_minus_numerals(1)
% 5.44/5.67 thf(fact_6152_insert__subset,axiom,
% 5.44/5.67 ! [X: int,A2: set_int,B2: set_int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 5.44/5.67 = ( ( member_int @ X @ B2 )
% 5.44/5.67 & ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % insert_subset
% 5.44/5.67 thf(fact_6153_insert__subset,axiom,
% 5.44/5.67 ! [X: complex,A2: set_complex,B2: set_complex] :
% 5.44/5.67 ( ( ord_le211207098394363844omplex @ ( insert_complex @ X @ A2 ) @ B2 )
% 5.44/5.67 = ( ( member_complex @ X @ B2 )
% 5.44/5.67 & ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % insert_subset
% 5.44/5.67 thf(fact_6154_insert__subset,axiom,
% 5.44/5.67 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 5.44/5.67 = ( ( member8440522571783428010at_nat @ X @ B2 )
% 5.44/5.67 & ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % insert_subset
% 5.44/5.67 thf(fact_6155_insert__subset,axiom,
% 5.44/5.67 ! [X: real,A2: set_real,B2: set_real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 5.44/5.67 = ( ( member_real @ X @ B2 )
% 5.44/5.67 & ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % insert_subset
% 5.44/5.67 thf(fact_6156_insert__subset,axiom,
% 5.44/5.67 ! [X: nat,A2: set_nat,B2: set_nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 5.44/5.67 = ( ( member_nat @ X @ B2 )
% 5.44/5.67 & ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % insert_subset
% 5.44/5.67 thf(fact_6157_singleton__insert__inj__eq_H,axiom,
% 5.44/5.67 ! [A: int,A2: set_int,B: int] :
% 5.44/5.67 ( ( ( insert_int @ A @ A2 )
% 5.44/5.67 = ( insert_int @ B @ bot_bot_set_int ) )
% 5.44/5.67 = ( ( A = B )
% 5.44/5.67 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % singleton_insert_inj_eq'
% 5.44/5.67 thf(fact_6158_singleton__insert__inj__eq_H,axiom,
% 5.44/5.67 ! [A: real,A2: set_real,B: real] :
% 5.44/5.67 ( ( ( insert_real @ A @ A2 )
% 5.44/5.67 = ( insert_real @ B @ bot_bot_set_real ) )
% 5.44/5.67 = ( ( A = B )
% 5.44/5.67 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % singleton_insert_inj_eq'
% 5.44/5.67 thf(fact_6159_singleton__insert__inj__eq_H,axiom,
% 5.44/5.67 ! [A: nat,A2: set_nat,B: nat] :
% 5.44/5.67 ( ( ( insert_nat @ A @ A2 )
% 5.44/5.67 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 5.44/5.67 = ( ( A = B )
% 5.44/5.67 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % singleton_insert_inj_eq'
% 5.44/5.67 thf(fact_6160_singleton__insert__inj__eq,axiom,
% 5.44/5.67 ! [B: int,A: int,A2: set_int] :
% 5.44/5.67 ( ( ( insert_int @ B @ bot_bot_set_int )
% 5.44/5.67 = ( insert_int @ A @ A2 ) )
% 5.44/5.67 = ( ( A = B )
% 5.44/5.67 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % singleton_insert_inj_eq
% 5.44/5.67 thf(fact_6161_singleton__insert__inj__eq,axiom,
% 5.44/5.67 ! [B: real,A: real,A2: set_real] :
% 5.44/5.67 ( ( ( insert_real @ B @ bot_bot_set_real )
% 5.44/5.67 = ( insert_real @ A @ A2 ) )
% 5.44/5.67 = ( ( A = B )
% 5.44/5.67 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % singleton_insert_inj_eq
% 5.44/5.67 thf(fact_6162_singleton__insert__inj__eq,axiom,
% 5.44/5.67 ! [B: nat,A: nat,A2: set_nat] :
% 5.44/5.67 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 5.44/5.67 = ( insert_nat @ A @ A2 ) )
% 5.44/5.67 = ( ( A = B )
% 5.44/5.67 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % singleton_insert_inj_eq
% 5.44/5.67 thf(fact_6163_round__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.67 = ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % round_numeral
% 5.44/5.67 thf(fact_6164_round__1,axiom,
% 5.44/5.67 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.44/5.67 = one_one_int ) ).
% 5.44/5.67
% 5.44/5.67 % round_1
% 5.44/5.67 thf(fact_6165_and__nat__numerals_I3_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_nat_numerals(3)
% 5.44/5.67 thf(fact_6166_and__nat__numerals_I1_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.67 = zero_zero_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_nat_numerals(1)
% 5.44/5.67 thf(fact_6167_or__nat__numerals_I2_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_nat_numerals(2)
% 5.44/5.67 thf(fact_6168_or__nat__numerals_I4_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_nat_numerals(4)
% 5.44/5.67 thf(fact_6169_subset__Compl__singleton,axiom,
% 5.44/5.67 ! [A2: set_complex,B: complex] :
% 5.44/5.67 ( ( ord_le211207098394363844omplex @ A2 @ ( uminus8566677241136511917omplex @ ( insert_complex @ B @ bot_bot_set_complex ) ) )
% 5.44/5.67 = ( ~ ( member_complex @ B @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Compl_singleton
% 5.44/5.67 thf(fact_6170_subset__Compl__singleton,axiom,
% 5.44/5.67 ! [A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 5.44/5.67 ( ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 5.44/5.67 = ( ~ ( member8440522571783428010at_nat @ B @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Compl_singleton
% 5.44/5.67 thf(fact_6171_subset__Compl__singleton,axiom,
% 5.44/5.67 ! [A2: set_int,B: int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 5.44/5.67 = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Compl_singleton
% 5.44/5.67 thf(fact_6172_subset__Compl__singleton,axiom,
% 5.44/5.67 ! [A2: set_real,B: real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 5.44/5.67 = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Compl_singleton
% 5.44/5.67 thf(fact_6173_subset__Compl__singleton,axiom,
% 5.44/5.67 ! [A2: set_nat,B: nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 5.44/5.67 = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Compl_singleton
% 5.44/5.67 thf(fact_6174_or__nat__numerals_I3_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_nat_numerals(3)
% 5.44/5.67 thf(fact_6175_or__nat__numerals_I1_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.67 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_nat_numerals(1)
% 5.44/5.67 thf(fact_6176_and__nat__numerals_I2_J,axiom,
% 5.44/5.67 ! [Y: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.67 = one_one_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_nat_numerals(2)
% 5.44/5.67 thf(fact_6177_and__nat__numerals_I4_J,axiom,
% 5.44/5.67 ! [X: num] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.67 = one_one_nat ) ).
% 5.44/5.67
% 5.44/5.67 % and_nat_numerals(4)
% 5.44/5.67 thf(fact_6178_set__replicate,axiom,
% 5.44/5.67 ! [N2: nat,X: vEBT_VEBT] :
% 5.44/5.67 ( ( N2 != zero_zero_nat )
% 5.44/5.67 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.44/5.67 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % set_replicate
% 5.44/5.67 thf(fact_6179_set__replicate,axiom,
% 5.44/5.67 ! [N2: nat,X: nat] :
% 5.44/5.67 ( ( N2 != zero_zero_nat )
% 5.44/5.67 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 5.44/5.67 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % set_replicate
% 5.44/5.67 thf(fact_6180_set__replicate,axiom,
% 5.44/5.67 ! [N2: nat,X: int] :
% 5.44/5.67 ( ( N2 != zero_zero_nat )
% 5.44/5.67 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 5.44/5.67 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % set_replicate
% 5.44/5.67 thf(fact_6181_set__replicate,axiom,
% 5.44/5.67 ! [N2: nat,X: real] :
% 5.44/5.67 ( ( N2 != zero_zero_nat )
% 5.44/5.67 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 5.44/5.67 = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % set_replicate
% 5.44/5.67 thf(fact_6182_round__neg__numeral,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % round_neg_numeral
% 5.44/5.67 thf(fact_6183_Suc__0__and__eq,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.67 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % Suc_0_and_eq
% 5.44/5.67 thf(fact_6184_and__Suc__0__eq,axiom,
% 5.44/5.67 ! [N2: nat] :
% 5.44/5.67 ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.44/5.67 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % and_Suc_0_eq
% 5.44/5.67 thf(fact_6185_or__minus__numerals_I8_J,axiom,
% 5.44/5.67 ! [N2: num,M: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_minus_numerals(8)
% 5.44/5.67 thf(fact_6186_or__minus__numerals_I4_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_minus_numerals(4)
% 5.44/5.67 thf(fact_6187_or__minus__numerals_I7_J,axiom,
% 5.44/5.67 ! [N2: num,M: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_minus_numerals(7)
% 5.44/5.67 thf(fact_6188_or__minus__numerals_I3_J,axiom,
% 5.44/5.67 ! [M: num,N2: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_minus_numerals(3)
% 5.44/5.67 thf(fact_6189_or__minus__numerals_I5_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.44/5.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_minus_numerals(5)
% 5.44/5.67 thf(fact_6190_subset__insertI2,axiom,
% 5.44/5.67 ! [A2: set_int,B2: set_int,B: int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.67 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insertI2
% 5.44/5.67 thf(fact_6191_subset__insertI2,axiom,
% 5.44/5.67 ! [A2: set_real,B2: set_real,B: real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.67 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insertI2
% 5.44/5.67 thf(fact_6192_subset__insertI2,axiom,
% 5.44/5.67 ! [A2: set_nat,B2: set_nat,B: nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.67 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insertI2
% 5.44/5.67 thf(fact_6193_subset__insertI,axiom,
% 5.44/5.67 ! [B2: set_int,A: int] : ( ord_less_eq_set_int @ B2 @ ( insert_int @ A @ B2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insertI
% 5.44/5.67 thf(fact_6194_subset__insertI,axiom,
% 5.44/5.67 ! [B2: set_real,A: real] : ( ord_less_eq_set_real @ B2 @ ( insert_real @ A @ B2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insertI
% 5.44/5.67 thf(fact_6195_subset__insertI,axiom,
% 5.44/5.67 ! [B2: set_nat,A: nat] : ( ord_less_eq_set_nat @ B2 @ ( insert_nat @ A @ B2 ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insertI
% 5.44/5.67 thf(fact_6196_subset__insert,axiom,
% 5.44/5.67 ! [X: int,A2: set_int,B2: set_int] :
% 5.44/5.67 ( ~ ( member_int @ X @ A2 )
% 5.44/5.67 => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 5.44/5.67 = ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert
% 5.44/5.67 thf(fact_6197_subset__insert,axiom,
% 5.44/5.67 ! [X: complex,A2: set_complex,B2: set_complex] :
% 5.44/5.67 ( ~ ( member_complex @ X @ A2 )
% 5.44/5.67 => ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B2 ) )
% 5.44/5.67 = ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert
% 5.44/5.67 thf(fact_6198_subset__insert,axiom,
% 5.44/5.67 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 5.44/5.67 => ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 5.44/5.67 = ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert
% 5.44/5.67 thf(fact_6199_subset__insert,axiom,
% 5.44/5.67 ! [X: real,A2: set_real,B2: set_real] :
% 5.44/5.67 ( ~ ( member_real @ X @ A2 )
% 5.44/5.67 => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 5.44/5.67 = ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert
% 5.44/5.67 thf(fact_6200_subset__insert,axiom,
% 5.44/5.67 ! [X: nat,A2: set_nat,B2: set_nat] :
% 5.44/5.67 ( ~ ( member_nat @ X @ A2 )
% 5.44/5.67 => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 5.44/5.67 = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert
% 5.44/5.67 thf(fact_6201_insert__mono,axiom,
% 5.44/5.67 ! [C4: set_int,D4: set_int,A: int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ C4 @ D4 )
% 5.44/5.67 => ( ord_less_eq_set_int @ ( insert_int @ A @ C4 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % insert_mono
% 5.44/5.67 thf(fact_6202_insert__mono,axiom,
% 5.44/5.67 ! [C4: set_real,D4: set_real,A: real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ C4 @ D4 )
% 5.44/5.67 => ( ord_less_eq_set_real @ ( insert_real @ A @ C4 ) @ ( insert_real @ A @ D4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % insert_mono
% 5.44/5.67 thf(fact_6203_insert__mono,axiom,
% 5.44/5.67 ! [C4: set_nat,D4: set_nat,A: nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ C4 @ D4 )
% 5.44/5.67 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C4 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % insert_mono
% 5.44/5.67 thf(fact_6204_or__not__num__neg_Osimps_I1_J,axiom,
% 5.44/5.67 ( ( bit_or_not_num_neg @ one @ one )
% 5.44/5.67 = one ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(1)
% 5.44/5.67 thf(fact_6205_subset__singleton__iff,axiom,
% 5.44/5.67 ! [X8: set_int,A: int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 5.44/5.67 = ( ( X8 = bot_bot_set_int )
% 5.44/5.67 | ( X8
% 5.44/5.67 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_singleton_iff
% 5.44/5.67 thf(fact_6206_subset__singleton__iff,axiom,
% 5.44/5.67 ! [X8: set_real,A: real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 5.44/5.67 = ( ( X8 = bot_bot_set_real )
% 5.44/5.67 | ( X8
% 5.44/5.67 = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_singleton_iff
% 5.44/5.67 thf(fact_6207_subset__singleton__iff,axiom,
% 5.44/5.67 ! [X8: set_nat,A: nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 5.44/5.67 = ( ( X8 = bot_bot_set_nat )
% 5.44/5.67 | ( X8
% 5.44/5.67 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_singleton_iff
% 5.44/5.67 thf(fact_6208_subset__singletonD,axiom,
% 5.44/5.67 ! [A2: set_int,X: int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 5.44/5.67 => ( ( A2 = bot_bot_set_int )
% 5.44/5.67 | ( A2
% 5.44/5.67 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_singletonD
% 5.44/5.67 thf(fact_6209_subset__singletonD,axiom,
% 5.44/5.67 ! [A2: set_real,X: real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) )
% 5.44/5.67 => ( ( A2 = bot_bot_set_real )
% 5.44/5.67 | ( A2
% 5.44/5.67 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_singletonD
% 5.44/5.67 thf(fact_6210_subset__singletonD,axiom,
% 5.44/5.67 ! [A2: set_nat,X: nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 5.44/5.67 => ( ( A2 = bot_bot_set_nat )
% 5.44/5.67 | ( A2
% 5.44/5.67 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_singletonD
% 5.44/5.67 thf(fact_6211_subset__Diff__insert,axiom,
% 5.44/5.67 ! [A2: set_int,B2: set_int,X: int,C4: set_int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ ( insert_int @ X @ C4 ) ) )
% 5.44/5.67 = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ C4 ) )
% 5.44/5.67 & ~ ( member_int @ X @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Diff_insert
% 5.44/5.67 thf(fact_6212_subset__Diff__insert,axiom,
% 5.44/5.67 ! [A2: set_complex,B2: set_complex,X: complex,C4: set_complex] :
% 5.44/5.67 ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B2 @ ( insert_complex @ X @ C4 ) ) )
% 5.44/5.67 = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B2 @ C4 ) )
% 5.44/5.67 & ~ ( member_complex @ X @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Diff_insert
% 5.44/5.67 thf(fact_6213_subset__Diff__insert,axiom,
% 5.44/5.67 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ ( insert8211810215607154385at_nat @ X @ C4 ) ) )
% 5.44/5.67 = ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ C4 ) )
% 5.44/5.67 & ~ ( member8440522571783428010at_nat @ X @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Diff_insert
% 5.44/5.67 thf(fact_6214_subset__Diff__insert,axiom,
% 5.44/5.67 ! [A2: set_real,B2: set_real,X: real,C4: set_real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ ( insert_real @ X @ C4 ) ) )
% 5.44/5.67 = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ C4 ) )
% 5.44/5.67 & ~ ( member_real @ X @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Diff_insert
% 5.44/5.67 thf(fact_6215_subset__Diff__insert,axiom,
% 5.44/5.67 ! [A2: set_nat,B2: set_nat,X: nat,C4: set_nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ ( insert_nat @ X @ C4 ) ) )
% 5.44/5.67 = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ C4 ) )
% 5.44/5.67 & ~ ( member_nat @ X @ A2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_Diff_insert
% 5.44/5.67 thf(fact_6216_or__not__num__neg_Osimps_I4_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
% 5.44/5.67 = ( bit0 @ one ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(4)
% 5.44/5.67 thf(fact_6217_or__not__num__neg_Osimps_I6_J,axiom,
% 5.44/5.67 ! [N2: num,M: num] :
% 5.44/5.67 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit1 @ M ) )
% 5.44/5.67 = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(6)
% 5.44/5.67 thf(fact_6218_or__not__num__neg_Osimps_I7_J,axiom,
% 5.44/5.67 ! [N2: num] :
% 5.44/5.67 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ one )
% 5.44/5.67 = one ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(7)
% 5.44/5.67 thf(fact_6219_or__not__num__neg_Osimps_I3_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.44/5.67 = ( bit1 @ M ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(3)
% 5.44/5.67 thf(fact_6220_or__not__num__neg_Osimps_I5_J,axiom,
% 5.44/5.67 ! [N2: num,M: num] :
% 5.44/5.67 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit0 @ M ) )
% 5.44/5.67 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(5)
% 5.44/5.67 thf(fact_6221_or__not__num__neg_Osimps_I9_J,axiom,
% 5.44/5.67 ! [N2: num,M: num] :
% 5.44/5.67 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit1 @ M ) )
% 5.44/5.67 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(9)
% 5.44/5.67 thf(fact_6222_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_complex,P: set_complex > $o,F: complex > num] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_complex )
% 5.44/5.67 => ( ! [X5: complex,S4: set_complex] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ S4 )
% 5.44/5.67 => ( ! [Y2: complex] :
% 5.44/5.67 ( ( member_complex @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_complex @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6223_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_nat,P: set_nat > $o,F: nat > num] :
% 5.44/5.67 ( ( finite_finite_nat @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ! [X5: nat,S4: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ S4 )
% 5.44/5.67 => ( ! [Y2: nat] :
% 5.44/5.67 ( ( member_nat @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_nat @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6224_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_int,P: set_int > $o,F: int > num] :
% 5.44/5.67 ( ( finite_finite_int @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_int )
% 5.44/5.67 => ( ! [X5: int,S4: set_int] :
% 5.44/5.67 ( ( finite_finite_int @ S4 )
% 5.44/5.67 => ( ! [Y2: int] :
% 5.44/5.67 ( ( member_int @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_int @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6225_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_real,P: set_real > $o,F: real > num] :
% 5.44/5.67 ( ( finite_finite_real @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_real )
% 5.44/5.67 => ( ! [X5: real,S4: set_real] :
% 5.44/5.67 ( ( finite_finite_real @ S4 )
% 5.44/5.67 => ( ! [Y2: real] :
% 5.44/5.67 ( ( member_real @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_real @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6226_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_complex,P: set_complex > $o,F: complex > nat] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_complex )
% 5.44/5.67 => ( ! [X5: complex,S4: set_complex] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ S4 )
% 5.44/5.67 => ( ! [Y2: complex] :
% 5.44/5.67 ( ( member_complex @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_complex @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6227_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_nat,P: set_nat > $o,F: nat > nat] :
% 5.44/5.67 ( ( finite_finite_nat @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ! [X5: nat,S4: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ S4 )
% 5.44/5.67 => ( ! [Y2: nat] :
% 5.44/5.67 ( ( member_nat @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_nat @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6228_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_int,P: set_int > $o,F: int > nat] :
% 5.44/5.67 ( ( finite_finite_int @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_int )
% 5.44/5.67 => ( ! [X5: int,S4: set_int] :
% 5.44/5.67 ( ( finite_finite_int @ S4 )
% 5.44/5.67 => ( ! [Y2: int] :
% 5.44/5.67 ( ( member_int @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_int @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6229_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_real,P: set_real > $o,F: real > nat] :
% 5.44/5.67 ( ( finite_finite_real @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_real )
% 5.44/5.67 => ( ! [X5: real,S4: set_real] :
% 5.44/5.67 ( ( finite_finite_real @ S4 )
% 5.44/5.67 => ( ! [Y2: real] :
% 5.44/5.67 ( ( member_real @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_real @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6230_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_complex,P: set_complex > $o,F: complex > int] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_complex )
% 5.44/5.67 => ( ! [X5: complex,S4: set_complex] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ S4 )
% 5.44/5.67 => ( ! [Y2: complex] :
% 5.44/5.67 ( ( member_complex @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_int @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_complex @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6231_finite__ranking__induct,axiom,
% 5.44/5.67 ! [S: set_nat,P: set_nat > $o,F: nat > int] :
% 5.44/5.67 ( ( finite_finite_nat @ S )
% 5.44/5.67 => ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ! [X5: nat,S4: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ S4 )
% 5.44/5.67 => ( ! [Y2: nat] :
% 5.44/5.67 ( ( member_nat @ Y2 @ S4 )
% 5.44/5.67 => ( ord_less_eq_int @ ( F @ Y2 ) @ ( F @ X5 ) ) )
% 5.44/5.67 => ( ( P @ S4 )
% 5.44/5.67 => ( P @ ( insert_nat @ X5 @ S4 ) ) ) ) )
% 5.44/5.67 => ( P @ S ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_ranking_induct
% 5.44/5.67 thf(fact_6232_finite__linorder__max__induct,axiom,
% 5.44/5.67 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.44/5.67 ( ( finite4001608067531595151d_enat @ A2 )
% 5.44/5.67 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.44/5.67 => ( ! [B3: extended_enat,A7: set_Extended_enat] :
% 5.44/5.67 ( ( finite4001608067531595151d_enat @ A7 )
% 5.44/5.67 => ( ! [X3: extended_enat] :
% 5.44/5.67 ( ( member_Extended_enat @ X3 @ A7 )
% 5.44/5.67 => ( ord_le72135733267957522d_enat @ X3 @ B3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_Extended_enat @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_max_induct
% 5.44/5.67 thf(fact_6233_finite__linorder__max__induct,axiom,
% 5.44/5.67 ! [A2: set_real,P: set_real > $o] :
% 5.44/5.67 ( ( finite_finite_real @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_real )
% 5.44/5.67 => ( ! [B3: real,A7: set_real] :
% 5.44/5.67 ( ( finite_finite_real @ A7 )
% 5.44/5.67 => ( ! [X3: real] :
% 5.44/5.67 ( ( member_real @ X3 @ A7 )
% 5.44/5.67 => ( ord_less_real @ X3 @ B3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_real @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_max_induct
% 5.44/5.67 thf(fact_6234_finite__linorder__max__induct,axiom,
% 5.44/5.67 ! [A2: set_num,P: set_num > $o] :
% 5.44/5.67 ( ( finite_finite_num @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_num )
% 5.44/5.67 => ( ! [B3: num,A7: set_num] :
% 5.44/5.67 ( ( finite_finite_num @ A7 )
% 5.44/5.67 => ( ! [X3: num] :
% 5.44/5.67 ( ( member_num @ X3 @ A7 )
% 5.44/5.67 => ( ord_less_num @ X3 @ B3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_num @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_max_induct
% 5.44/5.67 thf(fact_6235_finite__linorder__max__induct,axiom,
% 5.44/5.67 ! [A2: set_nat,P: set_nat > $o] :
% 5.44/5.67 ( ( finite_finite_nat @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ! [B3: nat,A7: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ A7 )
% 5.44/5.67 => ( ! [X3: nat] :
% 5.44/5.67 ( ( member_nat @ X3 @ A7 )
% 5.44/5.67 => ( ord_less_nat @ X3 @ B3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_nat @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_max_induct
% 5.44/5.67 thf(fact_6236_finite__linorder__max__induct,axiom,
% 5.44/5.67 ! [A2: set_int,P: set_int > $o] :
% 5.44/5.67 ( ( finite_finite_int @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_int )
% 5.44/5.67 => ( ! [B3: int,A7: set_int] :
% 5.44/5.67 ( ( finite_finite_int @ A7 )
% 5.44/5.67 => ( ! [X3: int] :
% 5.44/5.67 ( ( member_int @ X3 @ A7 )
% 5.44/5.67 => ( ord_less_int @ X3 @ B3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_int @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_max_induct
% 5.44/5.67 thf(fact_6237_finite__linorder__min__induct,axiom,
% 5.44/5.67 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 5.44/5.67 ( ( finite4001608067531595151d_enat @ A2 )
% 5.44/5.67 => ( ( P @ bot_bo7653980558646680370d_enat )
% 5.44/5.67 => ( ! [B3: extended_enat,A7: set_Extended_enat] :
% 5.44/5.67 ( ( finite4001608067531595151d_enat @ A7 )
% 5.44/5.67 => ( ! [X3: extended_enat] :
% 5.44/5.67 ( ( member_Extended_enat @ X3 @ A7 )
% 5.44/5.67 => ( ord_le72135733267957522d_enat @ B3 @ X3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_Extended_enat @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_min_induct
% 5.44/5.67 thf(fact_6238_finite__linorder__min__induct,axiom,
% 5.44/5.67 ! [A2: set_real,P: set_real > $o] :
% 5.44/5.67 ( ( finite_finite_real @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_real )
% 5.44/5.67 => ( ! [B3: real,A7: set_real] :
% 5.44/5.67 ( ( finite_finite_real @ A7 )
% 5.44/5.67 => ( ! [X3: real] :
% 5.44/5.67 ( ( member_real @ X3 @ A7 )
% 5.44/5.67 => ( ord_less_real @ B3 @ X3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_real @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_min_induct
% 5.44/5.67 thf(fact_6239_finite__linorder__min__induct,axiom,
% 5.44/5.67 ! [A2: set_num,P: set_num > $o] :
% 5.44/5.67 ( ( finite_finite_num @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_num )
% 5.44/5.67 => ( ! [B3: num,A7: set_num] :
% 5.44/5.67 ( ( finite_finite_num @ A7 )
% 5.44/5.67 => ( ! [X3: num] :
% 5.44/5.67 ( ( member_num @ X3 @ A7 )
% 5.44/5.67 => ( ord_less_num @ B3 @ X3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_num @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_min_induct
% 5.44/5.67 thf(fact_6240_finite__linorder__min__induct,axiom,
% 5.44/5.67 ! [A2: set_nat,P: set_nat > $o] :
% 5.44/5.67 ( ( finite_finite_nat @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ! [B3: nat,A7: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ A7 )
% 5.44/5.67 => ( ! [X3: nat] :
% 5.44/5.67 ( ( member_nat @ X3 @ A7 )
% 5.44/5.67 => ( ord_less_nat @ B3 @ X3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_nat @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_min_induct
% 5.44/5.67 thf(fact_6241_finite__linorder__min__induct,axiom,
% 5.44/5.67 ! [A2: set_int,P: set_int > $o] :
% 5.44/5.67 ( ( finite_finite_int @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_int )
% 5.44/5.67 => ( ! [B3: int,A7: set_int] :
% 5.44/5.67 ( ( finite_finite_int @ A7 )
% 5.44/5.67 => ( ! [X3: int] :
% 5.44/5.67 ( ( member_int @ X3 @ A7 )
% 5.44/5.67 => ( ord_less_int @ B3 @ X3 ) )
% 5.44/5.67 => ( ( P @ A7 )
% 5.44/5.67 => ( P @ ( insert_int @ B3 @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ A2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_linorder_min_induct
% 5.44/5.67 thf(fact_6242_finite__subset__induct_H,axiom,
% 5.44/5.67 ! [F3: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.44/5.67 ( ( finite6177210948735845034at_nat @ F3 )
% 5.44/5.67 => ( ( ord_le3146513528884898305at_nat @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.44/5.67 => ( ! [A3: product_prod_nat_nat,F4: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ( finite6177210948735845034at_nat @ F4 )
% 5.44/5.67 => ( ( member8440522571783428010at_nat @ A3 @ A2 )
% 5.44/5.67 => ( ( ord_le3146513528884898305at_nat @ F4 @ A2 )
% 5.44/5.67 => ( ~ ( member8440522571783428010at_nat @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert8211810215607154385at_nat @ A3 @ F4 ) ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct'
% 5.44/5.67 thf(fact_6243_finite__subset__induct_H,axiom,
% 5.44/5.67 ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ F3 )
% 5.44/5.67 => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_complex )
% 5.44/5.67 => ( ! [A3: complex,F4: set_complex] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ F4 )
% 5.44/5.67 => ( ( member_complex @ A3 @ A2 )
% 5.44/5.67 => ( ( ord_le211207098394363844omplex @ F4 @ A2 )
% 5.44/5.67 => ( ~ ( member_complex @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert_complex @ A3 @ F4 ) ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct'
% 5.44/5.67 thf(fact_6244_finite__subset__induct_H,axiom,
% 5.44/5.67 ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 5.44/5.67 ( ( finite_finite_int @ F3 )
% 5.44/5.67 => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_int )
% 5.44/5.67 => ( ! [A3: int,F4: set_int] :
% 5.44/5.67 ( ( finite_finite_int @ F4 )
% 5.44/5.67 => ( ( member_int @ A3 @ A2 )
% 5.44/5.67 => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 5.44/5.67 => ( ~ ( member_int @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert_int @ A3 @ F4 ) ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct'
% 5.44/5.67 thf(fact_6245_finite__subset__induct_H,axiom,
% 5.44/5.67 ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 5.44/5.67 ( ( finite_finite_real @ F3 )
% 5.44/5.67 => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_real )
% 5.44/5.67 => ( ! [A3: real,F4: set_real] :
% 5.44/5.67 ( ( finite_finite_real @ F4 )
% 5.44/5.67 => ( ( member_real @ A3 @ A2 )
% 5.44/5.67 => ( ( ord_less_eq_set_real @ F4 @ A2 )
% 5.44/5.67 => ( ~ ( member_real @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert_real @ A3 @ F4 ) ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct'
% 5.44/5.67 thf(fact_6246_finite__subset__induct_H,axiom,
% 5.44/5.67 ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 5.44/5.67 ( ( finite_finite_nat @ F3 )
% 5.44/5.67 => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ! [A3: nat,F4: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ F4 )
% 5.44/5.67 => ( ( member_nat @ A3 @ A2 )
% 5.44/5.67 => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 5.44/5.67 => ( ~ ( member_nat @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert_nat @ A3 @ F4 ) ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct'
% 5.44/5.67 thf(fact_6247_finite__subset__induct,axiom,
% 5.44/5.67 ! [F3: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.44/5.67 ( ( finite6177210948735845034at_nat @ F3 )
% 5.44/5.67 => ( ( ord_le3146513528884898305at_nat @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.44/5.67 => ( ! [A3: product_prod_nat_nat,F4: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ( finite6177210948735845034at_nat @ F4 )
% 5.44/5.67 => ( ( member8440522571783428010at_nat @ A3 @ A2 )
% 5.44/5.67 => ( ~ ( member8440522571783428010at_nat @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert8211810215607154385at_nat @ A3 @ F4 ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct
% 5.44/5.67 thf(fact_6248_finite__subset__induct,axiom,
% 5.44/5.67 ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ F3 )
% 5.44/5.67 => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_complex )
% 5.44/5.67 => ( ! [A3: complex,F4: set_complex] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ F4 )
% 5.44/5.67 => ( ( member_complex @ A3 @ A2 )
% 5.44/5.67 => ( ~ ( member_complex @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert_complex @ A3 @ F4 ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct
% 5.44/5.67 thf(fact_6249_finite__subset__induct,axiom,
% 5.44/5.67 ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 5.44/5.67 ( ( finite_finite_int @ F3 )
% 5.44/5.67 => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_int )
% 5.44/5.67 => ( ! [A3: int,F4: set_int] :
% 5.44/5.67 ( ( finite_finite_int @ F4 )
% 5.44/5.67 => ( ( member_int @ A3 @ A2 )
% 5.44/5.67 => ( ~ ( member_int @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert_int @ A3 @ F4 ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct
% 5.44/5.67 thf(fact_6250_finite__subset__induct,axiom,
% 5.44/5.67 ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 5.44/5.67 ( ( finite_finite_real @ F3 )
% 5.44/5.67 => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_real )
% 5.44/5.67 => ( ! [A3: real,F4: set_real] :
% 5.44/5.67 ( ( finite_finite_real @ F4 )
% 5.44/5.67 => ( ( member_real @ A3 @ A2 )
% 5.44/5.67 => ( ~ ( member_real @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert_real @ A3 @ F4 ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct
% 5.44/5.67 thf(fact_6251_finite__subset__induct,axiom,
% 5.44/5.67 ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 5.44/5.67 ( ( finite_finite_nat @ F3 )
% 5.44/5.67 => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ! [A3: nat,F4: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ F4 )
% 5.44/5.67 => ( ( member_nat @ A3 @ A2 )
% 5.44/5.67 => ( ~ ( member_nat @ A3 @ F4 )
% 5.44/5.67 => ( ( P @ F4 )
% 5.44/5.67 => ( P @ ( insert_nat @ A3 @ F4 ) ) ) ) ) )
% 5.44/5.67 => ( P @ F3 ) ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_subset_induct
% 5.44/5.67 thf(fact_6252_subset__insert__iff,axiom,
% 5.44/5.67 ! [A2: set_complex,X: complex,B2: set_complex] :
% 5.44/5.67 ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B2 ) )
% 5.44/5.67 = ( ( ( member_complex @ X @ A2 )
% 5.44/5.67 => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B2 ) )
% 5.44/5.67 & ( ~ ( member_complex @ X @ A2 )
% 5.44/5.67 => ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert_iff
% 5.44/5.67 thf(fact_6253_subset__insert__iff,axiom,
% 5.44/5.67 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 5.44/5.67 = ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.44/5.67 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 5.44/5.67 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 5.44/5.67 => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert_iff
% 5.44/5.67 thf(fact_6254_subset__insert__iff,axiom,
% 5.44/5.67 ! [A2: set_int,X: int,B2: set_int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 5.44/5.67 = ( ( ( member_int @ X @ A2 )
% 5.44/5.67 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 5.44/5.67 & ( ~ ( member_int @ X @ A2 )
% 5.44/5.67 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert_iff
% 5.44/5.67 thf(fact_6255_subset__insert__iff,axiom,
% 5.44/5.67 ! [A2: set_real,X: real,B2: set_real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 5.44/5.67 = ( ( ( member_real @ X @ A2 )
% 5.44/5.67 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 ) )
% 5.44/5.67 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.67 => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert_iff
% 5.44/5.67 thf(fact_6256_subset__insert__iff,axiom,
% 5.44/5.67 ! [A2: set_nat,X: nat,B2: set_nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 5.44/5.67 = ( ( ( member_nat @ X @ A2 )
% 5.44/5.67 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 5.44/5.67 & ( ~ ( member_nat @ X @ A2 )
% 5.44/5.67 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % subset_insert_iff
% 5.44/5.67 thf(fact_6257_Diff__single__insert,axiom,
% 5.44/5.67 ! [A2: set_int,X: int,B2: set_int] :
% 5.44/5.67 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 )
% 5.44/5.67 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % Diff_single_insert
% 5.44/5.67 thf(fact_6258_Diff__single__insert,axiom,
% 5.44/5.67 ! [A2: set_real,X: real,B2: set_real] :
% 5.44/5.67 ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 )
% 5.44/5.67 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % Diff_single_insert
% 5.44/5.67 thf(fact_6259_Diff__single__insert,axiom,
% 5.44/5.67 ! [A2: set_nat,X: nat,B2: set_nat] :
% 5.44/5.67 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 )
% 5.44/5.67 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % Diff_single_insert
% 5.44/5.67 thf(fact_6260_set__update__subset__insert,axiom,
% 5.44/5.67 ! [Xs2: list_int,I2: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % set_update_subset_insert
% 5.44/5.67 thf(fact_6261_set__update__subset__insert,axiom,
% 5.44/5.67 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % set_update_subset_insert
% 5.44/5.67 thf(fact_6262_set__update__subset__insert,axiom,
% 5.44/5.67 ! [Xs2: list_real,I2: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % set_update_subset_insert
% 5.44/5.67 thf(fact_6263_set__update__subset__insert,axiom,
% 5.44/5.67 ! [Xs2: list_nat,I2: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % set_update_subset_insert
% 5.44/5.67 thf(fact_6264_or__not__num__neg_Osimps_I2_J,axiom,
% 5.44/5.67 ! [M: num] :
% 5.44/5.67 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.44/5.67 = ( bit1 @ M ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(2)
% 5.44/5.67 thf(fact_6265_or__not__num__neg_Osimps_I8_J,axiom,
% 5.44/5.67 ! [N2: num,M: num] :
% 5.44/5.67 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit0 @ M ) )
% 5.44/5.67 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % or_not_num_neg.simps(8)
% 5.44/5.67 thf(fact_6266_remove__induct,axiom,
% 5.44/5.67 ! [P: set_Pr1261947904930325089at_nat > $o,B2: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ( P @ bot_bo2099793752762293965at_nat )
% 5.44/5.67 => ( ( ~ ( finite6177210948735845034at_nat @ B2 )
% 5.44/5.67 => ( P @ B2 ) )
% 5.44/5.67 => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ( finite6177210948735845034at_nat @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bo2099793752762293965at_nat )
% 5.44/5.67 => ( ( ord_le3146513528884898305at_nat @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: product_prod_nat_nat] :
% 5.44/5.67 ( ( member8440522571783428010at_nat @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % remove_induct
% 5.44/5.67 thf(fact_6267_remove__induct,axiom,
% 5.44/5.67 ! [P: set_complex > $o,B2: set_complex] :
% 5.44/5.67 ( ( P @ bot_bot_set_complex )
% 5.44/5.67 => ( ( ~ ( finite3207457112153483333omplex @ B2 )
% 5.44/5.67 => ( P @ B2 ) )
% 5.44/5.67 => ( ! [A7: set_complex] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bot_set_complex )
% 5.44/5.67 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: complex] :
% 5.44/5.67 ( ( member_complex @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % remove_induct
% 5.44/5.67 thf(fact_6268_remove__induct,axiom,
% 5.44/5.67 ! [P: set_int > $o,B2: set_int] :
% 5.44/5.67 ( ( P @ bot_bot_set_int )
% 5.44/5.67 => ( ( ~ ( finite_finite_int @ B2 )
% 5.44/5.67 => ( P @ B2 ) )
% 5.44/5.67 => ( ! [A7: set_int] :
% 5.44/5.67 ( ( finite_finite_int @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bot_set_int )
% 5.44/5.67 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: int] :
% 5.44/5.67 ( ( member_int @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % remove_induct
% 5.44/5.67 thf(fact_6269_remove__induct,axiom,
% 5.44/5.67 ! [P: set_real > $o,B2: set_real] :
% 5.44/5.67 ( ( P @ bot_bot_set_real )
% 5.44/5.67 => ( ( ~ ( finite_finite_real @ B2 )
% 5.44/5.67 => ( P @ B2 ) )
% 5.44/5.67 => ( ! [A7: set_real] :
% 5.44/5.67 ( ( finite_finite_real @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bot_set_real )
% 5.44/5.67 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: real] :
% 5.44/5.67 ( ( member_real @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % remove_induct
% 5.44/5.67 thf(fact_6270_remove__induct,axiom,
% 5.44/5.67 ! [P: set_nat > $o,B2: set_nat] :
% 5.44/5.67 ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ( ~ ( finite_finite_nat @ B2 )
% 5.44/5.67 => ( P @ B2 ) )
% 5.44/5.67 => ( ! [A7: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bot_set_nat )
% 5.44/5.67 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: nat] :
% 5.44/5.67 ( ( member_nat @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % remove_induct
% 5.44/5.67 thf(fact_6271_finite__remove__induct,axiom,
% 5.44/5.67 ! [B2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.44/5.67 ( ( finite6177210948735845034at_nat @ B2 )
% 5.44/5.67 => ( ( P @ bot_bo2099793752762293965at_nat )
% 5.44/5.67 => ( ! [A7: set_Pr1261947904930325089at_nat] :
% 5.44/5.67 ( ( finite6177210948735845034at_nat @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bo2099793752762293965at_nat )
% 5.44/5.67 => ( ( ord_le3146513528884898305at_nat @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: product_prod_nat_nat] :
% 5.44/5.67 ( ( member8440522571783428010at_nat @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_1356011639430497352at_nat @ A7 @ ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_remove_induct
% 5.44/5.67 thf(fact_6272_finite__remove__induct,axiom,
% 5.44/5.67 ! [B2: set_complex,P: set_complex > $o] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_complex )
% 5.44/5.67 => ( ! [A7: set_complex] :
% 5.44/5.67 ( ( finite3207457112153483333omplex @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bot_set_complex )
% 5.44/5.67 => ( ( ord_le211207098394363844omplex @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: complex] :
% 5.44/5.67 ( ( member_complex @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_remove_induct
% 5.44/5.67 thf(fact_6273_finite__remove__induct,axiom,
% 5.44/5.67 ! [B2: set_int,P: set_int > $o] :
% 5.44/5.67 ( ( finite_finite_int @ B2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_int )
% 5.44/5.67 => ( ! [A7: set_int] :
% 5.44/5.67 ( ( finite_finite_int @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bot_set_int )
% 5.44/5.67 => ( ( ord_less_eq_set_int @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: int] :
% 5.44/5.67 ( ( member_int @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_remove_induct
% 5.44/5.67 thf(fact_6274_finite__remove__induct,axiom,
% 5.44/5.67 ! [B2: set_real,P: set_real > $o] :
% 5.44/5.67 ( ( finite_finite_real @ B2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_real )
% 5.44/5.67 => ( ! [A7: set_real] :
% 5.44/5.67 ( ( finite_finite_real @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bot_set_real )
% 5.44/5.67 => ( ( ord_less_eq_set_real @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: real] :
% 5.44/5.67 ( ( member_real @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_remove_induct
% 5.44/5.67 thf(fact_6275_finite__remove__induct,axiom,
% 5.44/5.67 ! [B2: set_nat,P: set_nat > $o] :
% 5.44/5.67 ( ( finite_finite_nat @ B2 )
% 5.44/5.67 => ( ( P @ bot_bot_set_nat )
% 5.44/5.67 => ( ! [A7: set_nat] :
% 5.44/5.67 ( ( finite_finite_nat @ A7 )
% 5.44/5.67 => ( ( A7 != bot_bot_set_nat )
% 5.44/5.67 => ( ( ord_less_eq_set_nat @ A7 @ B2 )
% 5.44/5.67 => ( ! [X3: nat] :
% 5.44/5.67 ( ( member_nat @ X3 @ A7 )
% 5.44/5.67 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) )
% 5.44/5.67 => ( P @ A7 ) ) ) ) )
% 5.44/5.67 => ( P @ B2 ) ) ) ) ).
% 5.44/5.67
% 5.44/5.67 % finite_remove_induct
% 5.44/5.67 thf(fact_6276_psubset__insert__iff,axiom,
% 5.44/5.67 ! [A2: set_complex,X: complex,B2: set_complex] :
% 5.44/5.67 ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X @ B2 ) )
% 5.44/5.67 = ( ( ( member_complex @ X @ B2 )
% 5.44/5.67 => ( ord_less_set_complex @ A2 @ B2 ) )
% 5.44/5.67 & ( ~ ( member_complex @ X @ B2 )
% 5.44/5.67 => ( ( ( member_complex @ X @ A2 )
% 5.44/5.67 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B2 ) )
% 5.44/5.68 & ( ~ ( member_complex @ X @ A2 )
% 5.44/5.68 => ( ord_le211207098394363844omplex @ A2 @ B2 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % psubset_insert_iff
% 5.44/5.68 thf(fact_6277_psubset__insert__iff,axiom,
% 5.44/5.68 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.44/5.68 ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 5.44/5.68 = ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 5.44/5.68 => ( ord_le7866589430770878221at_nat @ A2 @ B2 ) )
% 5.44/5.68 & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 5.44/5.68 => ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.44/5.68 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 5.44/5.68 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 5.44/5.68 => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % psubset_insert_iff
% 5.44/5.68 thf(fact_6278_psubset__insert__iff,axiom,
% 5.44/5.68 ! [A2: set_int,X: int,B2: set_int] :
% 5.44/5.68 ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 5.44/5.68 = ( ( ( member_int @ X @ B2 )
% 5.44/5.68 => ( ord_less_set_int @ A2 @ B2 ) )
% 5.44/5.68 & ( ~ ( member_int @ X @ B2 )
% 5.44/5.68 => ( ( ( member_int @ X @ A2 )
% 5.44/5.68 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 5.44/5.68 & ( ~ ( member_int @ X @ A2 )
% 5.44/5.68 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % psubset_insert_iff
% 5.44/5.68 thf(fact_6279_psubset__insert__iff,axiom,
% 5.44/5.68 ! [A2: set_real,X: real,B2: set_real] :
% 5.44/5.68 ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 5.44/5.68 = ( ( ( member_real @ X @ B2 )
% 5.44/5.68 => ( ord_less_set_real @ A2 @ B2 ) )
% 5.44/5.68 & ( ~ ( member_real @ X @ B2 )
% 5.44/5.68 => ( ( ( member_real @ X @ A2 )
% 5.44/5.68 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 ) )
% 5.44/5.68 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.68 => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % psubset_insert_iff
% 5.44/5.68 thf(fact_6280_psubset__insert__iff,axiom,
% 5.44/5.68 ! [A2: set_nat,X: nat,B2: set_nat] :
% 5.44/5.68 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 5.44/5.68 = ( ( ( member_nat @ X @ B2 )
% 5.44/5.68 => ( ord_less_set_nat @ A2 @ B2 ) )
% 5.44/5.68 & ( ~ ( member_nat @ X @ B2 )
% 5.44/5.68 => ( ( ( member_nat @ X @ A2 )
% 5.44/5.68 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 5.44/5.68 & ( ~ ( member_nat @ X @ A2 )
% 5.44/5.68 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % psubset_insert_iff
% 5.44/5.68 thf(fact_6281_set__replicate__Suc,axiom,
% 5.44/5.68 ! [N2: nat,X: vEBT_VEBT] :
% 5.44/5.68 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N2 ) @ X ) )
% 5.44/5.68 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_replicate_Suc
% 5.44/5.68 thf(fact_6282_set__replicate__Suc,axiom,
% 5.44/5.68 ! [N2: nat,X: nat] :
% 5.44/5.68 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N2 ) @ X ) )
% 5.44/5.68 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_replicate_Suc
% 5.44/5.68 thf(fact_6283_set__replicate__Suc,axiom,
% 5.44/5.68 ! [N2: nat,X: int] :
% 5.44/5.68 ( ( set_int2 @ ( replicate_int @ ( suc @ N2 ) @ X ) )
% 5.44/5.68 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_replicate_Suc
% 5.44/5.68 thf(fact_6284_set__replicate__Suc,axiom,
% 5.44/5.68 ! [N2: nat,X: real] :
% 5.44/5.68 ( ( set_real2 @ ( replicate_real @ ( suc @ N2 ) @ X ) )
% 5.44/5.68 = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_replicate_Suc
% 5.44/5.68 thf(fact_6285_set__replicate__conv__if,axiom,
% 5.44/5.68 ! [N2: nat,X: vEBT_VEBT] :
% 5.44/5.68 ( ( ( N2 = zero_zero_nat )
% 5.44/5.68 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.44/5.68 = bot_bo8194388402131092736T_VEBT ) )
% 5.44/5.68 & ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.44/5.68 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_replicate_conv_if
% 5.44/5.68 thf(fact_6286_set__replicate__conv__if,axiom,
% 5.44/5.68 ! [N2: nat,X: nat] :
% 5.44/5.68 ( ( ( N2 = zero_zero_nat )
% 5.44/5.68 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 5.44/5.68 = bot_bot_set_nat ) )
% 5.44/5.68 & ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 5.44/5.68 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_replicate_conv_if
% 5.44/5.68 thf(fact_6287_set__replicate__conv__if,axiom,
% 5.44/5.68 ! [N2: nat,X: int] :
% 5.44/5.68 ( ( ( N2 = zero_zero_nat )
% 5.44/5.68 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 5.44/5.68 = bot_bot_set_int ) )
% 5.44/5.68 & ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 5.44/5.68 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_replicate_conv_if
% 5.44/5.68 thf(fact_6288_set__replicate__conv__if,axiom,
% 5.44/5.68 ! [N2: nat,X: real] :
% 5.44/5.68 ( ( ( N2 = zero_zero_nat )
% 5.44/5.68 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 5.44/5.68 = bot_bot_set_real ) )
% 5.44/5.68 & ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 5.44/5.68 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_replicate_conv_if
% 5.44/5.68 thf(fact_6289_or__not__num__neg_Oelims,axiom,
% 5.44/5.68 ! [X: num,Xa2: num,Y: num] :
% 5.44/5.68 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.44/5.68 = Y )
% 5.44/5.68 => ( ( ( X = one )
% 5.44/5.68 => ( ( Xa2 = one )
% 5.44/5.68 => ( Y != one ) ) )
% 5.44/5.68 => ( ( ( X = one )
% 5.44/5.68 => ! [M5: num] :
% 5.44/5.68 ( ( Xa2
% 5.44/5.68 = ( bit0 @ M5 ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 != ( bit1 @ M5 ) ) ) )
% 5.44/5.68 => ( ( ( X = one )
% 5.44/5.68 => ! [M5: num] :
% 5.44/5.68 ( ( Xa2
% 5.44/5.68 = ( bit1 @ M5 ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 != ( bit1 @ M5 ) ) ) )
% 5.44/5.68 => ( ( ? [N4: num] :
% 5.44/5.68 ( X
% 5.44/5.68 = ( bit0 @ N4 ) )
% 5.44/5.68 => ( ( Xa2 = one )
% 5.44/5.68 => ( Y
% 5.44/5.68 != ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ! [N4: num] :
% 5.44/5.68 ( ( X
% 5.44/5.68 = ( bit0 @ N4 ) )
% 5.44/5.68 => ! [M5: num] :
% 5.44/5.68 ( ( Xa2
% 5.44/5.68 = ( bit0 @ M5 ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) ) ) )
% 5.44/5.68 => ( ! [N4: num] :
% 5.44/5.68 ( ( X
% 5.44/5.68 = ( bit0 @ N4 ) )
% 5.44/5.68 => ! [M5: num] :
% 5.44/5.68 ( ( Xa2
% 5.44/5.68 = ( bit1 @ M5 ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 != ( bit0 @ ( bit_or_not_num_neg @ N4 @ M5 ) ) ) ) )
% 5.44/5.68 => ( ( ? [N4: num] :
% 5.44/5.68 ( X
% 5.44/5.68 = ( bit1 @ N4 ) )
% 5.44/5.68 => ( ( Xa2 = one )
% 5.44/5.68 => ( Y != one ) ) )
% 5.44/5.68 => ( ! [N4: num] :
% 5.44/5.68 ( ( X
% 5.44/5.68 = ( bit1 @ N4 ) )
% 5.44/5.68 => ! [M5: num] :
% 5.44/5.68 ( ( Xa2
% 5.44/5.68 = ( bit0 @ M5 ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) ) ) )
% 5.44/5.68 => ~ ! [N4: num] :
% 5.44/5.68 ( ( X
% 5.44/5.68 = ( bit1 @ N4 ) )
% 5.44/5.68 => ! [M5: num] :
% 5.44/5.68 ( ( Xa2
% 5.44/5.68 = ( bit1 @ M5 ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % or_not_num_neg.elims
% 5.44/5.68 thf(fact_6290_round__diff__minimal,axiom,
% 5.44/5.68 ! [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 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % round_diff_minimal
% 5.44/5.68 thf(fact_6291_and__nat__unfold,axiom,
% 5.44/5.68 ( bit_se727722235901077358nd_nat
% 5.44/5.68 = ( ^ [M6: nat,N: nat] :
% 5.44/5.68 ( if_nat
% 5.44/5.68 @ ( ( M6 = zero_zero_nat )
% 5.44/5.68 | ( N = zero_zero_nat ) )
% 5.44/5.68 @ zero_zero_nat
% 5.44/5.68 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % and_nat_unfold
% 5.44/5.68 thf(fact_6292_Suc__0__or__eq,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.68 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % Suc_0_or_eq
% 5.44/5.68 thf(fact_6293_or__Suc__0__eq,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.44/5.68 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % or_Suc_0_eq
% 5.44/5.68 thf(fact_6294_or__nat__rec,axiom,
% 5.44/5.68 ( bit_se1412395901928357646or_nat
% 5.44/5.68 = ( ^ [M6: nat,N: nat] :
% 5.44/5.68 ( plus_plus_nat
% 5.44/5.68 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.68 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.44/5.68 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.44/5.68 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % or_nat_rec
% 5.44/5.68 thf(fact_6295_and__nat__rec,axiom,
% 5.44/5.68 ( bit_se727722235901077358nd_nat
% 5.44/5.68 = ( ^ [M6: nat,N: nat] :
% 5.44/5.68 ( plus_plus_nat
% 5.44/5.68 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.68 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.44/5.68 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.44/5.68 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % and_nat_rec
% 5.44/5.68 thf(fact_6296_or__nat__unfold,axiom,
% 5.44/5.68 ( bit_se1412395901928357646or_nat
% 5.44/5.68 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % or_nat_unfold
% 5.44/5.68 thf(fact_6297_of__int__round__le,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_int_round_le
% 5.44/5.68 thf(fact_6298_of__int__round__ge,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_int_round_ge
% 5.44/5.68 thf(fact_6299_of__int__round__gt,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_int_round_gt
% 5.44/5.68 thf(fact_6300_and__int_Opelims,axiom,
% 5.44/5.68 ! [X: int,Xa2: int,Y: int] :
% 5.44/5.68 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.44/5.68 = Y )
% 5.44/5.68 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.44/5.68 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.44/5.68 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 = ( uminus_uminus_int
% 5.44/5.68 @ ( zero_n2684676970156552555ol_int
% 5.44/5.68 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.44/5.68 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.44/5.68 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.44/5.68 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 = ( plus_plus_int
% 5.44/5.68 @ ( zero_n2684676970156552555ol_int
% 5.44/5.68 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.44/5.68 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.44/5.68 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.44/5.68 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % and_int.pelims
% 5.44/5.68 thf(fact_6301_and__int_Opsimps,axiom,
% 5.44/5.68 ! [K: int,L2: int] :
% 5.44/5.68 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 5.44/5.68 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.44/5.68 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.44/5.68 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.44/5.68 = ( uminus_uminus_int
% 5.44/5.68 @ ( zero_n2684676970156552555ol_int
% 5.44/5.68 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.44/5.68 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 5.44/5.68 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.44/5.68 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.44/5.68 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.44/5.68 = ( plus_plus_int
% 5.44/5.68 @ ( zero_n2684676970156552555ol_int
% 5.44/5.68 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.44/5.68 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.44/5.68 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % and_int.psimps
% 5.44/5.68 thf(fact_6302_log__base__10__eq1,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.68 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_base_10_eq1
% 5.44/5.68 thf(fact_6303_signed__take__bit__eq__take__bit__minus,axiom,
% 5.44/5.68 ( bit_ri631733984087533419it_int
% 5.44/5.68 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % signed_take_bit_eq_take_bit_minus
% 5.44/5.68 thf(fact_6304_arctan__half,axiom,
% 5.44/5.68 ( arctan
% 5.44/5.68 = ( ^ [X2: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X2 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arctan_half
% 5.44/5.68 thf(fact_6305_log__base__10__eq2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.68 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_base_10_eq2
% 5.44/5.68 thf(fact_6306_real__sqrt__eq__iff,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ( sqrt @ X )
% 5.44/5.68 = ( sqrt @ Y ) )
% 5.44/5.68 = ( X = Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_eq_iff
% 5.44/5.68 thf(fact_6307_bit__0__eq,axiom,
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ zero_zero_int )
% 5.44/5.68 = bot_bot_nat_o ) ).
% 5.44/5.68
% 5.44/5.68 % bit_0_eq
% 5.44/5.68 thf(fact_6308_bit__0__eq,axiom,
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ zero_zero_nat )
% 5.44/5.68 = bot_bot_nat_o ) ).
% 5.44/5.68
% 5.44/5.68 % bit_0_eq
% 5.44/5.68 thf(fact_6309_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( sqrt @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( X = zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_eq_zero_cancel_iff
% 5.44/5.68 thf(fact_6310_real__sqrt__zero,axiom,
% 5.44/5.68 ( ( sqrt @ zero_zero_real )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_zero
% 5.44/5.68 thf(fact_6311_real__sqrt__less__iff,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 5.44/5.68 = ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_less_iff
% 5.44/5.68 thf(fact_6312_real__sqrt__le__iff,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 5.44/5.68 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_le_iff
% 5.44/5.68 thf(fact_6313_real__sqrt__one,axiom,
% 5.44/5.68 ( ( sqrt @ one_one_real )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_one
% 5.44/5.68 thf(fact_6314_real__sqrt__eq__1__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( sqrt @ X )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 = ( X = one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_eq_1_iff
% 5.44/5.68 thf(fact_6315_real__sqrt__gt__0__iff,axiom,
% 5.44/5.68 ! [Y: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.44/5.68 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_gt_0_iff
% 5.44/5.68 thf(fact_6316_real__sqrt__lt__0__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.44/5.68 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_lt_0_iff
% 5.44/5.68 thf(fact_6317_real__sqrt__ge__0__iff,axiom,
% 5.44/5.68 ! [Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.44/5.68 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_ge_0_iff
% 5.44/5.68 thf(fact_6318_real__sqrt__le__0__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.44/5.68 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_le_0_iff
% 5.44/5.68 thf(fact_6319_real__sqrt__lt__1__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 5.44/5.68 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_lt_1_iff
% 5.44/5.68 thf(fact_6320_real__sqrt__gt__1__iff,axiom,
% 5.44/5.68 ! [Y: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.44/5.68 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_gt_1_iff
% 5.44/5.68 thf(fact_6321_real__sqrt__ge__1__iff,axiom,
% 5.44/5.68 ! [Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.44/5.68 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_ge_1_iff
% 5.44/5.68 thf(fact_6322_real__sqrt__le__1__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 5.44/5.68 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_le_1_iff
% 5.44/5.68 thf(fact_6323_log__one,axiom,
% 5.44/5.68 ! [A: real] :
% 5.44/5.68 ( ( log @ A @ one_one_real )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % log_one
% 5.44/5.68 thf(fact_6324_real__sqrt__abs2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 5.44/5.68 = ( abs_abs_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_abs2
% 5.44/5.68 thf(fact_6325_real__sqrt__mult__self,axiom,
% 5.44/5.68 ! [A: real] :
% 5.44/5.68 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.44/5.68 = ( abs_abs_real @ A ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_mult_self
% 5.44/5.68 thf(fact_6326_bit__numeral__Bit0__Suc__iff,axiom,
% 5.44/5.68 ! [M: num,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_Bit0_Suc_iff
% 5.44/5.68 thf(fact_6327_bit__numeral__Bit0__Suc__iff,axiom,
% 5.44/5.68 ! [M: num,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_Bit0_Suc_iff
% 5.44/5.68 thf(fact_6328_bit__numeral__Bit1__Suc__iff,axiom,
% 5.44/5.68 ! [M: num,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_Bit1_Suc_iff
% 5.44/5.68 thf(fact_6329_bit__numeral__Bit1__Suc__iff,axiom,
% 5.44/5.68 ! [M: num,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_Bit1_Suc_iff
% 5.44/5.68 thf(fact_6330_real__sqrt__four,axiom,
% 5.44/5.68 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_four
% 5.44/5.68 thf(fact_6331_zero__less__log__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.44/5.68 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % zero_less_log_cancel_iff
% 5.44/5.68 thf(fact_6332_log__less__zero__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.44/5.68 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_less_zero_cancel_iff
% 5.44/5.68 thf(fact_6333_one__less__log__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 5.44/5.68 = ( ord_less_real @ A @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % one_less_log_cancel_iff
% 5.44/5.68 thf(fact_6334_log__less__one__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 5.44/5.68 = ( ord_less_real @ X @ A ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_less_one_cancel_iff
% 5.44/5.68 thf(fact_6335_log__less__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 5.44/5.68 = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_less_cancel_iff
% 5.44/5.68 thf(fact_6336_log__eq__one,axiom,
% 5.44/5.68 ! [A: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( A != one_one_real )
% 5.44/5.68 => ( ( log @ A @ A )
% 5.44/5.68 = one_one_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_eq_one
% 5.44/5.68 thf(fact_6337_signed__take__bit__nonnegative__iff,axiom,
% 5.44/5.68 ! [N2: nat,K: int] :
% 5.44/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.44/5.68 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % signed_take_bit_nonnegative_iff
% 5.44/5.68 thf(fact_6338_signed__take__bit__negative__iff,axiom,
% 5.44/5.68 ! [N2: nat,K: int] :
% 5.44/5.68 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % signed_take_bit_negative_iff
% 5.44/5.68 thf(fact_6339_zero__le__log__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.44/5.68 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % zero_le_log_cancel_iff
% 5.44/5.68 thf(fact_6340_log__le__zero__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.44/5.68 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_le_zero_cancel_iff
% 5.44/5.68 thf(fact_6341_one__le__log__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 5.44/5.68 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % one_le_log_cancel_iff
% 5.44/5.68 thf(fact_6342_log__le__one__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 5.44/5.68 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_le_one_cancel_iff
% 5.44/5.68 thf(fact_6343_log__le__cancel__iff,axiom,
% 5.44/5.68 ! [A: real,X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 5.44/5.68 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_le_cancel_iff
% 5.44/5.68 thf(fact_6344_bit__numeral__simps_I2_J,axiom,
% 5.44/5.68 ! [W: num,N2: num] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_simps(2)
% 5.44/5.68 thf(fact_6345_bit__numeral__simps_I2_J,axiom,
% 5.44/5.68 ! [W: num,N2: num] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_simps(2)
% 5.44/5.68 thf(fact_6346_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.44/5.68 ! [W: num,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N2 ) )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_minus_numeral_Bit0_Suc_iff
% 5.44/5.68 thf(fact_6347_bit__numeral__simps_I3_J,axiom,
% 5.44/5.68 ! [W: num,N2: num] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_simps(3)
% 5.44/5.68 thf(fact_6348_bit__numeral__simps_I3_J,axiom,
% 5.44/5.68 ! [W: num,N2: num] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_simps(3)
% 5.44/5.68 thf(fact_6349_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.44/5.68 ! [W: num,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N2 ) )
% 5.44/5.68 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_minus_numeral_Bit1_Suc_iff
% 5.44/5.68 thf(fact_6350_bit__0,axiom,
% 5.44/5.68 ! [A: code_integer] :
% 5.44/5.68 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.44/5.68 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_0
% 5.44/5.68 thf(fact_6351_bit__0,axiom,
% 5.44/5.68 ! [A: int] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.44/5.68 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_0
% 5.44/5.68 thf(fact_6352_bit__0,axiom,
% 5.44/5.68 ! [A: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.44/5.68 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_0
% 5.44/5.68 thf(fact_6353_real__sqrt__abs,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = ( abs_abs_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_abs
% 5.44/5.68 thf(fact_6354_bit__minus__numeral__int_I1_J,axiom,
% 5.44/5.68 ! [W: num,N2: num] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_minus_numeral_int(1)
% 5.44/5.68 thf(fact_6355_bit__minus__numeral__int_I2_J,axiom,
% 5.44/5.68 ! [W: num,N2: num] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_minus_numeral_int(2)
% 5.44/5.68 thf(fact_6356_bit__mod__2__iff,axiom,
% 5.44/5.68 ! [A: code_integer,N2: nat] :
% 5.44/5.68 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 )
% 5.44/5.68 = ( ( N2 = zero_zero_nat )
% 5.44/5.68 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_mod_2_iff
% 5.44/5.68 thf(fact_6357_bit__mod__2__iff,axiom,
% 5.44/5.68 ! [A: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 )
% 5.44/5.68 = ( ( N2 = zero_zero_nat )
% 5.44/5.68 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_mod_2_iff
% 5.44/5.68 thf(fact_6358_bit__mod__2__iff,axiom,
% 5.44/5.68 ! [A: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 5.44/5.68 = ( ( N2 = zero_zero_nat )
% 5.44/5.68 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_mod_2_iff
% 5.44/5.68 thf(fact_6359_real__sqrt__pow2__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = X )
% 5.44/5.68 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_pow2_iff
% 5.44/5.68 thf(fact_6360_real__sqrt__pow2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = X ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_pow2
% 5.44/5.68 thf(fact_6361_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.44/5.68 ! [X: real,Y: real,Xa2: real,Ya: real] :
% 5.44/5.68 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( 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 ) ) )
% 5.44/5.68 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_sum_squares_mult_squared_eq
% 5.44/5.68 thf(fact_6362_set__encode__insert,axiom,
% 5.44/5.68 ! [A2: set_nat,N2: nat] :
% 5.44/5.68 ( ( finite_finite_nat @ A2 )
% 5.44/5.68 => ( ~ ( member_nat @ N2 @ A2 )
% 5.44/5.68 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 5.44/5.68 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_encode_insert
% 5.44/5.68 thf(fact_6363_bit__disjunctive__add__iff,axiom,
% 5.44/5.68 ! [A: int,B: int,N2: nat] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( ~ ( bit_se1146084159140164899it_int @ A @ N4 )
% 5.44/5.68 | ~ ( bit_se1146084159140164899it_int @ B @ N4 ) )
% 5.44/5.68 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.44/5.68 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.44/5.68 | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_disjunctive_add_iff
% 5.44/5.68 thf(fact_6364_bit__disjunctive__add__iff,axiom,
% 5.44/5.68 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( ~ ( bit_se1148574629649215175it_nat @ A @ N4 )
% 5.44/5.68 | ~ ( bit_se1148574629649215175it_nat @ B @ N4 ) )
% 5.44/5.68 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.44/5.68 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.44/5.68 | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_disjunctive_add_iff
% 5.44/5.68 thf(fact_6365_bit__numeral__iff,axiom,
% 5.44/5.68 ! [M: num,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_iff
% 5.44/5.68 thf(fact_6366_bit__numeral__iff,axiom,
% 5.44/5.68 ! [M: num,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_iff
% 5.44/5.68 thf(fact_6367_real__sqrt__less__mono,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ X @ Y )
% 5.44/5.68 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_less_mono
% 5.44/5.68 thf(fact_6368_real__sqrt__le__mono,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.68 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_le_mono
% 5.44/5.68 thf(fact_6369_real__sqrt__divide,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( sqrt @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.68 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_divide
% 5.44/5.68 thf(fact_6370_real__sqrt__mult,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 5.44/5.68 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_mult
% 5.44/5.68 thf(fact_6371_real__sqrt__power,axiom,
% 5.44/5.68 ! [X: real,K: nat] :
% 5.44/5.68 ( ( sqrt @ ( power_power_real @ X @ K ) )
% 5.44/5.68 = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_power
% 5.44/5.68 thf(fact_6372_real__sqrt__minus,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 5.44/5.68 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_minus
% 5.44/5.68 thf(fact_6373_bit__and__iff,axiom,
% 5.44/5.68 ! [A: int,B: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N2 )
% 5.44/5.68 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.44/5.68 & ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_and_iff
% 5.44/5.68 thf(fact_6374_bit__and__iff,axiom,
% 5.44/5.68 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N2 )
% 5.44/5.68 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.44/5.68 & ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_and_iff
% 5.44/5.68 thf(fact_6375_bit__or__iff,axiom,
% 5.44/5.68 ! [A: int,B: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ N2 )
% 5.44/5.68 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.44/5.68 | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_or_iff
% 5.44/5.68 thf(fact_6376_bit__or__iff,axiom,
% 5.44/5.68 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ N2 )
% 5.44/5.68 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.44/5.68 | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_or_iff
% 5.44/5.68 thf(fact_6377_bit__and__int__iff,axiom,
% 5.44/5.68 ! [K: int,L2: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N2 )
% 5.44/5.68 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.44/5.68 & ( bit_se1146084159140164899it_int @ L2 @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_and_int_iff
% 5.44/5.68 thf(fact_6378_bit__unset__bit__iff,axiom,
% 5.44/5.68 ! [M: nat,A: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N2 )
% 5.44/5.68 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.44/5.68 & ( M != N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_unset_bit_iff
% 5.44/5.68 thf(fact_6379_bit__unset__bit__iff,axiom,
% 5.44/5.68 ! [M: nat,A: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N2 )
% 5.44/5.68 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.44/5.68 & ( M != N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_unset_bit_iff
% 5.44/5.68 thf(fact_6380_bit__or__int__iff,axiom,
% 5.44/5.68 ! [K: int,L2: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N2 )
% 5.44/5.68 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.44/5.68 | ( bit_se1146084159140164899it_int @ L2 @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_or_int_iff
% 5.44/5.68 thf(fact_6381_not__bit__1__Suc,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % not_bit_1_Suc
% 5.44/5.68 thf(fact_6382_not__bit__1__Suc,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % not_bit_1_Suc
% 5.44/5.68 thf(fact_6383_bit__numeral__simps_I1_J,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_simps(1)
% 5.44/5.68 thf(fact_6384_bit__numeral__simps_I1_J,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_numeral_simps(1)
% 5.44/5.68 thf(fact_6385_bit__1__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ one_one_int @ N2 )
% 5.44/5.68 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_1_iff
% 5.44/5.68 thf(fact_6386_bit__1__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N2 )
% 5.44/5.68 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_1_iff
% 5.44/5.68 thf(fact_6387_real__sqrt__gt__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_gt_zero
% 5.44/5.68 thf(fact_6388_real__sqrt__ge__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_ge_zero
% 5.44/5.68 thf(fact_6389_real__sqrt__eq__zero__cancel,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ( sqrt @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 => ( X = zero_zero_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_eq_zero_cancel
% 5.44/5.68 thf(fact_6390_disjunctive__add,axiom,
% 5.44/5.68 ! [A: int,B: int] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( ~ ( bit_se1146084159140164899it_int @ A @ N4 )
% 5.44/5.68 | ~ ( bit_se1146084159140164899it_int @ B @ N4 ) )
% 5.44/5.68 => ( ( plus_plus_int @ A @ B )
% 5.44/5.68 = ( bit_se1409905431419307370or_int @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % disjunctive_add
% 5.44/5.68 thf(fact_6391_disjunctive__add,axiom,
% 5.44/5.68 ! [A: nat,B: nat] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( ~ ( bit_se1148574629649215175it_nat @ A @ N4 )
% 5.44/5.68 | ~ ( bit_se1148574629649215175it_nat @ B @ N4 ) )
% 5.44/5.68 => ( ( plus_plus_nat @ A @ B )
% 5.44/5.68 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % disjunctive_add
% 5.44/5.68 thf(fact_6392_real__sqrt__ge__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.44/5.68 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_ge_one
% 5.44/5.68 thf(fact_6393_bit__take__bit__iff,axiom,
% 5.44/5.68 ! [M: nat,A: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N2 )
% 5.44/5.68 = ( ( ord_less_nat @ N2 @ M )
% 5.44/5.68 & ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_take_bit_iff
% 5.44/5.68 thf(fact_6394_bit__take__bit__iff,axiom,
% 5.44/5.68 ! [M: nat,A: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N2 )
% 5.44/5.68 = ( ( ord_less_nat @ N2 @ M )
% 5.44/5.68 & ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_take_bit_iff
% 5.44/5.68 thf(fact_6395_bit__of__bool__iff,axiom,
% 5.44/5.68 ! [B: $o,N2: nat] :
% 5.44/5.68 ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N2 )
% 5.44/5.68 = ( B
% 5.44/5.68 & ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_of_bool_iff
% 5.44/5.68 thf(fact_6396_bit__of__bool__iff,axiom,
% 5.44/5.68 ! [B: $o,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N2 )
% 5.44/5.68 = ( B
% 5.44/5.68 & ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_of_bool_iff
% 5.44/5.68 thf(fact_6397_bit__of__bool__iff,axiom,
% 5.44/5.68 ! [B: $o,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N2 )
% 5.44/5.68 = ( B
% 5.44/5.68 & ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_of_bool_iff
% 5.44/5.68 thf(fact_6398_log__def,axiom,
% 5.44/5.68 ( log
% 5.44/5.68 = ( ^ [A4: real,X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ A4 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_def
% 5.44/5.68 thf(fact_6399_signed__take__bit__eq__if__positive,axiom,
% 5.44/5.68 ! [A: int,N2: nat] :
% 5.44/5.68 ( ~ ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.44/5.68 => ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 5.44/5.68 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % signed_take_bit_eq_if_positive
% 5.44/5.68 thf(fact_6400_real__div__sqrt,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 5.44/5.68 = ( sqrt @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_div_sqrt
% 5.44/5.68 thf(fact_6401_sqrt__add__le__add__sqrt,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sqrt_add_le_add_sqrt
% 5.44/5.68 thf(fact_6402_le__real__sqrt__sumsq,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % le_real_sqrt_sumsq
% 5.44/5.68 thf(fact_6403_bit__not__int__iff_H,axiom,
% 5.44/5.68 ! [K: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N2 )
% 5.44/5.68 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_not_int_iff'
% 5.44/5.68 thf(fact_6404_log__ln,axiom,
% 5.44/5.68 ( ln_ln_real
% 5.44/5.68 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_ln
% 5.44/5.68 thf(fact_6405_atLeast0__atMost__Suc,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.44/5.68 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % atLeast0_atMost_Suc
% 5.44/5.68 thf(fact_6406_atLeastAtMost__insertL,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.68 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.44/5.68 = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % atLeastAtMost_insertL
% 5.44/5.68 thf(fact_6407_atLeastAtMostSuc__conv,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.68 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 5.44/5.68 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % atLeastAtMostSuc_conv
% 5.44/5.68 thf(fact_6408_Icc__eq__insert__lb__nat,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.68 => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 5.44/5.68 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % Icc_eq_insert_lb_nat
% 5.44/5.68 thf(fact_6409_flip__bit__eq__if,axiom,
% 5.44/5.68 ( bit_se2159334234014336723it_int
% 5.44/5.68 = ( ^ [N: nat,A4: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A4 @ N ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N @ A4 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % flip_bit_eq_if
% 5.44/5.68 thf(fact_6410_flip__bit__eq__if,axiom,
% 5.44/5.68 ( bit_se2161824704523386999it_nat
% 5.44/5.68 = ( ^ [N: nat,A4: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A4 @ N ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N @ A4 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % flip_bit_eq_if
% 5.44/5.68 thf(fact_6411_sqrt2__less__2,axiom,
% 5.44/5.68 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.44/5.68
% 5.44/5.68 % sqrt2_less_2
% 5.44/5.68 thf(fact_6412_log__base__change,axiom,
% 5.44/5.68 ! [A: real,B: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( A != one_one_real )
% 5.44/5.68 => ( ( log @ B @ X )
% 5.44/5.68 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_base_change
% 5.44/5.68 thf(fact_6413_bit__imp__take__bit__positive,axiom,
% 5.44/5.68 ! [N2: nat,M: nat,K: int] :
% 5.44/5.68 ( ( ord_less_nat @ N2 @ M )
% 5.44/5.68 => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.44/5.68 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_imp_take_bit_positive
% 5.44/5.68 thf(fact_6414_bit__concat__bit__iff,axiom,
% 5.44/5.68 ! [M: nat,K: int,L2: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N2 )
% 5.44/5.68 = ( ( ( ord_less_nat @ N2 @ M )
% 5.44/5.68 & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 5.44/5.68 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.68 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_concat_bit_iff
% 5.44/5.68 thf(fact_6415_signed__take__bit__eq__concat__bit,axiom,
% 5.44/5.68 ( bit_ri631733984087533419it_int
% 5.44/5.68 = ( ^ [N: nat,K3: int] : ( bit_concat_bit @ N @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % signed_take_bit_eq_concat_bit
% 5.44/5.68 thf(fact_6416_exp__eq__0__imp__not__bit,axiom,
% 5.44/5.68 ! [N2: nat,A: int] :
% 5.44/5.68 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 = zero_zero_int )
% 5.44/5.68 => ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_eq_0_imp_not_bit
% 5.44/5.68 thf(fact_6417_exp__eq__0__imp__not__bit,axiom,
% 5.44/5.68 ! [N2: nat,A: nat] :
% 5.44/5.68 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 = zero_zero_nat )
% 5.44/5.68 => ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_eq_0_imp_not_bit
% 5.44/5.68 thf(fact_6418_bit__Suc,axiom,
% 5.44/5.68 ! [A: code_integer,N2: nat] :
% 5.44/5.68 ( ( bit_se9216721137139052372nteger @ A @ ( suc @ N2 ) )
% 5.44/5.68 = ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_Suc
% 5.44/5.68 thf(fact_6419_bit__Suc,axiom,
% 5.44/5.68 ! [A: int,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N2 ) )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_Suc
% 5.44/5.68 thf(fact_6420_bit__Suc,axiom,
% 5.44/5.68 ! [A: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N2 ) )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_Suc
% 5.44/5.68 thf(fact_6421_stable__imp__bit__iff__odd,axiom,
% 5.44/5.68 ! [A: code_integer,N2: nat] :
% 5.44/5.68 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.68 = A )
% 5.44/5.68 => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.44/5.68 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % stable_imp_bit_iff_odd
% 5.44/5.68 thf(fact_6422_stable__imp__bit__iff__odd,axiom,
% 5.44/5.68 ! [A: int,N2: nat] :
% 5.44/5.68 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.68 = A )
% 5.44/5.68 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.44/5.68 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % stable_imp_bit_iff_odd
% 5.44/5.68 thf(fact_6423_stable__imp__bit__iff__odd,axiom,
% 5.44/5.68 ! [A: nat,N2: nat] :
% 5.44/5.68 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = A )
% 5.44/5.68 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.44/5.68 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % stable_imp_bit_iff_odd
% 5.44/5.68 thf(fact_6424_bit__iff__idd__imp__stable,axiom,
% 5.44/5.68 ! [A: code_integer] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( ( bit_se9216721137139052372nteger @ A @ N4 )
% 5.44/5.68 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.44/5.68 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.68 = A ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_iff_idd_imp_stable
% 5.44/5.68 thf(fact_6425_bit__iff__idd__imp__stable,axiom,
% 5.44/5.68 ! [A: int] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ A @ N4 )
% 5.44/5.68 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.44/5.68 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.68 = A ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_iff_idd_imp_stable
% 5.44/5.68 thf(fact_6426_bit__iff__idd__imp__stable,axiom,
% 5.44/5.68 ! [A: nat] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ A @ N4 )
% 5.44/5.68 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.44/5.68 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = A ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_iff_idd_imp_stable
% 5.44/5.68 thf(fact_6427_real__less__rsqrt,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.44/5.68 => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_less_rsqrt
% 5.44/5.68 thf(fact_6428_real__le__rsqrt,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.44/5.68 => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_le_rsqrt
% 5.44/5.68 thf(fact_6429_sqrt__le__D,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 5.44/5.68 => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sqrt_le_D
% 5.44/5.68 thf(fact_6430_log__mult,axiom,
% 5.44/5.68 ! [A: real,X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( A != one_one_real )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 5.44/5.68 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_mult
% 5.44/5.68 thf(fact_6431_int__bit__bound,axiom,
% 5.44/5.68 ! [K: int] :
% 5.44/5.68 ~ ! [N4: nat] :
% 5.44/5.68 ( ! [M2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N4 @ M2 )
% 5.44/5.68 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.44/5.68 = ( bit_se1146084159140164899it_int @ K @ N4 ) ) )
% 5.44/5.68 => ~ ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.44/5.68 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N4 @ one_one_nat ) )
% 5.44/5.68 = ( ~ ( bit_se1146084159140164899it_int @ K @ N4 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_bit_bound
% 5.44/5.68 thf(fact_6432_log__divide,axiom,
% 5.44/5.68 ! [A: real,X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( A != one_one_real )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.68 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_divide
% 5.44/5.68 thf(fact_6433_bit__iff__odd,axiom,
% 5.44/5.68 ( bit_se9216721137139052372nteger
% 5.44/5.68 = ( ^ [A4: code_integer,N: nat] :
% 5.44/5.68 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A4 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_iff_odd
% 5.44/5.68 thf(fact_6434_bit__iff__odd,axiom,
% 5.44/5.68 ( bit_se1146084159140164899it_int
% 5.44/5.68 = ( ^ [A4: int,N: nat] :
% 5.44/5.68 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_iff_odd
% 5.44/5.68 thf(fact_6435_bit__iff__odd,axiom,
% 5.44/5.68 ( bit_se1148574629649215175it_nat
% 5.44/5.68 = ( ^ [A4: nat,N: nat] :
% 5.44/5.68 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_iff_odd
% 5.44/5.68 thf(fact_6436_and__exp__eq__0__iff__not__bit,axiom,
% 5.44/5.68 ! [A: int,N2: nat] :
% 5.44/5.68 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.68 = zero_zero_int )
% 5.44/5.68 = ( ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % and_exp_eq_0_iff_not_bit
% 5.44/5.68 thf(fact_6437_and__exp__eq__0__iff__not__bit,axiom,
% 5.44/5.68 ! [A: nat,N2: nat] :
% 5.44/5.68 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.68 = zero_zero_nat )
% 5.44/5.68 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % and_exp_eq_0_iff_not_bit
% 5.44/5.68 thf(fact_6438_real__sqrt__unique,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( sqrt @ X )
% 5.44/5.68 = Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_unique
% 5.44/5.68 thf(fact_6439_real__le__lsqrt,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_le_lsqrt
% 5.44/5.68 thf(fact_6440_lemma__real__divide__sqrt__less,axiom,
% 5.44/5.68 ! [U: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ U )
% 5.44/5.68 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.44/5.68
% 5.44/5.68 % lemma_real_divide_sqrt_less
% 5.44/5.68 thf(fact_6441_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 = Y )
% 5.44/5.68 => ( X = zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_sum_squares_eq_cancel2
% 5.44/5.68 thf(fact_6442_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 = X )
% 5.44/5.68 => ( Y = zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_sum_squares_eq_cancel
% 5.44/5.68 thf(fact_6443_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.44/5.68 ! [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 ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_sum_squares_triangle_ineq
% 5.44/5.68 thf(fact_6444_real__sqrt__sum__squares__ge2,axiom,
% 5.44/5.68 ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_sum_squares_ge2
% 5.44/5.68 thf(fact_6445_real__sqrt__sum__squares__ge1,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_sum_squares_ge1
% 5.44/5.68 thf(fact_6446_sqrt__ge__absD,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % sqrt_ge_absD
% 5.44/5.68 thf(fact_6447_log__eq__div__ln__mult__log,axiom,
% 5.44/5.68 ! [A: real,B: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( A != one_one_real )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.68 => ( ( B != one_one_real )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( log @ A @ X )
% 5.44/5.68 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_eq_div_ln_mult_log
% 5.44/5.68 thf(fact_6448_bit__int__def,axiom,
% 5.44/5.68 ( bit_se1146084159140164899it_int
% 5.44/5.68 = ( ^ [K3: int,N: nat] :
% 5.44/5.68 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_int_def
% 5.44/5.68 thf(fact_6449_even__bit__succ__iff,axiom,
% 5.44/5.68 ! [A: code_integer,N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.68 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N2 )
% 5.44/5.68 = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % even_bit_succ_iff
% 5.44/5.68 thf(fact_6450_even__bit__succ__iff,axiom,
% 5.44/5.68 ! [A: int,N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.68 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 5.44/5.68 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % even_bit_succ_iff
% 5.44/5.68 thf(fact_6451_even__bit__succ__iff,axiom,
% 5.44/5.68 ! [A: nat,N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.68 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 5.44/5.68 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % even_bit_succ_iff
% 5.44/5.68 thf(fact_6452_odd__bit__iff__bit__pred,axiom,
% 5.44/5.68 ! [A: code_integer,N2: nat] :
% 5.44/5.68 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.44/5.68 => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.44/5.68 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N2 )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % odd_bit_iff_bit_pred
% 5.44/5.68 thf(fact_6453_odd__bit__iff__bit__pred,axiom,
% 5.44/5.68 ! [A: int,N2: nat] :
% 5.44/5.68 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.44/5.68 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.44/5.68 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N2 )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % odd_bit_iff_bit_pred
% 5.44/5.68 thf(fact_6454_odd__bit__iff__bit__pred,axiom,
% 5.44/5.68 ! [A: nat,N2: nat] :
% 5.44/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.44/5.68 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.44/5.68 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N2 )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % odd_bit_iff_bit_pred
% 5.44/5.68 thf(fact_6455_set__decode__plus__power__2,axiom,
% 5.44/5.68 ! [N2: nat,Z: nat] :
% 5.44/5.68 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 5.44/5.68 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 5.44/5.68 = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_decode_plus_power_2
% 5.44/5.68 thf(fact_6456_real__less__lsqrt,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_less_lsqrt
% 5.44/5.68 thf(fact_6457_sqrt__sum__squares__le__sum,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sqrt_sum_squares_le_sum
% 5.44/5.68 thf(fact_6458_sqrt__even__pow2,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.68 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sqrt_even_pow2
% 5.44/5.68 thf(fact_6459_sqrt__sum__squares__le__sum__abs,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sqrt_sum_squares_le_sum_abs
% 5.44/5.68 thf(fact_6460_real__sqrt__ge__abs2,axiom,
% 5.44/5.68 ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_ge_abs2
% 5.44/5.68 thf(fact_6461_real__sqrt__ge__abs1,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_ge_abs1
% 5.44/5.68 thf(fact_6462_ln__sqrt,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 5.44/5.68 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ln_sqrt
% 5.44/5.68 thf(fact_6463_bit__sum__mult__2__cases,axiom,
% 5.44/5.68 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.44/5.68 ( ! [J2: nat] :
% 5.44/5.68 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 5.44/5.68 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.44/5.68 = ( ( ( N2 = zero_zero_nat )
% 5.44/5.68 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.68 & ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_sum_mult_2_cases
% 5.44/5.68 thf(fact_6464_bit__sum__mult__2__cases,axiom,
% 5.44/5.68 ! [A: int,B: int,N2: nat] :
% 5.44/5.68 ( ! [J2: nat] :
% 5.44/5.68 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 5.44/5.68 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.44/5.68 = ( ( ( N2 = zero_zero_nat )
% 5.44/5.68 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.68 & ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_sum_mult_2_cases
% 5.44/5.68 thf(fact_6465_bit__sum__mult__2__cases,axiom,
% 5.44/5.68 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.68 ( ! [J2: nat] :
% 5.44/5.68 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 5.44/5.68 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.44/5.68 = ( ( ( N2 = zero_zero_nat )
% 5.44/5.68 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.44/5.68 & ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_sum_mult_2_cases
% 5.44/5.68 thf(fact_6466_bit__rec,axiom,
% 5.44/5.68 ( bit_se9216721137139052372nteger
% 5.44/5.68 = ( ^ [A4: code_integer,N: nat] :
% 5.44/5.68 ( ( ( N = zero_zero_nat )
% 5.44/5.68 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) )
% 5.44/5.68 & ( ( N != zero_zero_nat )
% 5.44/5.68 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_rec
% 5.44/5.68 thf(fact_6467_bit__rec,axiom,
% 5.44/5.68 ( bit_se1146084159140164899it_int
% 5.44/5.68 = ( ^ [A4: int,N: nat] :
% 5.44/5.68 ( ( ( N = zero_zero_nat )
% 5.44/5.68 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) )
% 5.44/5.68 & ( ( N != zero_zero_nat )
% 5.44/5.68 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_rec
% 5.44/5.68 thf(fact_6468_bit__rec,axiom,
% 5.44/5.68 ( bit_se1148574629649215175it_nat
% 5.44/5.68 = ( ^ [A4: nat,N: nat] :
% 5.44/5.68 ( ( ( N = zero_zero_nat )
% 5.44/5.68 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) )
% 5.44/5.68 & ( ( N != zero_zero_nat )
% 5.44/5.68 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_rec
% 5.44/5.68 thf(fact_6469_arsinh__real__aux,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arsinh_real_aux
% 5.44/5.68 thf(fact_6470_real__sqrt__power__even,axiom,
% 5.44/5.68 ! [N2: nat,X: real] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( power_power_real @ ( sqrt @ X ) @ N2 )
% 5.44/5.68 = ( power_power_real @ X @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_power_even
% 5.44/5.68 thf(fact_6471_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.44/5.68 ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( 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 ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_sum_squares_mult_ge_zero
% 5.44/5.68 thf(fact_6472_arith__geo__mean__sqrt,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arith_geo_mean_sqrt
% 5.44/5.68 thf(fact_6473_and__int_Opinduct,axiom,
% 5.44/5.68 ! [A0: int,A12: int,P: int > int > $o] :
% 5.44/5.68 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.44/5.68 => ( ! [K2: int,L4: int] :
% 5.44/5.68 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.44/5.68 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.44/5.68 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.44/5.68 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 => ( P @ K2 @ L4 ) ) )
% 5.44/5.68 => ( P @ A0 @ A12 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % and_int.pinduct
% 5.44/5.68 thf(fact_6474_set__bit__eq,axiom,
% 5.44/5.68 ( bit_se7879613467334960850it_int
% 5.44/5.68 = ( ^ [N: nat,K3: int] :
% 5.44/5.68 ( plus_plus_int @ K3
% 5.44/5.68 @ ( times_times_int
% 5.44/5.68 @ ( zero_n2684676970156552555ol_int
% 5.44/5.68 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N ) )
% 5.44/5.68 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % set_bit_eq
% 5.44/5.68 thf(fact_6475_unset__bit__eq,axiom,
% 5.44/5.68 ( bit_se4203085406695923979it_int
% 5.44/5.68 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % unset_bit_eq
% 5.44/5.68 thf(fact_6476_cos__x__y__le__one,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_x_y_le_one
% 5.44/5.68 thf(fact_6477_real__sqrt__sum__squares__less,axiom,
% 5.44/5.68 ! [X: real,U: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_sqrt_sum_squares_less
% 5.44/5.68 thf(fact_6478_arcosh__real__def,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.44/5.68 => ( ( arcosh_real @ X )
% 5.44/5.68 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arcosh_real_def
% 5.44/5.68 thf(fact_6479_take__bit__Suc__from__most,axiom,
% 5.44/5.68 ! [N2: nat,K: int] :
% 5.44/5.68 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 5.44/5.68 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % take_bit_Suc_from_most
% 5.44/5.68 thf(fact_6480_sqrt__sum__squares__half__less,axiom,
% 5.44/5.68 ! [X: real,U: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sqrt_sum_squares_half_less
% 5.44/5.68 thf(fact_6481_upto_Opinduct,axiom,
% 5.44/5.68 ! [A0: int,A12: int,P: int > int > $o] :
% 5.44/5.68 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.44/5.68 => ( ! [I4: int,J2: int] :
% 5.44/5.68 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J2 ) )
% 5.44/5.68 => ( ( ( ord_less_eq_int @ I4 @ J2 )
% 5.44/5.68 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) )
% 5.44/5.68 => ( P @ I4 @ J2 ) ) )
% 5.44/5.68 => ( P @ A0 @ A12 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % upto.pinduct
% 5.44/5.68 thf(fact_6482_arsinh__real__def,axiom,
% 5.44/5.68 ( arsinh_real
% 5.44/5.68 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arsinh_real_def
% 5.44/5.68 thf(fact_6483_log2__of__power__le,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.68 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log2_of_power_le
% 5.44/5.68 thf(fact_6484_machin,axiom,
% 5.44/5.68 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % machin
% 5.44/5.68 thf(fact_6485_machin__Euler,axiom,
% 5.44/5.68 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.44/5.68 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % machin_Euler
% 5.44/5.68 thf(fact_6486_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.44/5.68 ! [X: real,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.68 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_ge_one_minus_x_over_n_power_n
% 5.44/5.68 thf(fact_6487_of__nat__eq__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ( semiri5074537144036343181t_real @ M )
% 5.44/5.68 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 = ( M = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_iff
% 5.44/5.68 thf(fact_6488_of__nat__eq__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ( semiri1314217659103216013at_int @ M )
% 5.44/5.68 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( M = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_iff
% 5.44/5.68 thf(fact_6489_of__nat__eq__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.44/5.68 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 = ( M = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_iff
% 5.44/5.68 thf(fact_6490_of__nat__eq__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ( semiri8010041392384452111omplex @ M )
% 5.44/5.68 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.44/5.68 = ( M = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_iff
% 5.44/5.68 thf(fact_6491_of__nat__eq__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ( semiri4939895301339042750nteger @ M )
% 5.44/5.68 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( M = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_iff
% 5.44/5.68 thf(fact_6492_abs__of__nat,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % abs_of_nat
% 5.44/5.68 thf(fact_6493_abs__of__nat,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % abs_of_nat
% 5.44/5.68 thf(fact_6494_abs__of__nat,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % abs_of_nat
% 5.44/5.68 thf(fact_6495_of__nat__0,axiom,
% 5.44/5.68 ( ( semiri4216267220026989637d_enat @ zero_zero_nat )
% 5.44/5.68 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0
% 5.44/5.68 thf(fact_6496_of__nat__0,axiom,
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0
% 5.44/5.68 thf(fact_6497_of__nat__0,axiom,
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.44/5.68 = zero_zero_int ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0
% 5.44/5.68 thf(fact_6498_of__nat__0,axiom,
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.44/5.68 = zero_zero_nat ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0
% 5.44/5.68 thf(fact_6499_of__nat__0,axiom,
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.44/5.68 = zero_zero_complex ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0
% 5.44/5.68 thf(fact_6500_of__nat__0,axiom,
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 5.44/5.68 = zero_z3403309356797280102nteger ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0
% 5.44/5.68 thf(fact_6501_of__nat__0__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( zero_z5237406670263579293d_enat
% 5.44/5.68 = ( semiri4216267220026989637d_enat @ N2 ) )
% 5.44/5.68 = ( zero_zero_nat = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_eq_iff
% 5.44/5.68 thf(fact_6502_of__nat__0__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( zero_zero_real
% 5.44/5.68 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 = ( zero_zero_nat = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_eq_iff
% 5.44/5.68 thf(fact_6503_of__nat__0__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( zero_zero_int
% 5.44/5.68 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( zero_zero_nat = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_eq_iff
% 5.44/5.68 thf(fact_6504_of__nat__0__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( zero_zero_nat
% 5.44/5.68 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 = ( zero_zero_nat = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_eq_iff
% 5.44/5.68 thf(fact_6505_of__nat__0__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( zero_zero_complex
% 5.44/5.68 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.44/5.68 = ( zero_zero_nat = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_eq_iff
% 5.44/5.68 thf(fact_6506_of__nat__0__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( zero_z3403309356797280102nteger
% 5.44/5.68 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( zero_zero_nat = N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_eq_iff
% 5.44/5.68 thf(fact_6507_of__nat__eq__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ( semiri4216267220026989637d_enat @ M )
% 5.44/5.68 = zero_z5237406670263579293d_enat )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_0_iff
% 5.44/5.68 thf(fact_6508_of__nat__eq__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ( semiri5074537144036343181t_real @ M )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_0_iff
% 5.44/5.68 thf(fact_6509_of__nat__eq__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ( semiri1314217659103216013at_int @ M )
% 5.44/5.68 = zero_zero_int )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_0_iff
% 5.44/5.68 thf(fact_6510_of__nat__eq__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.44/5.68 = zero_zero_nat )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_0_iff
% 5.44/5.68 thf(fact_6511_of__nat__eq__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ( semiri8010041392384452111omplex @ M )
% 5.44/5.68 = zero_zero_complex )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_0_iff
% 5.44/5.68 thf(fact_6512_of__nat__eq__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ( semiri4939895301339042750nteger @ M )
% 5.44/5.68 = zero_z3403309356797280102nteger )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_0_iff
% 5.44/5.68 thf(fact_6513_of__nat__numeral,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_numeral
% 5.44/5.68 thf(fact_6514_of__nat__numeral,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( numeral_numeral_real @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_numeral
% 5.44/5.68 thf(fact_6515_of__nat__numeral,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_numeral
% 5.44/5.68 thf(fact_6516_of__nat__numeral,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_numeral
% 5.44/5.68 thf(fact_6517_of__nat__numeral,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_numeral
% 5.44/5.68 thf(fact_6518_of__nat__numeral,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_numeral
% 5.44/5.68 thf(fact_6519_of__nat__less__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_iff
% 5.44/5.68 thf(fact_6520_of__nat__less__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_iff
% 5.44/5.68 thf(fact_6521_of__nat__less__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_iff
% 5.44/5.68 thf(fact_6522_of__nat__less__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_iff
% 5.44/5.68 thf(fact_6523_of__nat__less__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_iff
% 5.44/5.68 thf(fact_6524_of__nat__le__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_iff
% 5.44/5.68 thf(fact_6525_of__nat__le__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_iff
% 5.44/5.68 thf(fact_6526_of__nat__le__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_iff
% 5.44/5.68 thf(fact_6527_of__nat__le__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_iff
% 5.44/5.68 thf(fact_6528_of__nat__add,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.68 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_add
% 5.44/5.68 thf(fact_6529_of__nat__add,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_add
% 5.44/5.68 thf(fact_6530_of__nat__add,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.68 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_add
% 5.44/5.68 thf(fact_6531_of__nat__add,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.68 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_add
% 5.44/5.68 thf(fact_6532_of__nat__add,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.68 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_add
% 5.44/5.68 thf(fact_6533_of__nat__mult,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.68 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mult
% 5.44/5.68 thf(fact_6534_of__nat__mult,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.68 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mult
% 5.44/5.68 thf(fact_6535_of__nat__mult,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.68 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mult
% 5.44/5.68 thf(fact_6536_of__nat__mult,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.68 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mult
% 5.44/5.68 thf(fact_6537_of__nat__mult,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N2 ) )
% 5.44/5.68 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mult
% 5.44/5.68 thf(fact_6538_of__nat__eq__1__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ( semiri4216267220026989637d_enat @ N2 )
% 5.44/5.68 = one_on7984719198319812577d_enat )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_1_iff
% 5.44/5.68 thf(fact_6539_of__nat__eq__1__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ( semiri5074537144036343181t_real @ N2 )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_1_iff
% 5.44/5.68 thf(fact_6540_of__nat__eq__1__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ( semiri1314217659103216013at_int @ N2 )
% 5.44/5.68 = one_one_int )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_1_iff
% 5.44/5.68 thf(fact_6541_of__nat__eq__1__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 5.44/5.68 = one_one_nat )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_1_iff
% 5.44/5.68 thf(fact_6542_of__nat__eq__1__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ( semiri8010041392384452111omplex @ N2 )
% 5.44/5.68 = one_one_complex )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_1_iff
% 5.44/5.68 thf(fact_6543_of__nat__eq__1__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ( semiri4939895301339042750nteger @ N2 )
% 5.44/5.68 = one_one_Code_integer )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_1_iff
% 5.44/5.68 thf(fact_6544_of__nat__1__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( one_on7984719198319812577d_enat
% 5.44/5.68 = ( semiri4216267220026989637d_enat @ N2 ) )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1_eq_iff
% 5.44/5.68 thf(fact_6545_of__nat__1__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( one_one_real
% 5.44/5.68 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1_eq_iff
% 5.44/5.68 thf(fact_6546_of__nat__1__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( one_one_int
% 5.44/5.68 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1_eq_iff
% 5.44/5.68 thf(fact_6547_of__nat__1__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( one_one_nat
% 5.44/5.68 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1_eq_iff
% 5.44/5.68 thf(fact_6548_of__nat__1__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( one_one_complex
% 5.44/5.68 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1_eq_iff
% 5.44/5.68 thf(fact_6549_of__nat__1__eq__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( one_one_Code_integer
% 5.44/5.68 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( N2 = one_one_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1_eq_iff
% 5.44/5.68 thf(fact_6550_of__nat__1,axiom,
% 5.44/5.68 ( ( semiri4216267220026989637d_enat @ one_one_nat )
% 5.44/5.68 = one_on7984719198319812577d_enat ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1
% 5.44/5.68 thf(fact_6551_of__nat__1,axiom,
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1
% 5.44/5.68 thf(fact_6552_of__nat__1,axiom,
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.44/5.68 = one_one_int ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1
% 5.44/5.68 thf(fact_6553_of__nat__1,axiom,
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.44/5.68 = one_one_nat ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1
% 5.44/5.68 thf(fact_6554_of__nat__1,axiom,
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.44/5.68 = one_one_complex ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1
% 5.44/5.68 thf(fact_6555_of__nat__1,axiom,
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 5.44/5.68 = one_one_Code_integer ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_1
% 5.44/5.68 thf(fact_6556_of__nat__power,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N2 ) )
% 5.44/5.68 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power
% 5.44/5.68 thf(fact_6557_of__nat__power,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N2 ) )
% 5.44/5.68 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power
% 5.44/5.68 thf(fact_6558_of__nat__power,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
% 5.44/5.68 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power
% 5.44/5.68 thf(fact_6559_of__nat__power,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N2 ) )
% 5.44/5.68 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power
% 5.44/5.68 thf(fact_6560_of__nat__power,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( power_power_nat @ M @ N2 ) )
% 5.44/5.68 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ M ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power
% 5.44/5.68 thf(fact_6561_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.44/5.68 = ( semiri5074537144036343181t_real @ X ) )
% 5.44/5.68 = ( ( power_power_nat @ B @ W )
% 5.44/5.68 = X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6562_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.44/5.68 = ( semiri1314217659103216013at_int @ X ) )
% 5.44/5.68 = ( ( power_power_nat @ B @ W )
% 5.44/5.68 = X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6563_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.44/5.68 = ( semiri1316708129612266289at_nat @ X ) )
% 5.44/5.68 = ( ( power_power_nat @ B @ W )
% 5.44/5.68 = X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6564_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.44/5.68 = ( semiri8010041392384452111omplex @ X ) )
% 5.44/5.68 = ( ( power_power_nat @ B @ W )
% 5.44/5.68 = X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6565_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W )
% 5.44/5.68 = ( semiri4939895301339042750nteger @ X ) )
% 5.44/5.68 = ( ( power_power_nat @ B @ W )
% 5.44/5.68 = X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_eq_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6566_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ( semiri5074537144036343181t_real @ X )
% 5.44/5.68 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.44/5.68 = ( X
% 5.44/5.68 = ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6567_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ( semiri1314217659103216013at_int @ X )
% 5.44/5.68 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.44/5.68 = ( X
% 5.44/5.68 = ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6568_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ( semiri1316708129612266289at_nat @ X )
% 5.44/5.68 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.44/5.68 = ( X
% 5.44/5.68 = ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6569_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ( semiri8010041392384452111omplex @ X )
% 5.44/5.68 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.44/5.68 = ( X
% 5.44/5.68 = ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6570_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ( semiri4939895301339042750nteger @ X )
% 5.44/5.68 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 5.44/5.68 = ( X
% 5.44/5.68 = ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6571_of__nat__of__bool,axiom,
% 5.44/5.68 ! [P: $o] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.44/5.68 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_of_bool
% 5.44/5.68 thf(fact_6572_of__nat__of__bool,axiom,
% 5.44/5.68 ! [P: $o] :
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.44/5.68 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_of_bool
% 5.44/5.68 thf(fact_6573_of__nat__of__bool,axiom,
% 5.44/5.68 ! [P: $o] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.44/5.68 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_of_bool
% 5.44/5.68 thf(fact_6574_of__nat__of__bool,axiom,
% 5.44/5.68 ! [P: $o] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.44/5.68 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_of_bool
% 5.44/5.68 thf(fact_6575_of__nat__of__bool,axiom,
% 5.44/5.68 ! [P: $o] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.44/5.68 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_of_bool
% 5.44/5.68 thf(fact_6576_of__nat__le__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ord_le2932123472753598470d_enat @ ( semiri4216267220026989637d_enat @ M ) @ zero_z5237406670263579293d_enat )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_0_iff
% 5.44/5.68 thf(fact_6577_of__nat__le__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_0_iff
% 5.44/5.68 thf(fact_6578_of__nat__le__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_0_iff
% 5.44/5.68 thf(fact_6579_of__nat__le__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_0_iff
% 5.44/5.68 thf(fact_6580_of__nat__le__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.44/5.68 = ( M = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_0_iff
% 5.44/5.68 thf(fact_6581_of__nat__Suc,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( semiri4216267220026989637d_enat @ ( suc @ M ) )
% 5.44/5.68 = ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( semiri4216267220026989637d_enat @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_Suc
% 5.44/5.68 thf(fact_6582_of__nat__Suc,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.44/5.68 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_Suc
% 5.44/5.68 thf(fact_6583_of__nat__Suc,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.44/5.68 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_Suc
% 5.44/5.68 thf(fact_6584_of__nat__Suc,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.44/5.68 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_Suc
% 5.44/5.68 thf(fact_6585_of__nat__Suc,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.44/5.68 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_Suc
% 5.44/5.68 thf(fact_6586_of__nat__Suc,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 5.44/5.68 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_Suc
% 5.44/5.68 thf(fact_6587_of__nat__0__less__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( semiri4216267220026989637d_enat @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_less_iff
% 5.44/5.68 thf(fact_6588_of__nat__0__less__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_less_iff
% 5.44/5.68 thf(fact_6589_of__nat__0__less__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_less_iff
% 5.44/5.68 thf(fact_6590_of__nat__0__less__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_less_iff
% 5.44/5.68 thf(fact_6591_of__nat__0__less__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_less_iff
% 5.44/5.68 thf(fact_6592_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: num,N2: nat,Y: nat] :
% 5.44/5.68 ( ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X ) @ N2 )
% 5.44/5.68 = ( semiri4216267220026989637d_enat @ Y ) )
% 5.44/5.68 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.44/5.68 = Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6593_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: num,N2: nat,Y: nat] :
% 5.44/5.68 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 )
% 5.44/5.68 = ( semiri5074537144036343181t_real @ Y ) )
% 5.44/5.68 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.44/5.68 = Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6594_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: num,N2: nat,Y: nat] :
% 5.44/5.68 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.44/5.68 = ( semiri1314217659103216013at_int @ Y ) )
% 5.44/5.68 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.44/5.68 = Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6595_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: num,N2: nat,Y: nat] :
% 5.44/5.68 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.44/5.68 = ( semiri1316708129612266289at_nat @ Y ) )
% 5.44/5.68 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.44/5.68 = Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6596_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: num,N2: nat,Y: nat] :
% 5.44/5.68 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 )
% 5.44/5.68 = ( semiri8010041392384452111omplex @ Y ) )
% 5.44/5.68 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.44/5.68 = Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6597_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: num,N2: nat,Y: nat] :
% 5.44/5.68 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 )
% 5.44/5.68 = ( semiri4939895301339042750nteger @ Y ) )
% 5.44/5.68 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.44/5.68 = Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_eq_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6598_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [Y: nat,X: num,N2: nat] :
% 5.44/5.68 ( ( ( semiri4216267220026989637d_enat @ Y )
% 5.44/5.68 = ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X ) @ N2 ) )
% 5.44/5.68 = ( Y
% 5.44/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_eq_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6599_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [Y: nat,X: num,N2: nat] :
% 5.44/5.68 ( ( ( semiri5074537144036343181t_real @ Y )
% 5.44/5.68 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.44/5.68 = ( Y
% 5.44/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_eq_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6600_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [Y: nat,X: num,N2: nat] :
% 5.44/5.68 ( ( ( semiri1314217659103216013at_int @ Y )
% 5.44/5.68 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.44/5.68 = ( Y
% 5.44/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_eq_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6601_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [Y: nat,X: num,N2: nat] :
% 5.44/5.68 ( ( ( semiri1316708129612266289at_nat @ Y )
% 5.44/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.44/5.68 = ( Y
% 5.44/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_eq_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6602_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [Y: nat,X: num,N2: nat] :
% 5.44/5.68 ( ( ( semiri8010041392384452111omplex @ Y )
% 5.44/5.68 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 ) )
% 5.44/5.68 = ( Y
% 5.44/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_eq_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6603_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [Y: nat,X: num,N2: nat] :
% 5.44/5.68 ( ( ( semiri4939895301339042750nteger @ Y )
% 5.44/5.68 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) )
% 5.44/5.68 = ( Y
% 5.44/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_eq_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6604_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.44/5.68 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6605_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.44/5.68 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6606_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.44/5.68 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6607_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.44/5.68 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6608_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.44/5.68 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_less_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6609_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.44/5.68 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_less_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6610_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.44/5.68 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_less_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6611_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 5.44/5.68 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_less_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6612_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6613_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6614_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6615_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.44/5.68 ! [B: nat,W: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_of_nat_power_cancel_iff
% 5.44/5.68 thf(fact_6616_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.44/5.68 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_le_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6617_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 5.44/5.68 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_le_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6618_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.44/5.68 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_le_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6619_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,B: nat,W: nat] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.44/5.68 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_power_le_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6620_numeral__less__real__of__nat__iff,axiom,
% 5.44/5.68 ! [W: num,N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_less_real_of_nat_iff
% 5.44/5.68 thf(fact_6621_real__of__nat__less__numeral__iff,axiom,
% 5.44/5.68 ! [N2: nat,W: num] :
% 5.44/5.68 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W ) )
% 5.44/5.68 = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_less_numeral_iff
% 5.44/5.68 thf(fact_6622_numeral__le__real__of__nat__iff,axiom,
% 5.44/5.68 ! [N2: num,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_le_real_of_nat_iff
% 5.44/5.68 thf(fact_6623_of__nat__zero__less__power__iff,axiom,
% 5.44/5.68 ! [X: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N2 ) )
% 5.44/5.68 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_zero_less_power_iff
% 5.44/5.68 thf(fact_6624_of__nat__zero__less__power__iff,axiom,
% 5.44/5.68 ! [X: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N2 ) )
% 5.44/5.68 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_zero_less_power_iff
% 5.44/5.68 thf(fact_6625_of__nat__zero__less__power__iff,axiom,
% 5.44/5.68 ! [X: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N2 ) )
% 5.44/5.68 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_zero_less_power_iff
% 5.44/5.68 thf(fact_6626_of__nat__zero__less__power__iff,axiom,
% 5.44/5.68 ! [X: nat,N2: nat] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X ) @ N2 ) )
% 5.44/5.68 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_zero_less_power_iff
% 5.44/5.68 thf(fact_6627_log__pow__cancel,axiom,
% 5.44/5.68 ! [A: real,B: nat] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( A != one_one_real )
% 5.44/5.68 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.44/5.68 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_pow_cancel
% 5.44/5.68 thf(fact_6628_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [I2: num,N2: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.44/5.68 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_less_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6629_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [I2: num,N2: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.44/5.68 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_less_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6630_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [I2: num,N2: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.44/5.68 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_less_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6631_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [I2: num,N2: nat,X: nat] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.44/5.68 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_less_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6632_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,I2: num,N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6633_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,I2: num,N2: nat] :
% 5.44/5.68 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6634_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,I2: num,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6635_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,I2: num,N2: nat] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) )
% 5.44/5.68 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6636_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [I2: num,N2: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_le_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6637_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [I2: num,N2: nat,X: nat] :
% 5.44/5.68 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_le_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6638_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [I2: num,N2: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_le_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6639_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.44/5.68 ! [I2: num,N2: nat,X: nat] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.44/5.68 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_power_le_of_nat_cancel_iff
% 5.44/5.68 thf(fact_6640_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,I2: num,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6641_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,I2: num,N2: nat] :
% 5.44/5.68 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6642_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,I2: num,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6643_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.44/5.68 ! [X: nat,I2: num,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_le_numeral_power_cancel_iff
% 5.44/5.68 thf(fact_6644_even__of__nat,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % even_of_nat
% 5.44/5.68 thf(fact_6645_even__of__nat,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % even_of_nat
% 5.44/5.68 thf(fact_6646_even__of__nat,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % even_of_nat
% 5.44/5.68 thf(fact_6647_real__arch__simple,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ? [N4: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N4 ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_arch_simple
% 5.44/5.68 thf(fact_6648_reals__Archimedean2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ? [N4: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N4 ) ) ).
% 5.44/5.68
% 5.44/5.68 % reals_Archimedean2
% 5.44/5.68 thf(fact_6649_mult__of__nat__commute,axiom,
% 5.44/5.68 ! [X: nat,Y: real] :
% 5.44/5.68 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 5.44/5.68 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mult_of_nat_commute
% 5.44/5.68 thf(fact_6650_mult__of__nat__commute,axiom,
% 5.44/5.68 ! [X: nat,Y: int] :
% 5.44/5.68 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 5.44/5.68 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mult_of_nat_commute
% 5.44/5.68 thf(fact_6651_mult__of__nat__commute,axiom,
% 5.44/5.68 ! [X: nat,Y: nat] :
% 5.44/5.68 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 5.44/5.68 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mult_of_nat_commute
% 5.44/5.68 thf(fact_6652_mult__of__nat__commute,axiom,
% 5.44/5.68 ! [X: nat,Y: complex] :
% 5.44/5.68 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y )
% 5.44/5.68 = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mult_of_nat_commute
% 5.44/5.68 thf(fact_6653_mult__of__nat__commute,axiom,
% 5.44/5.68 ! [X: nat,Y: code_integer] :
% 5.44/5.68 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 5.44/5.68 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mult_of_nat_commute
% 5.44/5.68 thf(fact_6654_bit__of__nat__iff__bit,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se9216721137139052372nteger @ ( semiri4939895301339042750nteger @ M ) @ N2 )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_of_nat_iff_bit
% 5.44/5.68 thf(fact_6655_bit__of__nat__iff__bit,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N2 )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_of_nat_iff_bit
% 5.44/5.68 thf(fact_6656_bit__of__nat__iff__bit,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 )
% 5.44/5.68 = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_of_nat_iff_bit
% 5.44/5.68 thf(fact_6657_of__nat__less__of__int__iff,axiom,
% 5.44/5.68 ! [N2: nat,X: int] :
% 5.44/5.68 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X ) )
% 5.44/5.68 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_of_int_iff
% 5.44/5.68 thf(fact_6658_of__nat__less__of__int__iff,axiom,
% 5.44/5.68 ! [N2: nat,X: int] :
% 5.44/5.68 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X ) )
% 5.44/5.68 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_of_int_iff
% 5.44/5.68 thf(fact_6659_of__nat__less__of__int__iff,axiom,
% 5.44/5.68 ! [N2: nat,X: int] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( ring_18347121197199848620nteger @ X ) )
% 5.44/5.68 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_of_int_iff
% 5.44/5.68 thf(fact_6660_not__bit__Suc__0__Suc,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % not_bit_Suc_0_Suc
% 5.44/5.68 thf(fact_6661_bit__Suc__0__iff,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.68 = ( N2 = zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_Suc_0_iff
% 5.44/5.68 thf(fact_6662_of__nat__0__le__iff,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( semiri4216267220026989637d_enat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_le_iff
% 5.44/5.68 thf(fact_6663_of__nat__0__le__iff,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_le_iff
% 5.44/5.68 thf(fact_6664_of__nat__0__le__iff,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_le_iff
% 5.44/5.68 thf(fact_6665_of__nat__0__le__iff,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_le_iff
% 5.44/5.68 thf(fact_6666_of__nat__0__le__iff,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_0_le_iff
% 5.44/5.68 thf(fact_6667_of__nat__less__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ~ ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M ) @ zero_z5237406670263579293d_enat ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_0_iff
% 5.44/5.68 thf(fact_6668_of__nat__less__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_0_iff
% 5.44/5.68 thf(fact_6669_of__nat__less__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_0_iff
% 5.44/5.68 thf(fact_6670_of__nat__less__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_0_iff
% 5.44/5.68 thf(fact_6671_of__nat__less__0__iff,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_0_iff
% 5.44/5.68 thf(fact_6672_of__nat__neq__0,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri4216267220026989637d_enat @ ( suc @ N2 ) )
% 5.44/5.68 != zero_z5237406670263579293d_enat ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_neq_0
% 5.44/5.68 thf(fact_6673_of__nat__neq__0,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 5.44/5.68 != zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_neq_0
% 5.44/5.68 thf(fact_6674_of__nat__neq__0,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.44/5.68 != zero_zero_int ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_neq_0
% 5.44/5.68 thf(fact_6675_of__nat__neq__0,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 5.44/5.68 != zero_zero_nat ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_neq_0
% 5.44/5.68 thf(fact_6676_of__nat__neq__0,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 5.44/5.68 != zero_zero_complex ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_neq_0
% 5.44/5.68 thf(fact_6677_of__nat__neq__0,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( suc @ N2 ) )
% 5.44/5.68 != zero_z3403309356797280102nteger ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_neq_0
% 5.44/5.68 thf(fact_6678_div__mult2__eq_H,axiom,
% 5.44/5.68 ! [A: int,M: nat,N2: nat] :
% 5.44/5.68 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.44/5.68 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % div_mult2_eq'
% 5.44/5.68 thf(fact_6679_div__mult2__eq_H,axiom,
% 5.44/5.68 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.68 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.44/5.68 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % div_mult2_eq'
% 5.44/5.68 thf(fact_6680_div__mult2__eq_H,axiom,
% 5.44/5.68 ! [A: code_integer,M: nat,N2: nat] :
% 5.44/5.68 ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.44/5.68 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % div_mult2_eq'
% 5.44/5.68 thf(fact_6681_less__imp__of__nat__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.68 => ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % less_imp_of_nat_less
% 5.44/5.68 thf(fact_6682_less__imp__of__nat__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.68 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % less_imp_of_nat_less
% 5.44/5.68 thf(fact_6683_less__imp__of__nat__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.68 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % less_imp_of_nat_less
% 5.44/5.68 thf(fact_6684_less__imp__of__nat__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.68 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % less_imp_of_nat_less
% 5.44/5.68 thf(fact_6685_less__imp__of__nat__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ M @ N2 )
% 5.44/5.68 => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % less_imp_of_nat_less
% 5.44/5.68 thf(fact_6686_of__nat__less__imp__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_le72135733267957522d_enat @ ( semiri4216267220026989637d_enat @ M ) @ ( semiri4216267220026989637d_enat @ N2 ) )
% 5.44/5.68 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_imp_less
% 5.44/5.68 thf(fact_6687_of__nat__less__imp__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.68 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_imp_less
% 5.44/5.68 thf(fact_6688_of__nat__less__imp__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_imp_less
% 5.44/5.68 thf(fact_6689_of__nat__less__imp__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_imp_less
% 5.44/5.68 thf(fact_6690_of__nat__less__imp__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_imp_less
% 5.44/5.68 thf(fact_6691_of__nat__mono,axiom,
% 5.44/5.68 ! [I2: nat,J: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.68 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mono
% 5.44/5.68 thf(fact_6692_of__nat__mono,axiom,
% 5.44/5.68 ! [I2: nat,J: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.68 => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I2 ) @ ( semiri4939895301339042750nteger @ J ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mono
% 5.44/5.68 thf(fact_6693_of__nat__mono,axiom,
% 5.44/5.68 ! [I2: nat,J: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.68 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mono
% 5.44/5.68 thf(fact_6694_of__nat__mono,axiom,
% 5.44/5.68 ! [I2: nat,J: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.68 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mono
% 5.44/5.68 thf(fact_6695_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) )
% 5.44/5.68 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.44/5.68 thf(fact_6696_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.44/5.68 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.44/5.68 thf(fact_6697_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( divide_divide_nat @ M @ N2 ) )
% 5.44/5.68 = ( divide6298287555418463151nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.44/5.68 thf(fact_6698_of__nat__dvd__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_dvd_iff
% 5.44/5.68 thf(fact_6699_of__nat__dvd__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.44/5.68 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_dvd_iff
% 5.44/5.68 thf(fact_6700_of__nat__dvd__iff,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.44/5.68 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_dvd_iff
% 5.44/5.68 thf(fact_6701_pi__gt__zero,axiom,
% 5.44/5.68 ord_less_real @ zero_zero_real @ pi ).
% 5.44/5.68
% 5.44/5.68 % pi_gt_zero
% 5.44/5.68 thf(fact_6702_pi__not__less__zero,axiom,
% 5.44/5.68 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % pi_not_less_zero
% 5.44/5.68 thf(fact_6703_pi__ge__zero,axiom,
% 5.44/5.68 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.44/5.68
% 5.44/5.68 % pi_ge_zero
% 5.44/5.68 thf(fact_6704_of__nat__mod,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.44/5.68 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mod
% 5.44/5.68 thf(fact_6705_of__nat__mod,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.44/5.68 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mod
% 5.44/5.68 thf(fact_6706_of__nat__mod,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.44/5.68 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mod
% 5.44/5.68 thf(fact_6707_of__nat__max,axiom,
% 5.44/5.68 ! [X: nat,Y: nat] :
% 5.44/5.68 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y ) )
% 5.44/5.68 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_max
% 5.44/5.68 thf(fact_6708_of__nat__max,axiom,
% 5.44/5.68 ! [X: nat,Y: nat] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 5.44/5.68 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_max
% 5.44/5.68 thf(fact_6709_of__nat__max,axiom,
% 5.44/5.68 ! [X: nat,Y: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 5.44/5.68 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_max
% 5.44/5.68 thf(fact_6710_of__nat__max,axiom,
% 5.44/5.68 ! [X: nat,Y: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 5.44/5.68 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_max
% 5.44/5.68 thf(fact_6711_of__nat__max,axiom,
% 5.44/5.68 ! [X: nat,Y: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y ) )
% 5.44/5.68 = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_max
% 5.44/5.68 thf(fact_6712_take__bit__of__nat,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( bit_se1745604003318907178nteger @ N2 @ ( semiri4939895301339042750nteger @ M ) )
% 5.44/5.68 = ( semiri4939895301339042750nteger @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % take_bit_of_nat
% 5.44/5.68 thf(fact_6713_take__bit__of__nat,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( bit_se2923211474154528505it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 5.44/5.68 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % take_bit_of_nat
% 5.44/5.68 thf(fact_6714_take__bit__of__nat,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( bit_se2925701944663578781it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 5.44/5.68 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % take_bit_of_nat
% 5.44/5.68 thf(fact_6715_of__nat__and__eq,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.44/5.68 = ( bit_se3949692690581998587nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_and_eq
% 5.44/5.68 thf(fact_6716_of__nat__and__eq,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.44/5.68 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_and_eq
% 5.44/5.68 thf(fact_6717_of__nat__and__eq,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.44/5.68 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_and_eq
% 5.44/5.68 thf(fact_6718_of__nat__or__eq,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( bit_se1412395901928357646or_nat @ M @ N2 ) )
% 5.44/5.68 = ( bit_se1080825931792720795nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_or_eq
% 5.44/5.68 thf(fact_6719_of__nat__or__eq,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( bit_se1412395901928357646or_nat @ M @ N2 ) )
% 5.44/5.68 = ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_or_eq
% 5.44/5.68 thf(fact_6720_of__nat__or__eq,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( bit_se1412395901928357646or_nat @ M @ N2 ) )
% 5.44/5.68 = ( bit_se1412395901928357646or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_or_eq
% 5.44/5.68 thf(fact_6721_of__nat__mask__eq,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri4939895301339042750nteger @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.44/5.68 = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mask_eq
% 5.44/5.68 thf(fact_6722_of__nat__mask__eq,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.44/5.68 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mask_eq
% 5.44/5.68 thf(fact_6723_of__nat__mask__eq,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.44/5.68 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_mask_eq
% 5.44/5.68 thf(fact_6724_not__bit__Suc__0__numeral,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % not_bit_Suc_0_numeral
% 5.44/5.68 thf(fact_6725_ex__less__of__nat__mult,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ? [N4: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ex_less_of_nat_mult
% 5.44/5.68 thf(fact_6726_of__nat__diff,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.68 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.68 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_diff
% 5.44/5.68 thf(fact_6727_of__nat__diff,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.68 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.68 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_diff
% 5.44/5.68 thf(fact_6728_of__nat__diff,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.68 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.68 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_diff
% 5.44/5.68 thf(fact_6729_of__nat__diff,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.68 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.68 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_diff
% 5.44/5.68 thf(fact_6730_of__nat__diff,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.68 => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N2 ) )
% 5.44/5.68 = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_diff
% 5.44/5.68 thf(fact_6731_exp__of__nat2__mult,axiom,
% 5.44/5.68 ! [X: real,N2: nat] :
% 5.44/5.68 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.44/5.68 = ( power_power_real @ ( exp_real @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_of_nat2_mult
% 5.44/5.68 thf(fact_6732_exp__of__nat2__mult,axiom,
% 5.44/5.68 ! [X: complex,N2: nat] :
% 5.44/5.68 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.44/5.68 = ( power_power_complex @ ( exp_complex @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_of_nat2_mult
% 5.44/5.68 thf(fact_6733_exp__of__nat__mult,axiom,
% 5.44/5.68 ! [N2: nat,X: real] :
% 5.44/5.68 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) )
% 5.44/5.68 = ( power_power_real @ ( exp_real @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_of_nat_mult
% 5.44/5.68 thf(fact_6734_exp__of__nat__mult,axiom,
% 5.44/5.68 ! [N2: nat,X: complex] :
% 5.44/5.68 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ X ) )
% 5.44/5.68 = ( power_power_complex @ ( exp_complex @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_of_nat_mult
% 5.44/5.68 thf(fact_6735_reals__Archimedean3,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ! [Y2: real] :
% 5.44/5.68 ? [N4: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % reals_Archimedean3
% 5.44/5.68 thf(fact_6736_real__of__nat__div4,axiom,
% 5.44/5.68 ! [N2: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_div4
% 5.44/5.68 thf(fact_6737_real__of__nat__div,axiom,
% 5.44/5.68 ! [D: nat,N2: nat] :
% 5.44/5.68 ( ( dvd_dvd_nat @ D @ N2 )
% 5.44/5.68 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ D ) )
% 5.44/5.68 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_div
% 5.44/5.68 thf(fact_6738_mod__mult2__eq_H,axiom,
% 5.44/5.68 ! [A: int,M: nat,N2: nat] :
% 5.44/5.68 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.44/5.68 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mod_mult2_eq'
% 5.44/5.68 thf(fact_6739_mod__mult2__eq_H,axiom,
% 5.44/5.68 ! [A: nat,M: nat,N2: nat] :
% 5.44/5.68 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.44/5.68 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mod_mult2_eq'
% 5.44/5.68 thf(fact_6740_mod__mult2__eq_H,axiom,
% 5.44/5.68 ! [A: code_integer,M: nat,N2: nat] :
% 5.44/5.68 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.44/5.68 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mod_mult2_eq'
% 5.44/5.68 thf(fact_6741_field__char__0__class_Oof__nat__div,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N2 ) )
% 5.44/5.68 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % field_char_0_class.of_nat_div
% 5.44/5.68 thf(fact_6742_field__char__0__class_Oof__nat__div,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N2 ) )
% 5.44/5.68 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % field_char_0_class.of_nat_div
% 5.44/5.68 thf(fact_6743_pi__less__4,axiom,
% 5.44/5.68 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % pi_less_4
% 5.44/5.68 thf(fact_6744_nat__less__real__le,axiom,
% 5.44/5.68 ( ord_less_nat
% 5.44/5.68 = ( ^ [N: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % nat_less_real_le
% 5.44/5.68 thf(fact_6745_pi__ge__two,axiom,
% 5.44/5.68 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.44/5.68
% 5.44/5.68 % pi_ge_two
% 5.44/5.68 thf(fact_6746_nat__le__real__less,axiom,
% 5.44/5.68 ( ord_less_eq_nat
% 5.44/5.68 = ( ^ [N: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % nat_le_real_less
% 5.44/5.68 thf(fact_6747_pi__half__neq__two,axiom,
% 5.44/5.68 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.68 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % pi_half_neq_two
% 5.44/5.68 thf(fact_6748_log__of__power__eq,axiom,
% 5.44/5.68 ! [M: nat,B: real,N2: nat] :
% 5.44/5.68 ( ( ( semiri5074537144036343181t_real @ M )
% 5.44/5.68 = ( power_power_real @ B @ N2 ) )
% 5.44/5.68 => ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.68 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.44/5.68 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_of_power_eq
% 5.44/5.68 thf(fact_6749_less__log__of__power,axiom,
% 5.44/5.68 ! [B: real,N2: nat,M: real] :
% 5.44/5.68 ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.44/5.68 => ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.68 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % less_log_of_power
% 5.44/5.68 thf(fact_6750_real__of__nat__div__aux,axiom,
% 5.44/5.68 ! [X: nat,D: nat] :
% 5.44/5.68 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.44/5.68 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_div_aux
% 5.44/5.68 thf(fact_6751_nat__approx__posE,axiom,
% 5.44/5.68 ! [E: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ E )
% 5.44/5.68 => ~ ! [N4: nat] :
% 5.44/5.68 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ E ) ) ).
% 5.44/5.68
% 5.44/5.68 % nat_approx_posE
% 5.44/5.68 thf(fact_6752_of__nat__less__two__power,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_two_power
% 5.44/5.68 thf(fact_6753_of__nat__less__two__power,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_two_power
% 5.44/5.68 thf(fact_6754_of__nat__less__two__power,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_less_two_power
% 5.44/5.68 thf(fact_6755_inverse__of__nat__le,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.68 => ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % inverse_of_nat_le
% 5.44/5.68 thf(fact_6756_exp__divide__power__eq,axiom,
% 5.44/5.68 ! [N2: nat,X: real] :
% 5.44/5.68 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.68 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.44/5.68 = ( exp_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_divide_power_eq
% 5.44/5.68 thf(fact_6757_exp__divide__power__eq,axiom,
% 5.44/5.68 ! [N2: nat,X: complex] :
% 5.44/5.68 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.68 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N2 ) ) ) @ N2 )
% 5.44/5.68 = ( exp_complex @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_divide_power_eq
% 5.44/5.68 thf(fact_6758_real__archimedian__rdiv__eq__0,axiom,
% 5.44/5.68 ! [X: real,C: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.68 => ( ! [M5: nat] :
% 5.44/5.68 ( ( ord_less_nat @ zero_zero_nat @ M5 )
% 5.44/5.68 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ X ) @ C ) )
% 5.44/5.68 => ( X = zero_zero_real ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_archimedian_rdiv_eq_0
% 5.44/5.68 thf(fact_6759_pi__half__neq__zero,axiom,
% 5.44/5.68 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.68 != zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % pi_half_neq_zero
% 5.44/5.68 thf(fact_6760_pi__half__less__two,axiom,
% 5.44/5.68 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.44/5.68
% 5.44/5.68 % pi_half_less_two
% 5.44/5.68 thf(fact_6761_pi__half__le__two,axiom,
% 5.44/5.68 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.44/5.68
% 5.44/5.68 % pi_half_le_two
% 5.44/5.68 thf(fact_6762_real__of__nat__div2,axiom,
% 5.44/5.68 ! [N2: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_div2
% 5.44/5.68 thf(fact_6763_real__of__nat__div3,axiom,
% 5.44/5.68 ! [N2: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) ) @ one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % real_of_nat_div3
% 5.44/5.68 thf(fact_6764_le__log__of__power,axiom,
% 5.44/5.68 ! [B: real,N2: nat,M: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.44/5.68 => ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.68 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % le_log_of_power
% 5.44/5.68 thf(fact_6765_log__base__pow,axiom,
% 5.44/5.68 ! [A: real,N2: nat,X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( log @ ( power_power_real @ A @ N2 ) @ X )
% 5.44/5.68 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_base_pow
% 5.44/5.68 thf(fact_6766_ln__realpow,axiom,
% 5.44/5.68 ! [X: real,N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ln_ln_real @ ( power_power_real @ X @ N2 ) )
% 5.44/5.68 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ln_realpow
% 5.44/5.68 thf(fact_6767_log__nat__power,axiom,
% 5.44/5.68 ! [X: real,B: real,N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( log @ B @ ( power_power_real @ X @ N2 ) )
% 5.44/5.68 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_nat_power
% 5.44/5.68 thf(fact_6768_bit__nat__def,axiom,
% 5.44/5.68 ( bit_se1148574629649215175it_nat
% 5.44/5.68 = ( ^ [M6: nat,N: nat] :
% 5.44/5.68 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % bit_nat_def
% 5.44/5.68 thf(fact_6769_log2__of__power__eq,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( M
% 5.44/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.68 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.44/5.68 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log2_of_power_eq
% 5.44/5.68 thf(fact_6770_pi__half__gt__zero,axiom,
% 5.44/5.68 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % pi_half_gt_zero
% 5.44/5.68 thf(fact_6771_pi__half__ge__zero,axiom,
% 5.44/5.68 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % pi_half_ge_zero
% 5.44/5.68 thf(fact_6772_linear__plus__1__le__power,axiom,
% 5.44/5.68 ! [X: real,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % linear_plus_1_le_power
% 5.44/5.68 thf(fact_6773_log__of__power__less,axiom,
% 5.44/5.68 ! [M: nat,B: real,N2: nat] :
% 5.44/5.68 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.44/5.68 => ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.68 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_of_power_less
% 5.44/5.68 thf(fact_6774_m2pi__less__pi,axiom,
% 5.44/5.68 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.44/5.68
% 5.44/5.68 % m2pi_less_pi
% 5.44/5.68 thf(fact_6775_Bernoulli__inequality,axiom,
% 5.44/5.68 ! [X: real,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % Bernoulli_inequality
% 5.44/5.68 thf(fact_6776_arctan__ubound,axiom,
% 5.44/5.68 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arctan_ubound
% 5.44/5.68 thf(fact_6777_arctan__one,axiom,
% 5.44/5.68 ( ( arctan @ one_one_real )
% 5.44/5.68 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arctan_one
% 5.44/5.68 thf(fact_6778_log__of__power__le,axiom,
% 5.44/5.68 ! [M: nat,B: real,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.44/5.68 => ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.68 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_of_power_le
% 5.44/5.68 thf(fact_6779_minus__pi__half__less__zero,axiom,
% 5.44/5.68 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.44/5.68
% 5.44/5.68 % minus_pi_half_less_zero
% 5.44/5.68 thf(fact_6780_arctan__bounded,axiom,
% 5.44/5.68 ! [Y: real] :
% 5.44/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.44/5.68 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arctan_bounded
% 5.44/5.68 thf(fact_6781_arctan__lbound,axiom,
% 5.44/5.68 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % arctan_lbound
% 5.44/5.68 thf(fact_6782_less__log2__of__power,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.44/5.68 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % less_log2_of_power
% 5.44/5.68 thf(fact_6783_le__log2__of__power,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.44/5.68 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % le_log2_of_power
% 5.44/5.68 thf(fact_6784_log2__of__power__less,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.68 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log2_of_power_less
% 5.44/5.68 thf(fact_6785_Bernoulli__inequality__even,axiom,
% 5.44/5.68 ! [N2: nat,X: real] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % Bernoulli_inequality_even
% 5.44/5.68 thf(fact_6786_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.44/5.68 ! [N2: nat,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.68 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_ge_one_plus_x_over_n_power_n
% 5.44/5.68 thf(fact_6787_of__nat__code__if,axiom,
% 5.44/5.68 ( semiri4216267220026989637d_enat
% 5.44/5.68 = ( ^ [N: nat] :
% 5.44/5.68 ( if_Extended_enat @ ( N = zero_zero_nat ) @ zero_z5237406670263579293d_enat
% 5.44/5.68 @ ( produc2676513652042109336d_enat
% 5.44/5.68 @ ^ [M6: nat,Q4: nat] : ( if_Extended_enat @ ( Q4 = zero_zero_nat ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M6 ) ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( semiri4216267220026989637d_enat @ M6 ) ) @ one_on7984719198319812577d_enat ) )
% 5.44/5.68 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_code_if
% 5.44/5.68 thf(fact_6788_of__nat__code__if,axiom,
% 5.44/5.68 ( semiri5074537144036343181t_real
% 5.44/5.68 = ( ^ [N: nat] :
% 5.44/5.68 ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 5.44/5.68 @ ( produc1703576794950452218t_real
% 5.44/5.68 @ ^ [M6: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ one_one_real ) )
% 5.44/5.68 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_code_if
% 5.44/5.68 thf(fact_6789_of__nat__code__if,axiom,
% 5.44/5.68 ( semiri1314217659103216013at_int
% 5.44/5.68 = ( ^ [N: nat] :
% 5.44/5.68 ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int
% 5.44/5.68 @ ( produc6840382203811409530at_int
% 5.44/5.68 @ ^ [M6: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ one_one_int ) )
% 5.44/5.68 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_code_if
% 5.44/5.68 thf(fact_6790_of__nat__code__if,axiom,
% 5.44/5.68 ( semiri8010041392384452111omplex
% 5.44/5.68 = ( ^ [N: nat] :
% 5.44/5.68 ( if_complex @ ( N = zero_zero_nat ) @ zero_zero_complex
% 5.44/5.68 @ ( produc1917071388513777916omplex
% 5.44/5.68 @ ^ [M6: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ one_one_complex ) )
% 5.44/5.68 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_code_if
% 5.44/5.68 thf(fact_6791_of__nat__code__if,axiom,
% 5.44/5.68 ( semiri4939895301339042750nteger
% 5.44/5.68 = ( ^ [N: nat] :
% 5.44/5.68 ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger
% 5.44/5.68 @ ( produc1830744345554046123nteger
% 5.44/5.68 @ ^ [M6: nat,Q4: nat] : ( if_Code_integer @ ( Q4 = zero_zero_nat ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ M6 ) ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ M6 ) ) @ one_one_Code_integer ) )
% 5.44/5.68 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_code_if
% 5.44/5.68 thf(fact_6792_of__nat__code__if,axiom,
% 5.44/5.68 ( semiri1316708129612266289at_nat
% 5.44/5.68 = ( ^ [N: nat] :
% 5.44/5.68 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 5.44/5.68 @ ( produc6842872674320459806at_nat
% 5.44/5.68 @ ^ [M6: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ one_one_nat ) )
% 5.44/5.68 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_nat_code_if
% 5.44/5.68 thf(fact_6793_monoseq__arctan__series,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.68 => ( topolo6980174941875973593q_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % monoseq_arctan_series
% 5.44/5.68 thf(fact_6794_lemma__termdiff3,axiom,
% 5.44/5.68 ! [H2: real,Z: real,K5: real,N2: nat] :
% 5.44/5.68 ( ( H2 != zero_zero_real )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % lemma_termdiff3
% 5.44/5.68 thf(fact_6795_lemma__termdiff3,axiom,
% 5.44/5.68 ! [H2: complex,Z: complex,K5: real,N2: nat] :
% 5.44/5.68 ( ( H2 != zero_zero_complex )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % lemma_termdiff3
% 5.44/5.68 thf(fact_6796_sin__cos__npi,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_npi
% 5.44/5.68 thf(fact_6797_ln__series,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.68 => ( ( ln_ln_real @ X )
% 5.44/5.68 = ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ln_series
% 5.44/5.68 thf(fact_6798_int__eq__iff__numeral,axiom,
% 5.44/5.68 ! [M: nat,V: num] :
% 5.44/5.68 ( ( ( semiri1314217659103216013at_int @ M )
% 5.44/5.68 = ( numeral_numeral_int @ V ) )
% 5.44/5.68 = ( M
% 5.44/5.68 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_eq_iff_numeral
% 5.44/5.68 thf(fact_6799_negative__zless,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.44/5.68
% 5.44/5.68 % negative_zless
% 5.44/5.68 thf(fact_6800_sin__periodic__pi,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 5.44/5.68 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_periodic_pi
% 5.44/5.68 thf(fact_6801_sin__periodic__pi2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 5.44/5.68 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_periodic_pi2
% 5.44/5.68 thf(fact_6802_sin__npi2,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_npi2
% 5.44/5.68 thf(fact_6803_sin__npi,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_npi
% 5.44/5.68 thf(fact_6804_sin__npi__int,axiom,
% 5.44/5.68 ! [N2: int] :
% 5.44/5.68 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_npi_int
% 5.44/5.68 thf(fact_6805_powser__zero,axiom,
% 5.44/5.68 ! [F: nat > complex] :
% 5.44/5.68 ( ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) )
% 5.44/5.68 = ( F @ zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_zero
% 5.44/5.68 thf(fact_6806_powser__zero,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) )
% 5.44/5.68 = ( F @ zero_zero_nat ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_zero
% 5.44/5.68 thf(fact_6807_sin__two__pi,axiom,
% 5.44/5.68 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_two_pi
% 5.44/5.68 thf(fact_6808_sin__pi__half,axiom,
% 5.44/5.68 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_pi_half
% 5.44/5.68 thf(fact_6809_sin__periodic,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.44/5.68 = ( sin_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_periodic
% 5.44/5.68 thf(fact_6810_sin__2npi,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_2npi
% 5.44/5.68 thf(fact_6811_sin__2pi__minus,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.44/5.68 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_2pi_minus
% 5.44/5.68 thf(fact_6812_sin__int__2pin,axiom,
% 5.44/5.68 ! [N2: int] :
% 5.44/5.68 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_int_2pin
% 5.44/5.68 thf(fact_6813_sin__3over2__pi,axiom,
% 5.44/5.68 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.44/5.68 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_3over2_pi
% 5.44/5.68 thf(fact_6814_sin__x__le__x,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_x_le_x
% 5.44/5.68 thf(fact_6815_sin__le__one,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_le_one
% 5.44/5.68 thf(fact_6816_abs__sin__x__le__abs__x,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % abs_sin_x_le_abs_x
% 5.44/5.68 thf(fact_6817_int__ops_I3_J,axiom,
% 5.44/5.68 ! [N2: num] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.68 = ( numeral_numeral_int @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_ops(3)
% 5.44/5.68 thf(fact_6818_complex__mod__minus__le__complex__mod,axiom,
% 5.44/5.68 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % complex_mod_minus_le_complex_mod
% 5.44/5.68 thf(fact_6819_int__cases,axiom,
% 5.44/5.68 ! [Z: int] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( Z
% 5.44/5.68 != ( semiri1314217659103216013at_int @ N4 ) )
% 5.44/5.68 => ~ ! [N4: nat] :
% 5.44/5.68 ( Z
% 5.44/5.68 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_cases
% 5.44/5.68 thf(fact_6820_int__of__nat__induct,axiom,
% 5.44/5.68 ! [P: int > $o,Z: int] :
% 5.44/5.68 ( ! [N4: nat] : ( P @ ( semiri1314217659103216013at_int @ N4 ) )
% 5.44/5.68 => ( ! [N4: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) )
% 5.44/5.68 => ( P @ Z ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_of_nat_induct
% 5.44/5.68 thf(fact_6821_nat__int__comparison_I2_J,axiom,
% 5.44/5.68 ( ord_less_nat
% 5.44/5.68 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % nat_int_comparison(2)
% 5.44/5.68 thf(fact_6822_zle__int,axiom,
% 5.44/5.68 ! [M: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.68 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % zle_int
% 5.44/5.68 thf(fact_6823_nat__int__comparison_I3_J,axiom,
% 5.44/5.68 ( ord_less_eq_nat
% 5.44/5.68 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % nat_int_comparison(3)
% 5.44/5.68 thf(fact_6824_complex__mod__triangle__ineq2,axiom,
% 5.44/5.68 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.44/5.68
% 5.44/5.68 % complex_mod_triangle_ineq2
% 5.44/5.68 thf(fact_6825_zadd__int__left,axiom,
% 5.44/5.68 ! [M: nat,N2: nat,Z: int] :
% 5.44/5.68 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z ) ) ).
% 5.44/5.68
% 5.44/5.68 % zadd_int_left
% 5.44/5.68 thf(fact_6826_int__plus,axiom,
% 5.44/5.68 ! [N2: nat,M: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_plus
% 5.44/5.68 thf(fact_6827_int__ops_I5_J,axiom,
% 5.44/5.68 ! [A: nat,B: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_ops(5)
% 5.44/5.68 thf(fact_6828_int__ops_I7_J,axiom,
% 5.44/5.68 ! [A: nat,B: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.44/5.68 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_ops(7)
% 5.44/5.68 thf(fact_6829_int__ops_I2_J,axiom,
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.44/5.68 = one_one_int ) ).
% 5.44/5.68
% 5.44/5.68 % int_ops(2)
% 5.44/5.68 thf(fact_6830_zdiv__int,axiom,
% 5.44/5.68 ! [A: nat,B: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.44/5.68 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % zdiv_int
% 5.44/5.68 thf(fact_6831_nat__less__as__int,axiom,
% 5.44/5.68 ( ord_less_nat
% 5.44/5.68 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % nat_less_as_int
% 5.44/5.68 thf(fact_6832_nat__leq__as__int,axiom,
% 5.44/5.68 ( ord_less_eq_nat
% 5.44/5.68 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % nat_leq_as_int
% 5.44/5.68 thf(fact_6833_sin__gt__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ pi )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_gt_zero
% 5.44/5.68 thf(fact_6834_sin__x__ge__neg__x,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_x_ge_neg_x
% 5.44/5.68 thf(fact_6835_sin__ge__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ pi )
% 5.44/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_ge_zero
% 5.44/5.68 thf(fact_6836_sin__ge__minus__one,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_ge_minus_one
% 5.44/5.68 thf(fact_6837_abs__sin__le__one,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % abs_sin_le_one
% 5.44/5.68 thf(fact_6838_int__cases4,axiom,
% 5.44/5.68 ! [M: int] :
% 5.44/5.68 ( ! [N4: nat] :
% 5.44/5.68 ( M
% 5.44/5.68 != ( semiri1314217659103216013at_int @ N4 ) )
% 5.44/5.68 => ~ ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.44/5.68 => ( M
% 5.44/5.68 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_cases4
% 5.44/5.68 thf(fact_6839_int__Suc,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_Suc
% 5.44/5.68 thf(fact_6840_int__ops_I4_J,axiom,
% 5.44/5.68 ! [A: nat] :
% 5.44/5.68 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_ops(4)
% 5.44/5.68 thf(fact_6841_zless__iff__Suc__zadd,axiom,
% 5.44/5.68 ( ord_less_int
% 5.44/5.68 = ( ^ [W3: int,Z5: int] :
% 5.44/5.68 ? [N: nat] :
% 5.44/5.68 ( Z5
% 5.44/5.68 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % zless_iff_Suc_zadd
% 5.44/5.68 thf(fact_6842_norm__exp,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_exp
% 5.44/5.68 thf(fact_6843_norm__exp,axiom,
% 5.44/5.68 ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_exp
% 5.44/5.68 thf(fact_6844_sin__eq__0__pi,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ pi )
% 5.44/5.68 => ( ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 => ( X = zero_zero_real ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_eq_0_pi
% 5.44/5.68 thf(fact_6845_sin__zero__pi__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 5.44/5.68 => ( ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( X = zero_zero_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_zero_pi_iff
% 5.44/5.68 thf(fact_6846_sin__zero__iff__int2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( ? [I5: int] :
% 5.44/5.68 ( X
% 5.44/5.68 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ pi ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_zero_iff_int2
% 5.44/5.68 thf(fact_6847_zero__less__imp__eq__int,axiom,
% 5.44/5.68 ! [K: int] :
% 5.44/5.68 ( ( ord_less_int @ zero_zero_int @ K )
% 5.44/5.68 => ? [N4: nat] :
% 5.44/5.68 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.44/5.68 & ( K
% 5.44/5.68 = ( semiri1314217659103216013at_int @ N4 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % zero_less_imp_eq_int
% 5.44/5.68 thf(fact_6848_pos__int__cases,axiom,
% 5.44/5.68 ! [K: int] :
% 5.44/5.68 ( ( ord_less_int @ zero_zero_int @ K )
% 5.44/5.68 => ~ ! [N4: nat] :
% 5.44/5.68 ( ( K
% 5.44/5.68 = ( semiri1314217659103216013at_int @ N4 ) )
% 5.44/5.68 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % pos_int_cases
% 5.44/5.68 thf(fact_6849_int__cases3,axiom,
% 5.44/5.68 ! [K: int] :
% 5.44/5.68 ( ( K != zero_zero_int )
% 5.44/5.68 => ( ! [N4: nat] :
% 5.44/5.68 ( ( K
% 5.44/5.68 = ( semiri1314217659103216013at_int @ N4 ) )
% 5.44/5.68 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) )
% 5.44/5.68 => ~ ! [N4: nat] :
% 5.44/5.68 ( ( K
% 5.44/5.68 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) )
% 5.44/5.68 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % int_cases3
% 5.44/5.68 thf(fact_6850_zmult__zless__mono2__lemma,axiom,
% 5.44/5.68 ! [I2: int,J: int,K: nat] :
% 5.44/5.68 ( ( ord_less_int @ I2 @ J )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.68 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % zmult_zless_mono2_lemma
% 5.44/5.68 thf(fact_6851_not__zle__0__negative,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % not_zle_0_negative
% 5.44/5.68 thf(fact_6852_negative__zless__0,axiom,
% 5.44/5.68 ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 5.44/5.68
% 5.44/5.68 % negative_zless_0
% 5.44/5.68 thf(fact_6853_negD,axiom,
% 5.44/5.68 ! [X: int] :
% 5.44/5.68 ( ( ord_less_int @ X @ zero_zero_int )
% 5.44/5.68 => ? [N4: nat] :
% 5.44/5.68 ( X
% 5.44/5.68 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % negD
% 5.44/5.68 thf(fact_6854_sin__gt__zero__02,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_gt_zero_02
% 5.44/5.68 thf(fact_6855_neg__int__cases,axiom,
% 5.44/5.68 ! [K: int] :
% 5.44/5.68 ( ( ord_less_int @ K @ zero_zero_int )
% 5.44/5.68 => ~ ! [N4: nat] :
% 5.44/5.68 ( ( K
% 5.44/5.68 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) )
% 5.44/5.68 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % neg_int_cases
% 5.44/5.68 thf(fact_6856_zdiff__int__split,axiom,
% 5.44/5.68 ! [P: int > $o,X: nat,Y: nat] :
% 5.44/5.68 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 5.44/5.68 = ( ( ( ord_less_eq_nat @ Y @ X )
% 5.44/5.68 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.44/5.68 & ( ( ord_less_nat @ X @ Y )
% 5.44/5.68 => ( P @ zero_zero_int ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % zdiff_int_split
% 5.44/5.68 thf(fact_6857_monoseq__realpow,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.68 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % monoseq_realpow
% 5.44/5.68 thf(fact_6858_sin__pi__divide__n__ge__0,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( N2 != zero_zero_nat )
% 5.44/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_pi_divide_n_ge_0
% 5.44/5.68 thf(fact_6859_sin__45,axiom,
% 5.44/5.68 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_45
% 5.44/5.68 thf(fact_6860_sin__gt__zero2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_gt_zero2
% 5.44/5.68 thf(fact_6861_sin__lt__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ pi @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.44/5.68 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_lt_zero
% 5.44/5.68 thf(fact_6862_sin__30,axiom,
% 5.44/5.68 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.44/5.68 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_30
% 5.44/5.68 thf(fact_6863_sin__inj__pi,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( ( sin_real @ X )
% 5.44/5.68 = ( sin_real @ Y ) )
% 5.44/5.68 => ( X = Y ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_inj_pi
% 5.44/5.68 thf(fact_6864_sin__mono__le__eq,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.44/5.68 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_mono_le_eq
% 5.44/5.68 thf(fact_6865_sin__monotone__2pi__le,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_monotone_2pi_le
% 5.44/5.68 thf(fact_6866_sin__60,axiom,
% 5.44/5.68 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.44/5.68 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_60
% 5.44/5.68 thf(fact_6867_exp__bound__half,axiom,
% 5.44/5.68 ! [Z: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_bound_half
% 5.44/5.68 thf(fact_6868_exp__bound__half,axiom,
% 5.44/5.68 ! [Z: complex] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_bound_half
% 5.44/5.68 thf(fact_6869_sin__le__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ pi @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_le_zero
% 5.44/5.68 thf(fact_6870_sin__less__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.68 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_less_zero
% 5.44/5.68 thf(fact_6871_sin__mono__less__eq,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.44/5.68 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_mono_less_eq
% 5.44/5.68 thf(fact_6872_sin__monotone__2pi,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.68 => ( ( ord_less_real @ Y @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_monotone_2pi
% 5.44/5.68 thf(fact_6873_sin__total,axiom,
% 5.44/5.68 ! [Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.68 => ? [X5: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.44/5.68 & ( ord_less_eq_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 & ( ( sin_real @ X5 )
% 5.44/5.68 = Y )
% 5.44/5.68 & ! [Y2: real] :
% 5.44/5.68 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.44/5.68 & ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 & ( ( sin_real @ Y2 )
% 5.44/5.68 = Y ) )
% 5.44/5.68 => ( Y2 = X5 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_total
% 5.44/5.68 thf(fact_6874_sin__pi__divide__n__gt__0,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_pi_divide_n_gt_0
% 5.44/5.68 thf(fact_6875_sin__arctan,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sin_real @ ( arctan @ X ) )
% 5.44/5.68 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_arctan
% 5.44/5.68 thf(fact_6876_exp__bound__lemma,axiom,
% 5.44/5.68 ! [Z: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( 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 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_bound_lemma
% 5.44/5.68 thf(fact_6877_exp__bound__lemma,axiom,
% 5.44/5.68 ! [Z: complex] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( 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 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % exp_bound_lemma
% 5.44/5.68 thf(fact_6878_sin__zero__iff__int,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( ? [I5: int] :
% 5.44/5.68 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_zero_iff_int
% 5.44/5.68 thf(fact_6879_sin__zero__lemma,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 => ? [N4: nat] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_zero_lemma
% 5.44/5.68 thf(fact_6880_sin__zero__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( ? [N: nat] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.68 | ? [N: nat] :
% 5.44/5.68 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_zero_iff
% 5.44/5.68 thf(fact_6881_pi__series,axiom,
% 5.44/5.68 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = ( suminf_real
% 5.44/5.68 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % pi_series
% 5.44/5.68 thf(fact_6882_arctan__series,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.68 => ( ( arctan @ X )
% 5.44/5.68 = ( suminf_real
% 5.44/5.68 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % arctan_series
% 5.44/5.68 thf(fact_6883_norm__divide__numeral,axiom,
% 5.44/5.68 ! [A: real,W: num] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.68 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_divide_numeral
% 5.44/5.68 thf(fact_6884_norm__divide__numeral,axiom,
% 5.44/5.68 ! [A: complex,W: num] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.68 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_divide_numeral
% 5.44/5.68 thf(fact_6885_norm__mult__numeral2,axiom,
% 5.44/5.68 ! [A: real,W: num] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.68 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult_numeral2
% 5.44/5.68 thf(fact_6886_norm__mult__numeral2,axiom,
% 5.44/5.68 ! [A: complex,W: num] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.68 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult_numeral2
% 5.44/5.68 thf(fact_6887_norm__mult__numeral1,axiom,
% 5.44/5.68 ! [W: num,A: real] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.44/5.68 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult_numeral1
% 5.44/5.68 thf(fact_6888_norm__mult__numeral1,axiom,
% 5.44/5.68 ! [W: num,A: complex] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.44/5.68 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult_numeral1
% 5.44/5.68 thf(fact_6889_norm__neg__numeral,axiom,
% 5.44/5.68 ! [W: num] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.68 = ( numeral_numeral_real @ W ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_neg_numeral
% 5.44/5.68 thf(fact_6890_norm__neg__numeral,axiom,
% 5.44/5.68 ! [W: num] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.68 = ( numeral_numeral_real @ W ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_neg_numeral
% 5.44/5.68 thf(fact_6891_norm__le__zero__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 5.44/5.68 = ( X = zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_le_zero_iff
% 5.44/5.68 thf(fact_6892_norm__le__zero__iff,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 5.44/5.68 = ( X = zero_zero_complex ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_le_zero_iff
% 5.44/5.68 thf(fact_6893_norm__one,axiom,
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % norm_one
% 5.44/5.68 thf(fact_6894_norm__one,axiom,
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % norm_one
% 5.44/5.68 thf(fact_6895_norm__numeral,axiom,
% 5.44/5.68 ! [W: num] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.68 = ( numeral_numeral_real @ W ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_numeral
% 5.44/5.68 thf(fact_6896_norm__numeral,axiom,
% 5.44/5.68 ! [W: num] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.68 = ( numeral_numeral_real @ W ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_numeral
% 5.44/5.68 thf(fact_6897_zero__less__norm__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 5.44/5.68 = ( X != zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % zero_less_norm_iff
% 5.44/5.68 thf(fact_6898_zero__less__norm__iff,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 5.44/5.68 = ( X != zero_zero_complex ) ) ).
% 5.44/5.68
% 5.44/5.68 % zero_less_norm_iff
% 5.44/5.68 thf(fact_6899_norm__not__less__zero,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % norm_not_less_zero
% 5.44/5.68 thf(fact_6900_norm__ge__zero,axiom,
% 5.44/5.68 ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_ge_zero
% 5.44/5.68 thf(fact_6901_norm__mult,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 5.44/5.68 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult
% 5.44/5.68 thf(fact_6902_norm__mult,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 5.44/5.68 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult
% 5.44/5.68 thf(fact_6903_norm__divide,axiom,
% 5.44/5.68 ! [A: real,B: real] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.68 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_divide
% 5.44/5.68 thf(fact_6904_norm__divide,axiom,
% 5.44/5.68 ! [A: complex,B: complex] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.68 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_divide
% 5.44/5.68 thf(fact_6905_norm__power,axiom,
% 5.44/5.68 ! [X: real,N2: nat] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N2 ) )
% 5.44/5.68 = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_power
% 5.44/5.68 thf(fact_6906_norm__power,axiom,
% 5.44/5.68 ! [X: complex,N2: nat] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N2 ) )
% 5.44/5.68 = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_power
% 5.44/5.68 thf(fact_6907_norm__uminus__minus,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 5.44/5.68 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_uminus_minus
% 5.44/5.68 thf(fact_6908_norm__uminus__minus,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 5.44/5.68 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_uminus_minus
% 5.44/5.68 thf(fact_6909_nonzero__norm__divide,axiom,
% 5.44/5.68 ! [B: real,A: real] :
% 5.44/5.68 ( ( B != zero_zero_real )
% 5.44/5.68 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.68 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % nonzero_norm_divide
% 5.44/5.68 thf(fact_6910_nonzero__norm__divide,axiom,
% 5.44/5.68 ! [B: complex,A: complex] :
% 5.44/5.68 ( ( B != zero_zero_complex )
% 5.44/5.68 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.68 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % nonzero_norm_divide
% 5.44/5.68 thf(fact_6911_power__eq__imp__eq__norm,axiom,
% 5.44/5.68 ! [W: real,N2: nat,Z: real] :
% 5.44/5.68 ( ( ( power_power_real @ W @ N2 )
% 5.44/5.68 = ( power_power_real @ Z @ N2 ) )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.68 => ( ( real_V7735802525324610683m_real @ W )
% 5.44/5.68 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % power_eq_imp_eq_norm
% 5.44/5.68 thf(fact_6912_power__eq__imp__eq__norm,axiom,
% 5.44/5.68 ! [W: complex,N2: nat,Z: complex] :
% 5.44/5.68 ( ( ( power_power_complex @ W @ N2 )
% 5.44/5.68 = ( power_power_complex @ Z @ N2 ) )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.68 => ( ( real_V1022390504157884413omplex @ W )
% 5.44/5.68 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % power_eq_imp_eq_norm
% 5.44/5.68 thf(fact_6913_norm__mult__less,axiom,
% 5.44/5.68 ! [X: real,R: real,Y: real,S3: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S3 )
% 5.44/5.68 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R @ S3 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult_less
% 5.44/5.68 thf(fact_6914_norm__mult__less,axiom,
% 5.44/5.68 ! [X: complex,R: real,Y: complex,S3: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S3 )
% 5.44/5.68 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R @ S3 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult_less
% 5.44/5.68 thf(fact_6915_norm__mult__ineq,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult_ineq
% 5.44/5.68 thf(fact_6916_norm__mult__ineq,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_mult_ineq
% 5.44/5.68 thf(fact_6917_norm__triangle__lt,axiom,
% 5.44/5.68 ! [X: real,Y: real,E: real] :
% 5.44/5.68 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.44/5.68 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_lt
% 5.44/5.68 thf(fact_6918_norm__triangle__lt,axiom,
% 5.44/5.68 ! [X: complex,Y: complex,E: real] :
% 5.44/5.68 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.44/5.68 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_lt
% 5.44/5.68 thf(fact_6919_norm__add__less,axiom,
% 5.44/5.68 ! [X: real,R: real,Y: real,S3: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S3 )
% 5.44/5.68 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_add_less
% 5.44/5.68 thf(fact_6920_norm__add__less,axiom,
% 5.44/5.68 ! [X: complex,R: real,Y: complex,S3: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S3 )
% 5.44/5.68 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_add_less
% 5.44/5.68 thf(fact_6921_norm__power__ineq,axiom,
% 5.44/5.68 ! [X: real,N2: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_power_ineq
% 5.44/5.68 thf(fact_6922_norm__power__ineq,axiom,
% 5.44/5.68 ! [X: complex,N2: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_power_ineq
% 5.44/5.68 thf(fact_6923_norm__add__leD,axiom,
% 5.44/5.68 ! [A: real,B: real,C: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_add_leD
% 5.44/5.68 thf(fact_6924_norm__add__leD,axiom,
% 5.44/5.68 ! [A: complex,B: complex,C: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_add_leD
% 5.44/5.68 thf(fact_6925_norm__triangle__le,axiom,
% 5.44/5.68 ! [X: real,Y: real,E: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_le
% 5.44/5.68 thf(fact_6926_norm__triangle__le,axiom,
% 5.44/5.68 ! [X: complex,Y: complex,E: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_le
% 5.44/5.68 thf(fact_6927_norm__triangle__ineq,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_ineq
% 5.44/5.68 thf(fact_6928_norm__triangle__ineq,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_ineq
% 5.44/5.68 thf(fact_6929_norm__triangle__mono,axiom,
% 5.44/5.68 ! [A: real,R: real,B: real,S3: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S3 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_mono
% 5.44/5.68 thf(fact_6930_norm__triangle__mono,axiom,
% 5.44/5.68 ! [A: complex,R: real,B: complex,S3: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S3 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S3 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_mono
% 5.44/5.68 thf(fact_6931_norm__diff__triangle__less,axiom,
% 5.44/5.68 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.44/5.68 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_diff_triangle_less
% 5.44/5.68 thf(fact_6932_norm__diff__triangle__less,axiom,
% 5.44/5.68 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.44/5.68 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_diff_triangle_less
% 5.44/5.68 thf(fact_6933_norm__triangle__le__diff,axiom,
% 5.44/5.68 ! [X: real,Y: real,E: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_le_diff
% 5.44/5.68 thf(fact_6934_norm__triangle__le__diff,axiom,
% 5.44/5.68 ! [X: complex,Y: complex,E: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_le_diff
% 5.44/5.68 thf(fact_6935_norm__diff__triangle__le,axiom,
% 5.44/5.68 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_diff_triangle_le
% 5.44/5.68 thf(fact_6936_norm__diff__triangle__le,axiom,
% 5.44/5.68 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_diff_triangle_le
% 5.44/5.68 thf(fact_6937_norm__triangle__ineq4,axiom,
% 5.44/5.68 ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_ineq4
% 5.44/5.68 thf(fact_6938_norm__triangle__ineq4,axiom,
% 5.44/5.68 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_ineq4
% 5.44/5.68 thf(fact_6939_norm__triangle__sub,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_sub
% 5.44/5.68 thf(fact_6940_norm__triangle__sub,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_sub
% 5.44/5.68 thf(fact_6941_norm__diff__ineq,axiom,
% 5.44/5.68 ! [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 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_diff_ineq
% 5.44/5.68 thf(fact_6942_norm__diff__ineq,axiom,
% 5.44/5.68 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_diff_ineq
% 5.44/5.68 thf(fact_6943_norm__triangle__ineq2,axiom,
% 5.44/5.68 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_ineq2
% 5.44/5.68 thf(fact_6944_norm__triangle__ineq2,axiom,
% 5.44/5.68 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_ineq2
% 5.44/5.68 thf(fact_6945_power__eq__1__iff,axiom,
% 5.44/5.68 ! [W: real,N2: nat] :
% 5.44/5.68 ( ( ( power_power_real @ W @ N2 )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % power_eq_1_iff
% 5.44/5.68 thf(fact_6946_power__eq__1__iff,axiom,
% 5.44/5.68 ! [W: complex,N2: nat] :
% 5.44/5.68 ( ( ( power_power_complex @ W @ N2 )
% 5.44/5.68 = one_one_complex )
% 5.44/5.68 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 | ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % power_eq_1_iff
% 5.44/5.68 thf(fact_6947_norm__diff__triangle__ineq,axiom,
% 5.44/5.68 ! [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 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_diff_triangle_ineq
% 5.44/5.68 thf(fact_6948_norm__diff__triangle__ineq,axiom,
% 5.44/5.68 ! [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 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_diff_triangle_ineq
% 5.44/5.68 thf(fact_6949_norm__triangle__ineq3,axiom,
% 5.44/5.68 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_ineq3
% 5.44/5.68 thf(fact_6950_norm__triangle__ineq3,axiom,
% 5.44/5.68 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_triangle_ineq3
% 5.44/5.68 thf(fact_6951_square__norm__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 => ( ( real_V7735802525324610683m_real @ X )
% 5.44/5.68 = one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % square_norm_one
% 5.44/5.68 thf(fact_6952_square__norm__one,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = one_one_complex )
% 5.44/5.68 => ( ( real_V1022390504157884413omplex @ X )
% 5.44/5.68 = one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % square_norm_one
% 5.44/5.68 thf(fact_6953_norm__power__diff,axiom,
% 5.44/5.68 ! [Z: real,W: real,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.44/5.68 => ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_power_diff
% 5.44/5.68 thf(fact_6954_norm__power__diff,axiom,
% 5.44/5.68 ! [Z: complex,W: complex,M: nat] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.44/5.68 => ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % norm_power_diff
% 5.44/5.68 thf(fact_6955_suminf__geometric,axiom,
% 5.44/5.68 ! [C: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.44/5.68 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.44/5.68 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_geometric
% 5.44/5.68 thf(fact_6956_suminf__geometric,axiom,
% 5.44/5.68 ! [C: complex] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.44/5.68 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.44/5.68 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_geometric
% 5.44/5.68 thf(fact_6957_ceiling__log__nat__eq__powr__iff,axiom,
% 5.44/5.68 ! [B: nat,K: nat,N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.68 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 5.44/5.68 = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.44/5.68 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_log_nat_eq_powr_iff
% 5.44/5.68 thf(fact_6958_summable__arctan__series,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_arctan_series
% 5.44/5.68 thf(fact_6959_cos__pi__eq__zero,axiom,
% 5.44/5.68 ! [M: nat] :
% 5.44/5.68 ( ( 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 ) ) ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_pi_eq_zero
% 5.44/5.68 thf(fact_6960_sincos__total__2pi,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 => ~ ! [T4: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.44/5.68 => ( ( ord_less_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.44/5.68 => ( ( X
% 5.44/5.68 = ( cos_real @ T4 ) )
% 5.44/5.68 => ( Y
% 5.44/5.68 != ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sincos_total_2pi
% 5.44/5.68 thf(fact_6961_of__int__ceiling__cancel,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = X )
% 5.44/5.68 = ( ? [N: int] :
% 5.44/5.68 ( X
% 5.44/5.68 = ( ring_1_of_int_real @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_int_ceiling_cancel
% 5.44/5.68 thf(fact_6962_summable__iff__shift,axiom,
% 5.44/5.68 ! [F: nat > real,K: nat] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.44/5.68 = ( summable_real @ F ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_iff_shift
% 5.44/5.68 thf(fact_6963_cos__zero,axiom,
% 5.44/5.68 ( ( cos_complex @ zero_zero_complex )
% 5.44/5.68 = one_one_complex ) ).
% 5.44/5.68
% 5.44/5.68 % cos_zero
% 5.44/5.68 thf(fact_6964_cos__zero,axiom,
% 5.44/5.68 ( ( cos_real @ zero_zero_real )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_zero
% 5.44/5.68 thf(fact_6965_ceiling__numeral,axiom,
% 5.44/5.68 ! [V: num] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.44/5.68 = ( numeral_numeral_int @ V ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_numeral
% 5.44/5.68 thf(fact_6966_ceiling__one,axiom,
% 5.44/5.68 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.44/5.68 = one_one_int ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_one
% 5.44/5.68 thf(fact_6967_summable__cmult__iff,axiom,
% 5.44/5.68 ! [C: complex,F: nat > complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 5.44/5.68 = ( ( C = zero_zero_complex )
% 5.44/5.68 | ( summable_complex @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_cmult_iff
% 5.44/5.68 thf(fact_6968_summable__cmult__iff,axiom,
% 5.44/5.68 ! [C: real,F: nat > real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 5.44/5.68 = ( ( C = zero_zero_real )
% 5.44/5.68 | ( summable_real @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_cmult_iff
% 5.44/5.68 thf(fact_6969_summable__divide__iff,axiom,
% 5.44/5.68 ! [F: nat > real,C: real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 5.44/5.68 = ( ( C = zero_zero_real )
% 5.44/5.68 | ( summable_real @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_divide_iff
% 5.44/5.68 thf(fact_6970_summable__divide__iff,axiom,
% 5.44/5.68 ! [F: nat > complex,C: complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 5.44/5.68 = ( ( C = zero_zero_complex )
% 5.44/5.68 | ( summable_complex @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_divide_iff
% 5.44/5.68 thf(fact_6971_ceiling__add__of__int,axiom,
% 5.44/5.68 ! [X: real,Z: int] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 5.44/5.68 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_add_of_int
% 5.44/5.68 thf(fact_6972_cos__pi,axiom,
% 5.44/5.68 ( ( cos_real @ pi )
% 5.44/5.68 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_pi
% 5.44/5.68 thf(fact_6973_cos__periodic__pi,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 5.44/5.68 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_periodic_pi
% 5.44/5.68 thf(fact_6974_cos__periodic__pi2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 5.44/5.68 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_periodic_pi2
% 5.44/5.68 thf(fact_6975_sin__cos__squared__add3,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 5.44/5.68 = one_one_complex ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_squared_add3
% 5.44/5.68 thf(fact_6976_sin__cos__squared__add3,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_squared_add3
% 5.44/5.68 thf(fact_6977_ceiling__le__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.44/5.68 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_le_zero
% 5.44/5.68 thf(fact_6978_zero__less__ceiling,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % zero_less_ceiling
% 5.44/5.68 thf(fact_6979_ceiling__le__numeral,axiom,
% 5.44/5.68 ! [X: real,V: num] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.68 = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_le_numeral
% 5.44/5.68 thf(fact_6980_ceiling__less__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.44/5.68 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_less_one
% 5.44/5.68 thf(fact_6981_numeral__less__ceiling,axiom,
% 5.44/5.68 ! [V: num,X: real] :
% 5.44/5.68 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_less_ceiling
% 5.44/5.68 thf(fact_6982_one__le__ceiling,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % one_le_ceiling
% 5.44/5.68 thf(fact_6983_ceiling__le__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.44/5.68 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_le_one
% 5.44/5.68 thf(fact_6984_one__less__ceiling,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ one_one_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % one_less_ceiling
% 5.44/5.68 thf(fact_6985_ceiling__add__numeral,axiom,
% 5.44/5.68 ! [X: real,V: num] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.68 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_add_numeral
% 5.44/5.68 thf(fact_6986_ceiling__neg__numeral,axiom,
% 5.44/5.68 ! [V: num] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.68 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_neg_numeral
% 5.44/5.68 thf(fact_6987_ceiling__add__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 5.44/5.68 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_add_one
% 5.44/5.68 thf(fact_6988_ceiling__diff__numeral,axiom,
% 5.44/5.68 ! [X: real,V: num] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.68 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_diff_numeral
% 5.44/5.68 thf(fact_6989_ceiling__diff__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.44/5.68 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_diff_one
% 5.44/5.68 thf(fact_6990_ceiling__numeral__power,axiom,
% 5.44/5.68 ! [X: num,N2: nat] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.44/5.68 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_numeral_power
% 5.44/5.68 thf(fact_6991_summable__geometric__iff,axiom,
% 5.44/5.68 ! [C: real] :
% 5.44/5.68 ( ( summable_real @ ( power_power_real @ C ) )
% 5.44/5.68 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_geometric_iff
% 5.44/5.68 thf(fact_6992_summable__geometric__iff,axiom,
% 5.44/5.68 ! [C: complex] :
% 5.44/5.68 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.44/5.68 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_geometric_iff
% 5.44/5.68 thf(fact_6993_ceiling__less__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.44/5.68 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_less_zero
% 5.44/5.68 thf(fact_6994_zero__le__ceiling,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % zero_le_ceiling
% 5.44/5.68 thf(fact_6995_ceiling__divide__eq__div__numeral,axiom,
% 5.44/5.68 ! [A: num,B: num] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.44/5.68 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_divide_eq_div_numeral
% 5.44/5.68 thf(fact_6996_ceiling__less__numeral,axiom,
% 5.44/5.68 ! [X: real,V: num] :
% 5.44/5.68 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.68 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_less_numeral
% 5.44/5.68 thf(fact_6997_numeral__le__ceiling,axiom,
% 5.44/5.68 ! [V: num,X: real] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_le_ceiling
% 5.44/5.68 thf(fact_6998_ceiling__le__neg__numeral,axiom,
% 5.44/5.68 ! [X: real,V: num] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.68 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_le_neg_numeral
% 5.44/5.68 thf(fact_6999_neg__numeral__less__ceiling,axiom,
% 5.44/5.68 ! [V: num,X: real] :
% 5.44/5.68 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % neg_numeral_less_ceiling
% 5.44/5.68 thf(fact_7000_cos__pi__half,axiom,
% 5.44/5.68 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_pi_half
% 5.44/5.68 thf(fact_7001_cos__two__pi,axiom,
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_two_pi
% 5.44/5.68 thf(fact_7002_cos__periodic,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.44/5.68 = ( cos_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_periodic
% 5.44/5.68 thf(fact_7003_cos__2pi__minus,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.44/5.68 = ( cos_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_2pi_minus
% 5.44/5.68 thf(fact_7004_cos__npi,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.44/5.68 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_npi
% 5.44/5.68 thf(fact_7005_cos__npi2,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.44/5.68 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_npi2
% 5.44/5.68 thf(fact_7006_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.44/5.68 ! [A: num,B: num] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.44/5.68 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_minus_divide_eq_div_numeral
% 5.44/5.68 thf(fact_7007_sin__cos__squared__add2,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_squared_add2
% 5.44/5.68 thf(fact_7008_sin__cos__squared__add2,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_complex ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_squared_add2
% 5.44/5.68 thf(fact_7009_sin__cos__squared__add,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_squared_add
% 5.44/5.68 thf(fact_7010_sin__cos__squared__add,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_complex ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_squared_add
% 5.44/5.68 thf(fact_7011_cos__2npi,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_2npi
% 5.44/5.68 thf(fact_7012_cos__int__2pin,axiom,
% 5.44/5.68 ! [N2: int] :
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_int_2pin
% 5.44/5.68 thf(fact_7013_ceiling__less__neg__numeral,axiom,
% 5.44/5.68 ! [X: real,V: num] :
% 5.44/5.68 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.68 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_less_neg_numeral
% 5.44/5.68 thf(fact_7014_neg__numeral__le__ceiling,axiom,
% 5.44/5.68 ! [V: num,X: real] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % neg_numeral_le_ceiling
% 5.44/5.68 thf(fact_7015_cos__3over2__pi,axiom,
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_3over2_pi
% 5.44/5.68 thf(fact_7016_cos__npi__int,axiom,
% 5.44/5.68 ! [N2: int] :
% 5.44/5.68 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.44/5.68 = one_one_real ) )
% 5.44/5.68 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.44/5.68 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_npi_int
% 5.44/5.68 thf(fact_7017_summable__comparison__test,axiom,
% 5.44/5.68 ! [F: nat > real,G: nat > real] :
% 5.44/5.68 ( ? [N7: nat] :
% 5.44/5.68 ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N7 @ N4 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N4 ) ) @ ( G @ N4 ) ) )
% 5.44/5.68 => ( ( summable_real @ G )
% 5.44/5.68 => ( summable_real @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_comparison_test
% 5.44/5.68 thf(fact_7018_summable__comparison__test,axiom,
% 5.44/5.68 ! [F: nat > complex,G: nat > real] :
% 5.44/5.68 ( ? [N7: nat] :
% 5.44/5.68 ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N7 @ N4 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N4 ) ) @ ( G @ N4 ) ) )
% 5.44/5.68 => ( ( summable_real @ G )
% 5.44/5.68 => ( summable_complex @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_comparison_test
% 5.44/5.68 thf(fact_7019_summable__comparison__test_H,axiom,
% 5.44/5.68 ! [G: nat > real,N3: nat,F: nat > real] :
% 5.44/5.68 ( ( summable_real @ G )
% 5.44/5.68 => ( ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N3 @ N4 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N4 ) ) @ ( G @ N4 ) ) )
% 5.44/5.68 => ( summable_real @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_comparison_test'
% 5.44/5.68 thf(fact_7020_summable__comparison__test_H,axiom,
% 5.44/5.68 ! [G: nat > real,N3: nat,F: nat > complex] :
% 5.44/5.68 ( ( summable_real @ G )
% 5.44/5.68 => ( ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N3 @ N4 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N4 ) ) @ ( G @ N4 ) ) )
% 5.44/5.68 => ( summable_complex @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_comparison_test'
% 5.44/5.68 thf(fact_7021_summable__add,axiom,
% 5.44/5.68 ! [F: nat > complex,G: nat > complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( ( summable_complex @ G )
% 5.44/5.68 => ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( plus_plus_complex @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_add
% 5.44/5.68 thf(fact_7022_summable__add,axiom,
% 5.44/5.68 ! [F: nat > real,G: nat > real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ( summable_real @ G )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_add
% 5.44/5.68 thf(fact_7023_summable__add,axiom,
% 5.44/5.68 ! [F: nat > nat,G: nat > nat] :
% 5.44/5.68 ( ( summable_nat @ F )
% 5.44/5.68 => ( ( summable_nat @ G )
% 5.44/5.68 => ( summable_nat
% 5.44/5.68 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_add
% 5.44/5.68 thf(fact_7024_summable__add,axiom,
% 5.44/5.68 ! [F: nat > int,G: nat > int] :
% 5.44/5.68 ( ( summable_int @ F )
% 5.44/5.68 => ( ( summable_int @ G )
% 5.44/5.68 => ( summable_int
% 5.44/5.68 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_add
% 5.44/5.68 thf(fact_7025_summable__ignore__initial__segment,axiom,
% 5.44/5.68 ! [F: nat > real,K: nat] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_ignore_initial_segment
% 5.44/5.68 thf(fact_7026_summable__Suc__iff,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.44/5.68 = ( summable_real @ F ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_Suc_iff
% 5.44/5.68 thf(fact_7027_summable__divide,axiom,
% 5.44/5.68 ! [F: nat > real,C: real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_divide
% 5.44/5.68 thf(fact_7028_summable__divide,axiom,
% 5.44/5.68 ! [F: nat > complex,C: complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_divide
% 5.44/5.68 thf(fact_7029_summable__mult,axiom,
% 5.44/5.68 ! [F: nat > complex,C: complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_mult
% 5.44/5.68 thf(fact_7030_summable__mult,axiom,
% 5.44/5.68 ! [F: nat > real,C: real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_mult
% 5.44/5.68 thf(fact_7031_summable__mult2,axiom,
% 5.44/5.68 ! [F: nat > complex,C: complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_mult2
% 5.44/5.68 thf(fact_7032_summable__mult2,axiom,
% 5.44/5.68 ! [F: nat > real,C: real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_mult2
% 5.44/5.68 thf(fact_7033_suminf__le,axiom,
% 5.44/5.68 ! [F: nat > real,G: nat > real] :
% 5.44/5.68 ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.44/5.68 => ( ( summable_real @ F )
% 5.44/5.68 => ( ( summable_real @ G )
% 5.44/5.68 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_le
% 5.44/5.68 thf(fact_7034_suminf__le,axiom,
% 5.44/5.68 ! [F: nat > nat,G: nat > nat] :
% 5.44/5.68 ( ! [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.44/5.68 => ( ( summable_nat @ F )
% 5.44/5.68 => ( ( summable_nat @ G )
% 5.44/5.68 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_le
% 5.44/5.68 thf(fact_7035_suminf__le,axiom,
% 5.44/5.68 ! [F: nat > int,G: nat > int] :
% 5.44/5.68 ( ! [N4: nat] : ( ord_less_eq_int @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.44/5.68 => ( ( summable_int @ F )
% 5.44/5.68 => ( ( summable_int @ G )
% 5.44/5.68 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_le
% 5.44/5.68 thf(fact_7036_summable__mult__D,axiom,
% 5.44/5.68 ! [C: complex,F: nat > complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 5.44/5.68 => ( ( C != zero_zero_complex )
% 5.44/5.68 => ( summable_complex @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_mult_D
% 5.44/5.68 thf(fact_7037_summable__mult__D,axiom,
% 5.44/5.68 ! [C: real,F: nat > real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 5.44/5.68 => ( ( C != zero_zero_real )
% 5.44/5.68 => ( summable_real @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_mult_D
% 5.44/5.68 thf(fact_7038_summable__zero__power,axiom,
% 5.44/5.68 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % summable_zero_power
% 5.44/5.68 thf(fact_7039_summable__zero__power,axiom,
% 5.44/5.68 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.44/5.68
% 5.44/5.68 % summable_zero_power
% 5.44/5.68 thf(fact_7040_summable__zero__power,axiom,
% 5.44/5.68 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.44/5.68
% 5.44/5.68 % summable_zero_power
% 5.44/5.68 thf(fact_7041_suminf__mult2,axiom,
% 5.44/5.68 ! [F: nat > complex,C: complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( ( times_times_complex @ ( suminf_complex @ F ) @ C )
% 5.44/5.68 = ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_mult2
% 5.44/5.68 thf(fact_7042_suminf__mult2,axiom,
% 5.44/5.68 ! [F: nat > real,C: real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.44/5.68 = ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_mult2
% 5.44/5.68 thf(fact_7043_suminf__mult,axiom,
% 5.44/5.68 ! [F: nat > complex,C: complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 5.44/5.68 = ( times_times_complex @ C @ ( suminf_complex @ F ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_mult
% 5.44/5.68 thf(fact_7044_suminf__mult,axiom,
% 5.44/5.68 ! [F: nat > real,C: real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 5.44/5.68 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_mult
% 5.44/5.68 thf(fact_7045_suminf__add,axiom,
% 5.44/5.68 ! [F: nat > complex,G: nat > complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( ( summable_complex @ G )
% 5.44/5.68 => ( ( plus_plus_complex @ ( suminf_complex @ F ) @ ( suminf_complex @ G ) )
% 5.44/5.68 = ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( plus_plus_complex @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_add
% 5.44/5.68 thf(fact_7046_suminf__add,axiom,
% 5.44/5.68 ! [F: nat > real,G: nat > real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ( summable_real @ G )
% 5.44/5.68 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.44/5.68 = ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_add
% 5.44/5.68 thf(fact_7047_suminf__add,axiom,
% 5.44/5.68 ! [F: nat > nat,G: nat > nat] :
% 5.44/5.68 ( ( summable_nat @ F )
% 5.44/5.68 => ( ( summable_nat @ G )
% 5.44/5.68 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.44/5.68 = ( suminf_nat
% 5.44/5.68 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_add
% 5.44/5.68 thf(fact_7048_suminf__add,axiom,
% 5.44/5.68 ! [F: nat > int,G: nat > int] :
% 5.44/5.68 ( ( summable_int @ F )
% 5.44/5.68 => ( ( summable_int @ G )
% 5.44/5.68 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.44/5.68 = ( suminf_int
% 5.44/5.68 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_add
% 5.44/5.68 thf(fact_7049_suminf__divide,axiom,
% 5.44/5.68 ! [F: nat > real,C: real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 5.44/5.68 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_divide
% 5.44/5.68 thf(fact_7050_suminf__divide,axiom,
% 5.44/5.68 ! [F: nat > complex,C: complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 5.44/5.68 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_divide
% 5.44/5.68 thf(fact_7051_powser__insidea,axiom,
% 5.44/5.68 ! [F: nat > real,X: real,Z: real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X @ N ) ) )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_insidea
% 5.44/5.68 thf(fact_7052_powser__insidea,axiom,
% 5.44/5.68 ! [F: nat > complex,X: complex,Z: complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X @ N ) ) )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_insidea
% 5.44/5.68 thf(fact_7053_suminf__nonneg,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N4 ) )
% 5.44/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_nonneg
% 5.44/5.68 thf(fact_7054_suminf__nonneg,axiom,
% 5.44/5.68 ! [F: nat > nat] :
% 5.44/5.68 ( ( summable_nat @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N4 ) )
% 5.44/5.68 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_nonneg
% 5.44/5.68 thf(fact_7055_suminf__nonneg,axiom,
% 5.44/5.68 ! [F: nat > int] :
% 5.44/5.68 ( ( summable_int @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N4 ) )
% 5.44/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_nonneg
% 5.44/5.68 thf(fact_7056_suminf__eq__zero__iff,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ( suminf_real @ F )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( ! [N: nat] :
% 5.44/5.68 ( ( F @ N )
% 5.44/5.68 = zero_zero_real ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_eq_zero_iff
% 5.44/5.68 thf(fact_7057_suminf__eq__zero__iff,axiom,
% 5.44/5.68 ! [F: nat > nat] :
% 5.44/5.68 ( ( summable_nat @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ( suminf_nat @ F )
% 5.44/5.68 = zero_zero_nat )
% 5.44/5.68 = ( ! [N: nat] :
% 5.44/5.68 ( ( F @ N )
% 5.44/5.68 = zero_zero_nat ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_eq_zero_iff
% 5.44/5.68 thf(fact_7058_suminf__eq__zero__iff,axiom,
% 5.44/5.68 ! [F: nat > int] :
% 5.44/5.68 ( ( summable_int @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ( suminf_int @ F )
% 5.44/5.68 = zero_zero_int )
% 5.44/5.68 = ( ! [N: nat] :
% 5.44/5.68 ( ( F @ N )
% 5.44/5.68 = zero_zero_int ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_eq_zero_iff
% 5.44/5.68 thf(fact_7059_suminf__pos,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N4 ) )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos
% 5.44/5.68 thf(fact_7060_suminf__pos,axiom,
% 5.44/5.68 ! [F: nat > nat] :
% 5.44/5.68 ( ( summable_nat @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N4 ) )
% 5.44/5.68 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos
% 5.44/5.68 thf(fact_7061_suminf__pos,axiom,
% 5.44/5.68 ! [F: nat > int] :
% 5.44/5.68 ( ( summable_int @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N4 ) )
% 5.44/5.68 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos
% 5.44/5.68 thf(fact_7062_ceiling__mono,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ Y @ X )
% 5.44/5.68 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_mono
% 5.44/5.68 thf(fact_7063_le__of__int__ceiling,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % le_of_int_ceiling
% 5.44/5.68 thf(fact_7064_ceiling__less__cancel,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) )
% 5.44/5.68 => ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_less_cancel
% 5.44/5.68 thf(fact_7065_cos__le__one,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_le_one
% 5.44/5.68 thf(fact_7066_summable__zero__power_H,axiom,
% 5.44/5.68 ! [F: nat > complex] :
% 5.44/5.68 ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_zero_power'
% 5.44/5.68 thf(fact_7067_summable__zero__power_H,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_zero_power'
% 5.44/5.68 thf(fact_7068_summable__zero__power_H,axiom,
% 5.44/5.68 ! [F: nat > int] :
% 5.44/5.68 ( summable_int
% 5.44/5.68 @ ^ [N: nat] : ( times_times_int @ ( F @ N ) @ ( power_power_int @ zero_zero_int @ N ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_zero_power'
% 5.44/5.68 thf(fact_7069_summable__0__powser,axiom,
% 5.44/5.68 ! [F: nat > complex] :
% 5.44/5.68 ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_0_powser
% 5.44/5.68 thf(fact_7070_summable__0__powser,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_0_powser
% 5.44/5.68 thf(fact_7071_summable__powser__split__head,axiom,
% 5.44/5.68 ! [F: nat > complex,Z: complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 = ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_powser_split_head
% 5.44/5.68 thf(fact_7072_summable__powser__split__head,axiom,
% 5.44/5.68 ! [F: nat > real,Z: real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 = ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_powser_split_head
% 5.44/5.68 thf(fact_7073_powser__split__head_I3_J,axiom,
% 5.44/5.68 ! [F: nat > complex,Z: complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 => ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_split_head(3)
% 5.44/5.68 thf(fact_7074_powser__split__head_I3_J,axiom,
% 5.44/5.68 ! [F: nat > real,Z: real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_split_head(3)
% 5.44/5.68 thf(fact_7075_summable__powser__ignore__initial__segment,axiom,
% 5.44/5.68 ! [F: nat > complex,M: nat,Z: complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 = ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_powser_ignore_initial_segment
% 5.44/5.68 thf(fact_7076_summable__powser__ignore__initial__segment,axiom,
% 5.44/5.68 ! [F: nat > real,M: nat,Z: real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 = ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_powser_ignore_initial_segment
% 5.44/5.68 thf(fact_7077_polar__Ex,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ? [R3: real,A3: real] :
% 5.44/5.68 ( ( X
% 5.44/5.68 = ( times_times_real @ R3 @ ( cos_real @ A3 ) ) )
% 5.44/5.68 & ( Y
% 5.44/5.68 = ( times_times_real @ R3 @ ( sin_real @ A3 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % polar_Ex
% 5.44/5.68 thf(fact_7078_summable__norm__comparison__test,axiom,
% 5.44/5.68 ! [F: nat > complex,G: nat > real] :
% 5.44/5.68 ( ? [N7: nat] :
% 5.44/5.68 ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N7 @ N4 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N4 ) ) @ ( G @ N4 ) ) )
% 5.44/5.68 => ( ( summable_real @ G )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_norm_comparison_test
% 5.44/5.68 thf(fact_7079_summable__rabs__comparison__test,axiom,
% 5.44/5.68 ! [F: nat > real,G: nat > real] :
% 5.44/5.68 ( ? [N7: nat] :
% 5.44/5.68 ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N7 @ N4 )
% 5.44/5.68 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N4 ) ) @ ( G @ N4 ) ) )
% 5.44/5.68 => ( ( summable_real @ G )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_rabs_comparison_test
% 5.44/5.68 thf(fact_7080_summable__rabs,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.44/5.68 @ ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_rabs
% 5.44/5.68 thf(fact_7081_suminf__pos__iff,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.44/5.68 = ( ? [I5: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I5 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos_iff
% 5.44/5.68 thf(fact_7082_suminf__pos__iff,axiom,
% 5.44/5.68 ! [F: nat > nat] :
% 5.44/5.68 ( ( summable_nat @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.44/5.68 = ( ? [I5: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I5 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos_iff
% 5.44/5.68 thf(fact_7083_suminf__pos__iff,axiom,
% 5.44/5.68 ! [F: nat > int] :
% 5.44/5.68 ( ( summable_int @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.44/5.68 = ( ? [I5: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I5 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos_iff
% 5.44/5.68 thf(fact_7084_suminf__pos2,axiom,
% 5.44/5.68 ! [F: nat > real,I2: nat] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos2
% 5.44/5.68 thf(fact_7085_suminf__pos2,axiom,
% 5.44/5.68 ! [F: nat > nat,I2: nat] :
% 5.44/5.68 ( ( summable_nat @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.44/5.68 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos2
% 5.44/5.68 thf(fact_7086_suminf__pos2,axiom,
% 5.44/5.68 ! [F: nat > int,I2: nat] :
% 5.44/5.68 ( ( summable_int @ F )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N4 ) )
% 5.44/5.68 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.44/5.68 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_pos2
% 5.44/5.68 thf(fact_7087_cos__one__sin__zero,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( ( cos_complex @ X )
% 5.44/5.68 = one_one_complex )
% 5.44/5.68 => ( ( sin_complex @ X )
% 5.44/5.68 = zero_zero_complex ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_one_sin_zero
% 5.44/5.68 thf(fact_7088_cos__one__sin__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( cos_real @ X )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 => ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_one_sin_zero
% 5.44/5.68 thf(fact_7089_sin__add,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] :
% 5.44/5.68 ( ( sin_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.68 = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_add
% 5.44/5.68 thf(fact_7090_sin__add,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( sin_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.68 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_add
% 5.44/5.68 thf(fact_7091_sin__diff,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] :
% 5.44/5.68 ( ( sin_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.44/5.68 = ( minus_minus_complex @ ( times_times_complex @ ( sin_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_diff
% 5.44/5.68 thf(fact_7092_sin__diff,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( sin_real @ ( minus_minus_real @ X @ Y ) )
% 5.44/5.68 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_diff
% 5.44/5.68 thf(fact_7093_summable__geometric,axiom,
% 5.44/5.68 ! [C: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.44/5.68 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_geometric
% 5.44/5.68 thf(fact_7094_summable__geometric,axiom,
% 5.44/5.68 ! [C: complex] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.44/5.68 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_geometric
% 5.44/5.68 thf(fact_7095_complete__algebra__summable__geometric,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ one_one_real )
% 5.44/5.68 => ( summable_real @ ( power_power_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % complete_algebra_summable_geometric
% 5.44/5.68 thf(fact_7096_complete__algebra__summable__geometric,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ one_one_real )
% 5.44/5.68 => ( summable_complex @ ( power_power_complex @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % complete_algebra_summable_geometric
% 5.44/5.68 thf(fact_7097_suminf__split__head,axiom,
% 5.44/5.68 ! [F: nat > complex] :
% 5.44/5.68 ( ( summable_complex @ F )
% 5.44/5.68 => ( ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.44/5.68 = ( minus_minus_complex @ ( suminf_complex @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_split_head
% 5.44/5.68 thf(fact_7098_suminf__split__head,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( summable_real @ F )
% 5.44/5.68 => ( ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.44/5.68 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_split_head
% 5.44/5.68 thf(fact_7099_ceiling__le__iff,axiom,
% 5.44/5.68 ! [X: real,Z: int] :
% 5.44/5.68 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 5.44/5.68 = ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_le_iff
% 5.44/5.68 thf(fact_7100_ceiling__le,axiom,
% 5.44/5.68 ! [X: real,A: int] :
% 5.44/5.68 ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 5.44/5.68 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_le
% 5.44/5.68 thf(fact_7101_less__ceiling__iff,axiom,
% 5.44/5.68 ! [Z: int,X: real] :
% 5.44/5.68 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % less_ceiling_iff
% 5.44/5.68 thf(fact_7102_ceiling__add__le,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_add_le
% 5.44/5.68 thf(fact_7103_cos__inj__pi,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ pi )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ pi )
% 5.44/5.68 => ( ( ( cos_real @ X )
% 5.44/5.68 = ( cos_real @ Y ) )
% 5.44/5.68 => ( X = Y ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_inj_pi
% 5.44/5.68 thf(fact_7104_cos__mono__le__eq,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ pi )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ pi )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.44/5.68 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_mono_le_eq
% 5.44/5.68 thf(fact_7105_cos__monotone__0__pi__le,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ pi )
% 5.44/5.68 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_monotone_0_pi_le
% 5.44/5.68 thf(fact_7106_cos__ge__minus__one,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_ge_minus_one
% 5.44/5.68 thf(fact_7107_abs__cos__le__one,axiom,
% 5.44/5.68 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % abs_cos_le_one
% 5.44/5.68 thf(fact_7108_summable__norm,axiom,
% 5.44/5.68 ! [F: nat > real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 5.44/5.68 @ ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_norm
% 5.44/5.68 thf(fact_7109_summable__norm,axiom,
% 5.44/5.68 ! [F: nat > complex] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 5.44/5.68 @ ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_norm
% 5.44/5.68 thf(fact_7110_cos__diff,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] :
% 5.44/5.68 ( ( cos_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.44/5.68 = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_diff
% 5.44/5.68 thf(fact_7111_cos__diff,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.44/5.68 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_diff
% 5.44/5.68 thf(fact_7112_cos__add,axiom,
% 5.44/5.68 ! [X: complex,Y: complex] :
% 5.44/5.68 ( ( cos_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.68 = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_add
% 5.44/5.68 thf(fact_7113_cos__add,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.68 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_add
% 5.44/5.68 thf(fact_7114_sin__zero__norm__cos__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 5.44/5.68 = one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_zero_norm_cos_one
% 5.44/5.68 thf(fact_7115_sin__zero__norm__cos__one,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( ( sin_complex @ X )
% 5.44/5.68 = zero_zero_complex )
% 5.44/5.68 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 5.44/5.68 = one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_zero_norm_cos_one
% 5.44/5.68 thf(fact_7116_of__int__ceiling__le__add__one,axiom,
% 5.44/5.68 ! [R: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ ( plus_plus_real @ R @ one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % of_int_ceiling_le_add_one
% 5.44/5.68 thf(fact_7117_of__int__ceiling__diff__one__le,axiom,
% 5.44/5.68 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ one_one_real ) @ R ) ).
% 5.44/5.68
% 5.44/5.68 % of_int_ceiling_diff_one_le
% 5.44/5.68 thf(fact_7118_cos__two__neq__zero,axiom,
% 5.44/5.68 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.68 != zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % cos_two_neq_zero
% 5.44/5.68 thf(fact_7119_powser__inside,axiom,
% 5.44/5.68 ! [F: nat > real,X: real,Z: real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X @ N ) ) )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_inside
% 5.44/5.68 thf(fact_7120_powser__inside,axiom,
% 5.44/5.68 ! [F: nat > complex,X: complex,Z: complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X @ N ) ) )
% 5.44/5.68 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.44/5.68 => ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_inside
% 5.44/5.68 thf(fact_7121_cos__monotone__0__pi,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_real @ Y @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ pi )
% 5.44/5.68 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_monotone_0_pi
% 5.44/5.68 thf(fact_7122_cos__mono__less__eq,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ pi )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ pi )
% 5.44/5.68 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.44/5.68 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_mono_less_eq
% 5.44/5.68 thf(fact_7123_cos__monotone__minus__pi__0_H,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.68 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_monotone_minus_pi_0'
% 5.44/5.68 thf(fact_7124_ceiling__divide__eq__div,axiom,
% 5.44/5.68 ! [A: int,B: int] :
% 5.44/5.68 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.44/5.68 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_divide_eq_div
% 5.44/5.68 thf(fact_7125_sin__zero__abs__cos__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( sin_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 => ( ( abs_abs_real @ ( cos_real @ X ) )
% 5.44/5.68 = one_one_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_zero_abs_cos_one
% 5.44/5.68 thf(fact_7126_powser__split__head_I1_J,axiom,
% 5.44/5.68 ! [F: nat > complex,Z: complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 => ( ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.44/5.68 @ ( times_times_complex
% 5.44/5.68 @ ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 @ Z ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_split_head(1)
% 5.44/5.68 thf(fact_7127_powser__split__head_I1_J,axiom,
% 5.44/5.68 ! [F: nat > real,Z: real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 => ( ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.44/5.68 @ ( times_times_real
% 5.44/5.68 @ ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 @ Z ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_split_head(1)
% 5.44/5.68 thf(fact_7128_powser__split__head_I2_J,axiom,
% 5.44/5.68 ! [F: nat > complex,Z: complex] :
% 5.44/5.68 ( ( summable_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 => ( ( times_times_complex
% 5.44/5.68 @ ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 @ Z )
% 5.44/5.68 = ( minus_minus_complex
% 5.44/5.68 @ ( suminf_complex
% 5.44/5.68 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.44/5.68 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_split_head(2)
% 5.44/5.68 thf(fact_7129_powser__split__head_I2_J,axiom,
% 5.44/5.68 ! [F: nat > real,Z: real] :
% 5.44/5.68 ( ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 => ( ( times_times_real
% 5.44/5.68 @ ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 @ Z )
% 5.44/5.68 = ( minus_minus_real
% 5.44/5.68 @ ( suminf_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.44/5.68 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powser_split_head(2)
% 5.44/5.68 thf(fact_7130_suminf__exist__split,axiom,
% 5.44/5.68 ! [R: real,F: nat > real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ R )
% 5.44/5.68 => ( ( summable_real @ F )
% 5.44/5.68 => ? [N8: nat] :
% 5.44/5.68 ! [N9: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N8 @ N9 )
% 5.44/5.68 => ( ord_less_real
% 5.44/5.68 @ ( real_V7735802525324610683m_real
% 5.44/5.68 @ ( suminf_real
% 5.44/5.68 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N9 ) ) ) )
% 5.44/5.68 @ R ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_exist_split
% 5.44/5.68 thf(fact_7131_suminf__exist__split,axiom,
% 5.44/5.68 ! [R: real,F: nat > complex] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ R )
% 5.44/5.68 => ( ( summable_complex @ F )
% 5.44/5.68 => ? [N8: nat] :
% 5.44/5.68 ! [N9: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N8 @ N9 )
% 5.44/5.68 => ( ord_less_real
% 5.44/5.68 @ ( real_V1022390504157884413omplex
% 5.44/5.68 @ ( suminf_complex
% 5.44/5.68 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N9 ) ) ) )
% 5.44/5.68 @ R ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % suminf_exist_split
% 5.44/5.68 thf(fact_7132_summable__power__series,axiom,
% 5.44/5.68 ! [F: nat > real,Z: real] :
% 5.44/5.68 ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 5.44/5.68 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.44/5.68 => ( ( ord_less_real @ Z @ one_one_real )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [I5: nat] : ( times_times_real @ ( F @ I5 ) @ ( power_power_real @ Z @ I5 ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_power_series
% 5.44/5.68 thf(fact_7133_Abel__lemma,axiom,
% 5.44/5.68 ! [R: real,R0: real,A: nat > complex,M7: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.44/5.68 => ( ( ord_less_real @ R @ R0 )
% 5.44/5.68 => ( ! [N4: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N4 ) ) @ ( power_power_real @ R0 @ N4 ) ) @ M7 )
% 5.44/5.68 => ( summable_real
% 5.44/5.68 @ ^ [N: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R @ N ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % Abel_lemma
% 5.44/5.68 thf(fact_7134_sin__double,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.68 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_double
% 5.44/5.68 thf(fact_7135_sin__double,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.68 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_double
% 5.44/5.68 thf(fact_7136_ceiling__correct,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 5.44/5.68 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_correct
% 5.44/5.68 thf(fact_7137_ceiling__unique,axiom,
% 5.44/5.68 ! [Z: int,X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) )
% 5.44/5.68 => ( ( archim7802044766580827645g_real @ X )
% 5.44/5.68 = Z ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_unique
% 5.44/5.68 thf(fact_7138_ceiling__eq__iff,axiom,
% 5.44/5.68 ! [X: real,A: int] :
% 5.44/5.68 ( ( ( archim7802044766580827645g_real @ X )
% 5.44/5.68 = A )
% 5.44/5.68 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 5.44/5.68 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_eq_iff
% 5.44/5.68 thf(fact_7139_ceiling__split,axiom,
% 5.44/5.68 ! [P: int > $o,T: real] :
% 5.44/5.68 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.44/5.68 = ( ! [I5: int] :
% 5.44/5.68 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I5 ) @ one_one_real ) @ T )
% 5.44/5.68 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I5 ) ) )
% 5.44/5.68 => ( P @ I5 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_split
% 5.44/5.68 thf(fact_7140_summable__ratio__test,axiom,
% 5.44/5.68 ! [C: real,N3: nat,F: nat > real] :
% 5.44/5.68 ( ( ord_less_real @ C @ one_one_real )
% 5.44/5.68 => ( ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N3 @ N4 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N4 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N4 ) ) ) ) )
% 5.44/5.68 => ( summable_real @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_ratio_test
% 5.44/5.68 thf(fact_7141_summable__ratio__test,axiom,
% 5.44/5.68 ! [C: real,N3: nat,F: nat > complex] :
% 5.44/5.68 ( ( ord_less_real @ C @ one_one_real )
% 5.44/5.68 => ( ! [N4: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ N3 @ N4 )
% 5.44/5.68 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N4 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N4 ) ) ) ) )
% 5.44/5.68 => ( summable_complex @ F ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % summable_ratio_test
% 5.44/5.68 thf(fact_7142_mult__ceiling__le,axiom,
% 5.44/5.68 ! [A: real,B: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.68 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % mult_ceiling_le
% 5.44/5.68 thf(fact_7143_ceiling__less__iff,axiom,
% 5.44/5.68 ! [X: real,Z: int] :
% 5.44/5.68 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 5.44/5.68 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_less_iff
% 5.44/5.68 thf(fact_7144_le__ceiling__iff,axiom,
% 5.44/5.68 ! [Z: int,X: real] :
% 5.44/5.68 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 5.44/5.68 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % le_ceiling_iff
% 5.44/5.68 thf(fact_7145_cos__two__less__zero,axiom,
% 5.44/5.68 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.44/5.68
% 5.44/5.68 % cos_two_less_zero
% 5.44/5.68 thf(fact_7146_cos__is__zero,axiom,
% 5.44/5.68 ? [X5: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.44/5.68 & ( ord_less_eq_real @ X5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.68 & ( ( cos_real @ X5 )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 & ! [Y2: real] :
% 5.44/5.68 ( ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.44/5.68 & ( ord_less_eq_real @ Y2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.68 & ( ( cos_real @ Y2 )
% 5.44/5.68 = zero_zero_real ) )
% 5.44/5.68 => ( Y2 = X5 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_is_zero
% 5.44/5.68 thf(fact_7147_cos__two__le__zero,axiom,
% 5.44/5.68 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.44/5.68
% 5.44/5.68 % cos_two_le_zero
% 5.44/5.68 thf(fact_7148_cos__monotone__minus__pi__0,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.44/5.68 => ( ( ord_less_real @ Y @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.68 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_monotone_minus_pi_0
% 5.44/5.68 thf(fact_7149_cos__total,axiom,
% 5.44/5.68 ! [Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.68 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.68 => ? [X5: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.44/5.68 & ( ord_less_eq_real @ X5 @ pi )
% 5.44/5.68 & ( ( cos_real @ X5 )
% 5.44/5.68 = Y )
% 5.44/5.68 & ! [Y2: real] :
% 5.44/5.68 ( ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.44/5.68 & ( ord_less_eq_real @ Y2 @ pi )
% 5.44/5.68 & ( ( cos_real @ Y2 )
% 5.44/5.68 = Y ) )
% 5.44/5.68 => ( Y2 = X5 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_total
% 5.44/5.68 thf(fact_7150_sincos__principal__value,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ? [Y5: real] :
% 5.44/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y5 )
% 5.44/5.68 & ( ord_less_eq_real @ Y5 @ pi )
% 5.44/5.68 & ( ( sin_real @ Y5 )
% 5.44/5.68 = ( sin_real @ X ) )
% 5.44/5.68 & ( ( cos_real @ Y5 )
% 5.44/5.68 = ( cos_real @ X ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sincos_principal_value
% 5.44/5.68 thf(fact_7151_ceiling__divide__upper,axiom,
% 5.44/5.68 ! [Q2: real,P5: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.44/5.68 => ( ord_less_eq_real @ P5 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P5 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_divide_upper
% 5.44/5.68 thf(fact_7152_cos__45,axiom,
% 5.44/5.68 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_45
% 5.44/5.68 thf(fact_7153_sin__cos__le1,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_le1
% 5.44/5.68 thf(fact_7154_cos__times__cos,axiom,
% 5.44/5.68 ! [W: real,Z: real] :
% 5.44/5.68 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_times_cos
% 5.44/5.68 thf(fact_7155_cos__times__cos,axiom,
% 5.44/5.68 ! [W: complex,Z: complex] :
% 5.44/5.68 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.44/5.68 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_times_cos
% 5.44/5.68 thf(fact_7156_cos__plus__cos,axiom,
% 5.44/5.68 ! [W: real,Z: real] :
% 5.44/5.68 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_plus_cos
% 5.44/5.68 thf(fact_7157_cos__plus__cos,axiom,
% 5.44/5.68 ! [W: complex,Z: complex] :
% 5.44/5.68 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_plus_cos
% 5.44/5.68 thf(fact_7158_sin__squared__eq,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_squared_eq
% 5.44/5.68 thf(fact_7159_sin__squared__eq,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_squared_eq
% 5.44/5.68 thf(fact_7160_cos__squared__eq,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_squared_eq
% 5.44/5.68 thf(fact_7161_cos__squared__eq,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.68 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_squared_eq
% 5.44/5.68 thf(fact_7162_ceiling__divide__lower,axiom,
% 5.44/5.68 ! [Q2: real,P5: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.44/5.68 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P5 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) @ P5 ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_divide_lower
% 5.44/5.68 thf(fact_7163_ceiling__eq,axiom,
% 5.44/5.68 ! [N2: int,X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.44/5.68 => ( ( archim7802044766580827645g_real @ X )
% 5.44/5.68 = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_eq
% 5.44/5.68 thf(fact_7164_cos__double__less__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.68 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_double_less_one
% 5.44/5.68 thf(fact_7165_cos__gt__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_gt_zero
% 5.44/5.68 thf(fact_7166_cos__60,axiom,
% 5.44/5.68 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.44/5.68 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_60
% 5.44/5.68 thf(fact_7167_cos__30,axiom,
% 5.44/5.68 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.44/5.68 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_30
% 5.44/5.68 thf(fact_7168_cos__one__2pi__int,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( cos_real @ X )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 = ( ? [X2: int] :
% 5.44/5.68 ( X
% 5.44/5.68 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_one_2pi_int
% 5.44/5.68 thf(fact_7169_cos__double__cos,axiom,
% 5.44/5.68 ! [W: complex] :
% 5.44/5.68 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.44/5.68 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_double_cos
% 5.44/5.68 thf(fact_7170_cos__double__cos,axiom,
% 5.44/5.68 ! [W: real] :
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.44/5.68 = ( 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 ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_double_cos
% 5.44/5.68 thf(fact_7171_cos__treble__cos,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 5.44/5.68 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_treble_cos
% 5.44/5.68 thf(fact_7172_cos__treble__cos,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 5.44/5.68 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_treble_cos
% 5.44/5.68 thf(fact_7173_sin__times__sin,axiom,
% 5.44/5.68 ! [W: real,Z: real] :
% 5.44/5.68 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_times_sin
% 5.44/5.68 thf(fact_7174_sin__times__sin,axiom,
% 5.44/5.68 ! [W: complex,Z: complex] :
% 5.44/5.68 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.44/5.68 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_times_sin
% 5.44/5.68 thf(fact_7175_sin__times__cos,axiom,
% 5.44/5.68 ! [W: real,Z: real] :
% 5.44/5.68 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_times_cos
% 5.44/5.68 thf(fact_7176_sin__times__cos,axiom,
% 5.44/5.68 ! [W: complex,Z: complex] :
% 5.44/5.68 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.44/5.68 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_times_cos
% 5.44/5.68 thf(fact_7177_cos__times__sin,axiom,
% 5.44/5.68 ! [W: real,Z: real] :
% 5.44/5.68 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_times_sin
% 5.44/5.68 thf(fact_7178_cos__times__sin,axiom,
% 5.44/5.68 ! [W: complex,Z: complex] :
% 5.44/5.68 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.44/5.68 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_times_sin
% 5.44/5.68 thf(fact_7179_sin__plus__sin,axiom,
% 5.44/5.68 ! [W: real,Z: real] :
% 5.44/5.68 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_plus_sin
% 5.44/5.68 thf(fact_7180_sin__plus__sin,axiom,
% 5.44/5.68 ! [W: complex,Z: complex] :
% 5.44/5.68 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_plus_sin
% 5.44/5.68 thf(fact_7181_sin__diff__sin,axiom,
% 5.44/5.68 ! [W: real,Z: real] :
% 5.44/5.68 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_diff_sin
% 5.44/5.68 thf(fact_7182_sin__diff__sin,axiom,
% 5.44/5.68 ! [W: complex,Z: complex] :
% 5.44/5.68 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_diff_sin
% 5.44/5.68 thf(fact_7183_cos__diff__cos,axiom,
% 5.44/5.68 ! [W: real,Z: real] :
% 5.44/5.68 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_diff_cos
% 5.44/5.68 thf(fact_7184_cos__diff__cos,axiom,
% 5.44/5.68 ! [W: complex,Z: complex] :
% 5.44/5.68 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_diff_cos
% 5.44/5.68 thf(fact_7185_cos__double,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.68 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_double
% 5.44/5.68 thf(fact_7186_cos__double,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.68 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_double
% 5.44/5.68 thf(fact_7187_cos__gt__zero__pi,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_gt_zero_pi
% 5.44/5.68 thf(fact_7188_cos__ge__zero,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_ge_zero
% 5.44/5.68 thf(fact_7189_cos__one__2pi,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( cos_real @ X )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 = ( ? [X2: nat] :
% 5.44/5.68 ( X
% 5.44/5.68 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.44/5.68 | ? [X2: nat] :
% 5.44/5.68 ( X
% 5.44/5.68 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_one_2pi
% 5.44/5.68 thf(fact_7190_cos__double__sin,axiom,
% 5.44/5.68 ! [W: complex] :
% 5.44/5.68 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.44/5.68 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_double_sin
% 5.44/5.68 thf(fact_7191_cos__double__sin,axiom,
% 5.44/5.68 ! [W: real] :
% 5.44/5.68 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.44/5.68 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_double_sin
% 5.44/5.68 thf(fact_7192_cos__arctan,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( cos_real @ ( arctan @ X ) )
% 5.44/5.68 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_arctan
% 5.44/5.68 thf(fact_7193_sincos__total__pi,axiom,
% 5.44/5.68 ! [Y: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 => ? [T4: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.44/5.68 & ( ord_less_eq_real @ T4 @ pi )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( cos_real @ T4 ) )
% 5.44/5.68 & ( Y
% 5.44/5.68 = ( sin_real @ T4 ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sincos_total_pi
% 5.44/5.68 thf(fact_7194_sin__cos__sqrt,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 5.44/5.68 => ( ( sin_real @ X )
% 5.44/5.68 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_cos_sqrt
% 5.44/5.68 thf(fact_7195_sin__expansion__lemma,axiom,
% 5.44/5.68 ! [X: real,M: nat] :
% 5.44/5.68 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_expansion_lemma
% 5.44/5.68 thf(fact_7196_cos__zero__iff__int,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( cos_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( ? [I5: int] :
% 5.44/5.68 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_zero_iff_int
% 5.44/5.68 thf(fact_7197_cos__zero__lemma,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ( cos_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 => ? [N4: nat] :
% 5.44/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_zero_lemma
% 5.44/5.68 thf(fact_7198_cos__zero__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( cos_real @ X )
% 5.44/5.68 = zero_zero_real )
% 5.44/5.68 = ( ? [N: nat] :
% 5.44/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.68 | ? [N: nat] :
% 5.44/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_zero_iff
% 5.44/5.68 thf(fact_7199_cos__expansion__lemma,axiom,
% 5.44/5.68 ! [X: real,M: nat] :
% 5.44/5.68 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.44/5.68 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_expansion_lemma
% 5.44/5.68 thf(fact_7200_sincos__total__pi__half,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.68 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 => ? [T4: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.44/5.68 & ( ord_less_eq_real @ T4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( cos_real @ T4 ) )
% 5.44/5.68 & ( Y
% 5.44/5.68 = ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sincos_total_pi_half
% 5.44/5.68 thf(fact_7201_sincos__total__2pi__le,axiom,
% 5.44/5.68 ! [X: real,Y: real] :
% 5.44/5.68 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 => ? [T4: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.44/5.68 & ( ord_less_eq_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.44/5.68 & ( X
% 5.44/5.68 = ( cos_real @ T4 ) )
% 5.44/5.68 & ( Y
% 5.44/5.68 = ( sin_real @ T4 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sincos_total_2pi_le
% 5.44/5.68 thf(fact_7202_ceiling__log__nat__eq__if,axiom,
% 5.44/5.68 ! [B: nat,N2: nat,K: nat] :
% 5.44/5.68 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.44/5.68 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.44/5.68 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.44/5.68 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_log_nat_eq_if
% 5.44/5.68 thf(fact_7203_ceiling__log2__div2,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.68 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.44/5.68 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_log2_div2
% 5.44/5.68 thf(fact_7204_tan__double,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( cos_real @ X )
% 5.44/5.68 != zero_zero_real )
% 5.44/5.68 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.68 != zero_zero_real )
% 5.44/5.68 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.68 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % tan_double
% 5.44/5.68 thf(fact_7205_tan__double,axiom,
% 5.44/5.68 ! [X: complex] :
% 5.44/5.68 ( ( ( cos_complex @ X )
% 5.44/5.68 != zero_zero_complex )
% 5.44/5.68 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.68 != zero_zero_complex )
% 5.44/5.68 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.68 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % tan_double
% 5.44/5.68 thf(fact_7206_sin__tan,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( sin_real @ X )
% 5.44/5.68 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % sin_tan
% 5.44/5.68 thf(fact_7207_cos__tan,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 => ( ( cos_real @ X )
% 5.44/5.68 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % cos_tan
% 5.44/5.68 thf(fact_7208_complex__unimodular__polar,axiom,
% 5.44/5.68 ! [Z: complex] :
% 5.44/5.68 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 => ~ ! [T4: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.44/5.68 => ( ( ord_less_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.44/5.68 => ( Z
% 5.44/5.68 != ( complex2 @ ( cos_real @ T4 ) @ ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % complex_unimodular_polar
% 5.44/5.68 thf(fact_7209_ceiling__log__eq__powr__iff,axiom,
% 5.44/5.68 ! [X: real,B: real,K: nat] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.68 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 5.44/5.68 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.44/5.68 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 5.44/5.68 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % ceiling_log_eq_powr_iff
% 5.44/5.68 thf(fact_7210_powr__one__eq__one,axiom,
% 5.44/5.68 ! [A: real] :
% 5.44/5.68 ( ( powr_real @ one_one_real @ A )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % powr_one_eq_one
% 5.44/5.68 thf(fact_7211_powr__zero__eq__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( X = zero_zero_real )
% 5.44/5.68 => ( ( powr_real @ X @ zero_zero_real )
% 5.44/5.68 = zero_zero_real ) )
% 5.44/5.68 & ( ( X != zero_zero_real )
% 5.44/5.68 => ( ( powr_real @ X @ zero_zero_real )
% 5.44/5.68 = one_one_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_zero_eq_one
% 5.44/5.68 thf(fact_7212_powr__gt__zero,axiom,
% 5.44/5.68 ! [X: real,A: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 5.44/5.68 = ( X != zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_gt_zero
% 5.44/5.68 thf(fact_7213_powr__nonneg__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 5.44/5.68 = ( A = zero_zero_real ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_nonneg_iff
% 5.44/5.68 thf(fact_7214_powr__less__cancel__iff,axiom,
% 5.44/5.68 ! [X: real,A: real,B: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.44/5.68 = ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_less_cancel_iff
% 5.44/5.68 thf(fact_7215_tan__periodic__pi,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 5.44/5.68 = ( tan_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % tan_periodic_pi
% 5.44/5.68 thf(fact_7216_powr__eq__one__iff,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ A )
% 5.44/5.68 => ( ( ( powr_real @ A @ X )
% 5.44/5.68 = one_one_real )
% 5.44/5.68 = ( X = zero_zero_real ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_eq_one_iff
% 5.44/5.68 thf(fact_7217_powr__one,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( powr_real @ X @ one_one_real )
% 5.44/5.68 = X ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_one
% 5.44/5.68 thf(fact_7218_powr__one__gt__zero__iff,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( ( powr_real @ X @ one_one_real )
% 5.44/5.68 = X )
% 5.44/5.68 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_one_gt_zero_iff
% 5.44/5.68 thf(fact_7219_powr__le__cancel__iff,axiom,
% 5.44/5.68 ! [X: real,A: real,B: real] :
% 5.44/5.68 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.44/5.68 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_le_cancel_iff
% 5.44/5.68 thf(fact_7220_numeral__powr__numeral__real,axiom,
% 5.44/5.68 ! [M: num,N2: num] :
% 5.44/5.68 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.68 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % numeral_powr_numeral_real
% 5.44/5.68 thf(fact_7221_log__powr__cancel,axiom,
% 5.44/5.68 ! [A: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( A != one_one_real )
% 5.44/5.68 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 5.44/5.68 = Y ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % log_powr_cancel
% 5.44/5.68 thf(fact_7222_powr__log__cancel,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( A != one_one_real )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 5.44/5.68 = X ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_log_cancel
% 5.44/5.68 thf(fact_7223_tan__npi,axiom,
% 5.44/5.68 ! [N2: nat] :
% 5.44/5.68 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.44/5.68 = zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % tan_npi
% 5.44/5.68 thf(fact_7224_tan__periodic__n,axiom,
% 5.44/5.68 ! [X: real,N2: num] :
% 5.44/5.68 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N2 ) @ pi ) ) )
% 5.44/5.68 = ( tan_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % tan_periodic_n
% 5.44/5.68 thf(fact_7225_tan__periodic__nat,axiom,
% 5.44/5.68 ! [X: real,N2: nat] :
% 5.44/5.68 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) ) )
% 5.44/5.68 = ( tan_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % tan_periodic_nat
% 5.44/5.68 thf(fact_7226_tan__periodic__int,axiom,
% 5.44/5.68 ! [X: real,I2: int] :
% 5.44/5.68 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 5.44/5.68 = ( tan_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % tan_periodic_int
% 5.44/5.68 thf(fact_7227_norm__cos__sin,axiom,
% 5.44/5.68 ! [T: real] :
% 5.44/5.68 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.44/5.68 = one_one_real ) ).
% 5.44/5.68
% 5.44/5.68 % norm_cos_sin
% 5.44/5.68 thf(fact_7228_powr__numeral,axiom,
% 5.44/5.68 ! [X: real,N2: num] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( powr_real @ X @ ( numeral_numeral_real @ N2 ) )
% 5.44/5.68 = ( power_power_real @ X @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_numeral
% 5.44/5.68 thf(fact_7229_tan__periodic,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.44/5.68 = ( tan_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % tan_periodic
% 5.44/5.68 thf(fact_7230_square__powr__half,axiom,
% 5.44/5.68 ! [X: real] :
% 5.44/5.68 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.68 = ( abs_abs_real @ X ) ) ).
% 5.44/5.68
% 5.44/5.68 % square_powr_half
% 5.44/5.68 thf(fact_7231_powr__powr,axiom,
% 5.44/5.68 ! [X: real,A: real,B: real] :
% 5.44/5.68 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.44/5.68 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_powr
% 5.44/5.68 thf(fact_7232_powr__non__neg,axiom,
% 5.44/5.68 ! [A: real,X: real] :
% 5.44/5.68 ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 5.44/5.68
% 5.44/5.68 % powr_non_neg
% 5.44/5.68 thf(fact_7233_powr__less__mono2__neg,axiom,
% 5.44/5.68 ! [A: real,X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_real @ X @ Y )
% 5.44/5.68 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_less_mono2_neg
% 5.44/5.68 thf(fact_7234_powr__ge__pzero,axiom,
% 5.44/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_ge_pzero
% 5.44/5.68 thf(fact_7235_powr__mono2,axiom,
% 5.44/5.68 ! [A: real,X: real,Y: real] :
% 5.44/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.68 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.68 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_mono2
% 5.44/5.68 thf(fact_7236_powr__less__mono,axiom,
% 5.44/5.68 ! [A: real,B: real,X: real] :
% 5.44/5.68 ( ( ord_less_real @ A @ B )
% 5.44/5.68 => ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.68 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.44/5.68
% 5.44/5.68 % powr_less_mono
% 5.44/5.68 thf(fact_7237_powr__less__cancel,axiom,
% 5.44/5.68 ! [X: real,A: real,B: real] :
% 5.44/5.68 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.44/5.69 => ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.69 => ( ord_less_real @ A @ B ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_less_cancel
% 5.44/5.69 thf(fact_7238_powr__mono,axiom,
% 5.44/5.69 ! [A: real,B: real,X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.69 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.44/5.69 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_mono
% 5.44/5.69 thf(fact_7239_one__complex_Ocode,axiom,
% 5.44/5.69 ( one_one_complex
% 5.44/5.69 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % one_complex.code
% 5.44/5.69 thf(fact_7240_Complex__eq__1,axiom,
% 5.44/5.69 ! [A: real,B: real] :
% 5.44/5.69 ( ( ( complex2 @ A @ B )
% 5.44/5.69 = one_one_complex )
% 5.44/5.69 = ( ( A = one_one_real )
% 5.44/5.69 & ( B = zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % Complex_eq_1
% 5.44/5.69 thf(fact_7241_Complex__eq__numeral,axiom,
% 5.44/5.69 ! [A: real,B: real,W: num] :
% 5.44/5.69 ( ( ( complex2 @ A @ B )
% 5.44/5.69 = ( numera6690914467698888265omplex @ W ) )
% 5.44/5.69 = ( ( A
% 5.44/5.69 = ( numeral_numeral_real @ W ) )
% 5.44/5.69 & ( B = zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % Complex_eq_numeral
% 5.44/5.69 thf(fact_7242_complex__add,axiom,
% 5.44/5.69 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.69 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.44/5.69 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % complex_add
% 5.44/5.69 thf(fact_7243_powr__mono2_H,axiom,
% 5.44/5.69 ! [A: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.69 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_mono2'
% 5.44/5.69 thf(fact_7244_powr__less__mono2,axiom,
% 5.44/5.69 ! [A: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ Y )
% 5.44/5.69 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_less_mono2
% 5.44/5.69 thf(fact_7245_powr__inj,axiom,
% 5.44/5.69 ! [A: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.69 => ( ( A != one_one_real )
% 5.44/5.69 => ( ( ( powr_real @ A @ X )
% 5.44/5.69 = ( powr_real @ A @ Y ) )
% 5.44/5.69 = ( X = Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_inj
% 5.44/5.69 thf(fact_7246_gr__one__powr,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.69 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % gr_one_powr
% 5.44/5.69 thf(fact_7247_powr__le1,axiom,
% 5.44/5.69 ! [A: real,X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.69 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_le1
% 5.44/5.69 thf(fact_7248_powr__mono__both,axiom,
% 5.44/5.69 ! [A: real,B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.69 => ( ( ord_less_eq_real @ A @ B )
% 5.44/5.69 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.69 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_mono_both
% 5.44/5.69 thf(fact_7249_ge__one__powr__ge__zero,axiom,
% 5.44/5.69 ! [X: real,A: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.69 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % ge_one_powr_ge_zero
% 5.44/5.69 thf(fact_7250_powr__divide,axiom,
% 5.44/5.69 ! [X: real,Y: real,A: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.69 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 5.44/5.69 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_divide
% 5.44/5.69 thf(fact_7251_powr__mult,axiom,
% 5.44/5.69 ! [X: real,Y: real,A: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.69 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 5.44/5.69 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_mult
% 5.44/5.69 thf(fact_7252_divide__powr__uminus,axiom,
% 5.44/5.69 ! [A: real,B: real,C: real] :
% 5.44/5.69 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.44/5.69 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % divide_powr_uminus
% 5.44/5.69 thf(fact_7253_log__base__powr,axiom,
% 5.44/5.69 ! [A: real,B: real,X: real] :
% 5.44/5.69 ( ( A != zero_zero_real )
% 5.44/5.69 => ( ( log @ ( powr_real @ A @ B ) @ X )
% 5.44/5.69 = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % log_base_powr
% 5.44/5.69 thf(fact_7254_ln__powr,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( X != zero_zero_real )
% 5.44/5.69 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 5.44/5.69 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % ln_powr
% 5.44/5.69 thf(fact_7255_log__powr,axiom,
% 5.44/5.69 ! [X: real,B: real,Y: real] :
% 5.44/5.69 ( ( X != zero_zero_real )
% 5.44/5.69 => ( ( log @ B @ ( powr_real @ X @ Y ) )
% 5.44/5.69 = ( times_times_real @ Y @ ( log @ B @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % log_powr
% 5.44/5.69 thf(fact_7256_Complex__eq__neg__1,axiom,
% 5.44/5.69 ! [A: real,B: real] :
% 5.44/5.69 ( ( ( complex2 @ A @ B )
% 5.44/5.69 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.44/5.69 = ( ( A
% 5.44/5.69 = ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.69 & ( B = zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % Complex_eq_neg_1
% 5.44/5.69 thf(fact_7257_Complex__eq__neg__numeral,axiom,
% 5.44/5.69 ! [A: real,B: real,W: num] :
% 5.44/5.69 ( ( ( complex2 @ A @ B )
% 5.44/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.69 = ( ( A
% 5.44/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.69 & ( B = zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % Complex_eq_neg_numeral
% 5.44/5.69 thf(fact_7258_powr__add,axiom,
% 5.44/5.69 ! [X: real,A: real,B: real] :
% 5.44/5.69 ( ( powr_real @ X @ ( plus_plus_real @ A @ B ) )
% 5.44/5.69 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_add
% 5.44/5.69 thf(fact_7259_powr__diff,axiom,
% 5.44/5.69 ! [W: real,Z1: real,Z22: real] :
% 5.44/5.69 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.44/5.69 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_diff
% 5.44/5.69 thf(fact_7260_complex__mult,axiom,
% 5.44/5.69 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.69 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.44/5.69 = ( 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 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % complex_mult
% 5.44/5.69 thf(fact_7261_tan__def,axiom,
% 5.44/5.69 ( tan_real
% 5.44/5.69 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_def
% 5.44/5.69 thf(fact_7262_tan__def,axiom,
% 5.44/5.69 ( tan_complex
% 5.44/5.69 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_def
% 5.44/5.69 thf(fact_7263_powr__realpow,axiom,
% 5.44/5.69 ! [X: real,N2: nat] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.44/5.69 = ( power_power_real @ X @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_realpow
% 5.44/5.69 thf(fact_7264_powr__less__iff,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 5.44/5.69 = ( ord_less_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_less_iff
% 5.44/5.69 thf(fact_7265_less__powr__iff,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 5.44/5.69 = ( ord_less_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % less_powr_iff
% 5.44/5.69 thf(fact_7266_log__less__iff,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ ( log @ B @ X ) @ Y )
% 5.44/5.69 = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % log_less_iff
% 5.44/5.69 thf(fact_7267_less__log__iff,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ Y @ ( log @ B @ X ) )
% 5.44/5.69 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % less_log_iff
% 5.44/5.69 thf(fact_7268_powr__minus__divide,axiom,
% 5.44/5.69 ! [X: real,A: real] :
% 5.44/5.69 ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 5.44/5.69 = ( divide_divide_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_minus_divide
% 5.44/5.69 thf(fact_7269_powr__neg__one,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.69 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_neg_one
% 5.44/5.69 thf(fact_7270_powr__mult__base,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 5.44/5.69 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_mult_base
% 5.44/5.69 thf(fact_7271_le__log__iff,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 5.44/5.69 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % le_log_iff
% 5.44/5.69 thf(fact_7272_log__le__iff,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 5.44/5.69 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % log_le_iff
% 5.44/5.69 thf(fact_7273_le__powr__iff,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 5.44/5.69 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % le_powr_iff
% 5.44/5.69 thf(fact_7274_powr__le__iff,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 5.44/5.69 = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_le_iff
% 5.44/5.69 thf(fact_7275_ln__powr__bound,axiom,
% 5.44/5.69 ! [X: real,A: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.69 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % ln_powr_bound
% 5.44/5.69 thf(fact_7276_ln__powr__bound2,axiom,
% 5.44/5.69 ! [X: real,A: real] :
% 5.44/5.69 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.69 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % ln_powr_bound2
% 5.44/5.69 thf(fact_7277_tan__45,axiom,
% 5.44/5.69 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.44/5.69 = one_one_real ) ).
% 5.44/5.69
% 5.44/5.69 % tan_45
% 5.44/5.69 thf(fact_7278_log__add__eq__powr,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.69 => ( ( B != one_one_real )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 5.44/5.69 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % log_add_eq_powr
% 5.44/5.69 thf(fact_7279_add__log__eq__powr,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.69 => ( ( B != one_one_real )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 5.44/5.69 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % add_log_eq_powr
% 5.44/5.69 thf(fact_7280_minus__log__eq__powr,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.69 => ( ( B != one_one_real )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 5.44/5.69 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % minus_log_eq_powr
% 5.44/5.69 thf(fact_7281_tan__60,axiom,
% 5.44/5.69 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.44/5.69 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_60
% 5.44/5.69 thf(fact_7282_powr__def,axiom,
% 5.44/5.69 ( powr_real
% 5.44/5.69 = ( ^ [X2: real,A4: real] : ( if_real @ ( X2 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A4 @ ( ln_ln_real @ X2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_def
% 5.44/5.69 thf(fact_7283_lemma__tan__total,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.44/5.69 => ? [X5: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.44/5.69 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 & ( ord_less_real @ Y @ ( tan_real @ X5 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lemma_tan_total
% 5.44/5.69 thf(fact_7284_tan__gt__zero,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_gt_zero
% 5.44/5.69 thf(fact_7285_tan__total,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ? [X5: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.44/5.69 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 & ( ( tan_real @ X5 )
% 5.44/5.69 = Y )
% 5.44/5.69 & ! [Y2: real] :
% 5.44/5.69 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.44/5.69 & ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 & ( ( tan_real @ Y2 )
% 5.44/5.69 = Y ) )
% 5.44/5.69 => ( Y2 = X5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_total
% 5.44/5.69 thf(fact_7286_tan__monotone,axiom,
% 5.44/5.69 ! [Y: real,X: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.69 => ( ( ord_less_real @ Y @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_monotone
% 5.44/5.69 thf(fact_7287_tan__monotone_H,axiom,
% 5.44/5.69 ! [Y: real,X: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.69 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ord_less_real @ Y @ X )
% 5.44/5.69 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_monotone'
% 5.44/5.69 thf(fact_7288_tan__mono__lt__eq,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.69 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.44/5.69 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_mono_lt_eq
% 5.44/5.69 thf(fact_7289_lemma__tan__total1,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ? [X5: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.44/5.69 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 & ( ( tan_real @ X5 )
% 5.44/5.69 = Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % lemma_tan_total1
% 5.44/5.69 thf(fact_7290_tan__minus__45,axiom,
% 5.44/5.69 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.69 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_minus_45
% 5.44/5.69 thf(fact_7291_tan__inverse,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.44/5.69 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_inverse
% 5.44/5.69 thf(fact_7292_log__minus__eq__powr,axiom,
% 5.44/5.69 ! [B: real,X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.69 => ( ( B != one_one_real )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 5.44/5.69 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % log_minus_eq_powr
% 5.44/5.69 thf(fact_7293_complex__norm,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y ) )
% 5.44/5.69 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % complex_norm
% 5.44/5.69 thf(fact_7294_add__tan__eq,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ( cos_real @ X )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( ( cos_real @ Y )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.44/5.69 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % add_tan_eq
% 5.44/5.69 thf(fact_7295_add__tan__eq,axiom,
% 5.44/5.69 ! [X: complex,Y: complex] :
% 5.44/5.69 ( ( ( cos_complex @ X )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( ( cos_complex @ Y )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % add_tan_eq
% 5.44/5.69 thf(fact_7296_powr__half__sqrt,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 = ( sqrt @ X ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_half_sqrt
% 5.44/5.69 thf(fact_7297_powr__neg__numeral,axiom,
% 5.44/5.69 ! [X: real,N2: num] :
% 5.44/5.69 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.44/5.69 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % powr_neg_numeral
% 5.44/5.69 thf(fact_7298_tan__total__pos,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.69 => ? [X5: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.44/5.69 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 & ( ( tan_real @ X5 )
% 5.44/5.69 = Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_total_pos
% 5.44/5.69 thf(fact_7299_tan__pos__pi2__le,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_pos_pi2_le
% 5.44/5.69 thf(fact_7300_tan__less__zero,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.69 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_less_zero
% 5.44/5.69 thf(fact_7301_tan__mono__le__eq,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.44/5.69 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.44/5.69 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_mono_le_eq
% 5.44/5.69 thf(fact_7302_tan__mono__le,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.69 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_mono_le
% 5.44/5.69 thf(fact_7303_tan__bound__pi2,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.44/5.69 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_bound_pi2
% 5.44/5.69 thf(fact_7304_tan__30,axiom,
% 5.44/5.69 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.44/5.69 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_30
% 5.44/5.69 thf(fact_7305_arctan__unique,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ( tan_real @ X )
% 5.44/5.69 = Y )
% 5.44/5.69 => ( ( arctan @ Y )
% 5.44/5.69 = X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arctan_unique
% 5.44/5.69 thf(fact_7306_arctan__tan,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( arctan @ ( tan_real @ X ) )
% 5.44/5.69 = X ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arctan_tan
% 5.44/5.69 thf(fact_7307_arctan,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.44/5.69 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 & ( ( tan_real @ ( arctan @ Y ) )
% 5.44/5.69 = Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % arctan
% 5.44/5.69 thf(fact_7308_tan__add,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ( cos_real @ X )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( ( cos_real @ Y )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( tan_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.69 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_add
% 5.44/5.69 thf(fact_7309_tan__add,axiom,
% 5.44/5.69 ! [X: complex,Y: complex] :
% 5.44/5.69 ( ( ( cos_complex @ X )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( ( cos_complex @ Y )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( tan_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_add
% 5.44/5.69 thf(fact_7310_tan__diff,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ( cos_real @ X )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( ( cos_real @ Y )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( tan_real @ ( minus_minus_real @ X @ Y ) )
% 5.44/5.69 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_diff
% 5.44/5.69 thf(fact_7311_tan__diff,axiom,
% 5.44/5.69 ! [X: complex,Y: complex] :
% 5.44/5.69 ( ( ( cos_complex @ X )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( ( cos_complex @ Y )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( tan_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_diff
% 5.44/5.69 thf(fact_7312_lemma__tan__add1,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ( cos_real @ X )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( ( cos_real @ Y )
% 5.44/5.69 != zero_zero_real )
% 5.44/5.69 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) )
% 5.44/5.69 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lemma_tan_add1
% 5.44/5.69 thf(fact_7313_lemma__tan__add1,axiom,
% 5.44/5.69 ! [X: complex,Y: complex] :
% 5.44/5.69 ( ( ( cos_complex @ X )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( ( cos_complex @ Y )
% 5.44/5.69 != zero_zero_complex )
% 5.44/5.69 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lemma_tan_add1
% 5.44/5.69 thf(fact_7314_tan__total__pi4,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.69 => ? [Z4: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z4 )
% 5.44/5.69 & ( ord_less_real @ Z4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.44/5.69 & ( ( tan_real @ Z4 )
% 5.44/5.69 = X ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_total_pi4
% 5.44/5.69 thf(fact_7315_tan__half,axiom,
% 5.44/5.69 ( tan_real
% 5.44/5.69 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_half
% 5.44/5.69 thf(fact_7316_tan__half,axiom,
% 5.44/5.69 ( tan_complex
% 5.44/5.69 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_complex ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % tan_half
% 5.44/5.69 thf(fact_7317_arcosh__def,axiom,
% 5.44/5.69 ( arcosh_real
% 5.44/5.69 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcosh_def
% 5.44/5.69 thf(fact_7318_cos__arcsin,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.69 => ( ( cos_real @ ( arcsin @ X ) )
% 5.44/5.69 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_arcsin
% 5.44/5.69 thf(fact_7319_sum__gp,axiom,
% 5.44/5.69 ! [N2: nat,M: nat,X: complex] :
% 5.44/5.69 ( ( ( ord_less_nat @ N2 @ M )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.44/5.69 => ( ( ( X = one_one_complex )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.44/5.69 & ( ( X != one_one_complex )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_gp
% 5.44/5.69 thf(fact_7320_sum__gp,axiom,
% 5.44/5.69 ! [N2: nat,M: nat,X: real] :
% 5.44/5.69 ( ( ( ord_less_nat @ N2 @ M )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.44/5.69 => ( ( ( X = one_one_real )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.44/5.69 & ( ( X != one_one_real )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_gp
% 5.44/5.69 thf(fact_7321_sin__arccos__abs,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.44/5.69 => ( ( sin_real @ ( arccos @ Y ) )
% 5.44/5.69 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sin_arccos_abs
% 5.44/5.69 thf(fact_7322_sin__arccos,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.69 => ( ( sin_real @ ( arccos @ X ) )
% 5.44/5.69 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sin_arccos
% 5.44/5.69 thf(fact_7323_of__real__1,axiom,
% 5.44/5.69 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.44/5.69 = one_one_real ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_1
% 5.44/5.69 thf(fact_7324_of__real__1,axiom,
% 5.44/5.69 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.44/5.69 = one_one_complex ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_1
% 5.44/5.69 thf(fact_7325_of__real__eq__1__iff,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ( real_V1803761363581548252l_real @ X )
% 5.44/5.69 = one_one_real )
% 5.44/5.69 = ( X = one_one_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_eq_1_iff
% 5.44/5.69 thf(fact_7326_of__real__eq__1__iff,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ( real_V4546457046886955230omplex @ X )
% 5.44/5.69 = one_one_complex )
% 5.44/5.69 = ( X = one_one_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_eq_1_iff
% 5.44/5.69 thf(fact_7327_of__real__mult,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X @ Y ) )
% 5.44/5.69 = ( times_times_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_mult
% 5.44/5.69 thf(fact_7328_of__real__mult,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X @ Y ) )
% 5.44/5.69 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_mult
% 5.44/5.69 thf(fact_7329_of__real__numeral,axiom,
% 5.44/5.69 ! [W: num] :
% 5.44/5.69 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.69 = ( numeral_numeral_real @ W ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_numeral
% 5.44/5.69 thf(fact_7330_of__real__numeral,axiom,
% 5.44/5.69 ! [W: num] :
% 5.44/5.69 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.44/5.69 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_numeral
% 5.44/5.69 thf(fact_7331_of__real__divide,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.69 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_divide
% 5.44/5.69 thf(fact_7332_of__real__divide,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_divide
% 5.44/5.69 thf(fact_7333_of__real__power,axiom,
% 5.44/5.69 ! [X: real,N2: nat] :
% 5.44/5.69 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X @ N2 ) )
% 5.44/5.69 = ( power_power_real @ ( real_V1803761363581548252l_real @ X ) @ N2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_power
% 5.44/5.69 thf(fact_7334_of__real__power,axiom,
% 5.44/5.69 ! [X: real,N2: nat] :
% 5.44/5.69 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X @ N2 ) )
% 5.44/5.69 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X ) @ N2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_power
% 5.44/5.69 thf(fact_7335_of__real__add,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.69 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_add
% 5.44/5.69 thf(fact_7336_of__real__add,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.69 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_add
% 5.44/5.69 thf(fact_7337_arccos__1,axiom,
% 5.44/5.69 ( ( arccos @ one_one_real )
% 5.44/5.69 = zero_zero_real ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_1
% 5.44/5.69 thf(fact_7338_sum__abs,axiom,
% 5.44/5.69 ! [F: nat > real,A2: set_nat] :
% 5.44/5.69 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.44/5.69 @ ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_abs
% 5.44/5.69 thf(fact_7339_sum__abs,axiom,
% 5.44/5.69 ! [F: int > int,A2: set_int] :
% 5.44/5.69 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.44/5.69 @ ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_abs
% 5.44/5.69 thf(fact_7340_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ~ ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups5754745047067104278omplex @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7341_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > complex] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ~ ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups3049146728041665814omplex @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups3049146728041665814omplex @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7342_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_nat,X: nat,G: nat > complex] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ~ ( member_nat @ X @ A2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups2073611262835488442omplex @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7343_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ~ ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7344_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ~ ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7345_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ~ ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7346_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ~ ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7347_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ~ ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7348_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_complex,X: complex,G: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ~ ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7349_sum_Oinsert,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > int] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ~ ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_int @ ( G @ X ) @ ( groups1932886352136224148al_int @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert
% 5.44/5.69 thf(fact_7350_arccos__minus__1,axiom,
% 5.44/5.69 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.69 = pi ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_minus_1
% 5.44/5.69 thf(fact_7351_sum__abs__ge__zero,axiom,
% 5.44/5.69 ! [F: nat > real,A2: set_nat] :
% 5.44/5.69 ( ord_less_eq_real @ zero_zero_real
% 5.44/5.69 @ ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_abs_ge_zero
% 5.44/5.69 thf(fact_7352_sum__abs__ge__zero,axiom,
% 5.44/5.69 ! [F: int > int,A2: set_int] :
% 5.44/5.69 ( ord_less_eq_int @ zero_zero_int
% 5.44/5.69 @ ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_abs_ge_zero
% 5.44/5.69 thf(fact_7353_of__real__neg__numeral,axiom,
% 5.44/5.69 ! [W: num] :
% 5.44/5.69 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_neg_numeral
% 5.44/5.69 thf(fact_7354_of__real__neg__numeral,axiom,
% 5.44/5.69 ! [W: num] :
% 5.44/5.69 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % of_real_neg_numeral
% 5.44/5.69 thf(fact_7355_cos__of__real__pi,axiom,
% 5.44/5.69 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.44/5.69 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_of_real_pi
% 5.44/5.69 thf(fact_7356_cos__of__real__pi,axiom,
% 5.44/5.69 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.44/5.69 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_of_real_pi
% 5.44/5.69 thf(fact_7357_cos__arccos,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( cos_real @ ( arccos @ Y ) )
% 5.44/5.69 = Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_arccos
% 5.44/5.69 thf(fact_7358_sin__arcsin,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.44/5.69 = Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sin_arcsin
% 5.44/5.69 thf(fact_7359_sum_Ocl__ivl__Suc,axiom,
% 5.44/5.69 ! [N2: nat,M: nat,G: nat > extended_enat] :
% 5.44/5.69 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_p3455044024723400733d_enat @ ( groups7108830773950497114d_enat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.cl_ivl_Suc
% 5.44/5.69 thf(fact_7360_sum_Ocl__ivl__Suc,axiom,
% 5.44/5.69 ! [N2: nat,M: nat,G: nat > complex] :
% 5.44/5.69 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.cl_ivl_Suc
% 5.44/5.69 thf(fact_7361_sum_Ocl__ivl__Suc,axiom,
% 5.44/5.69 ! [N2: nat,M: nat,G: nat > int] :
% 5.44/5.69 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.cl_ivl_Suc
% 5.44/5.69 thf(fact_7362_sum_Ocl__ivl__Suc,axiom,
% 5.44/5.69 ! [N2: nat,M: nat,G: nat > nat] :
% 5.44/5.69 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.cl_ivl_Suc
% 5.44/5.69 thf(fact_7363_sum_Ocl__ivl__Suc,axiom,
% 5.44/5.69 ! [N2: nat,M: nat,G: nat > real] :
% 5.44/5.69 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.cl_ivl_Suc
% 5.44/5.69 thf(fact_7364_sum__zero__power,axiom,
% 5.44/5.69 ! [A2: set_nat,C: nat > complex] :
% 5.44/5.69 ( ( ( ( finite_finite_nat @ A2 )
% 5.44/5.69 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.69 => ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = ( C @ zero_zero_nat ) ) )
% 5.44/5.69 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.44/5.69 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.69 => ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = zero_zero_complex ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_zero_power
% 5.44/5.69 thf(fact_7365_sum__zero__power,axiom,
% 5.44/5.69 ! [A2: set_nat,C: nat > real] :
% 5.44/5.69 ( ( ( ( finite_finite_nat @ A2 )
% 5.44/5.69 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.69 => ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = ( C @ zero_zero_nat ) ) )
% 5.44/5.69 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.44/5.69 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.69 => ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_zero_power
% 5.44/5.69 thf(fact_7366_norm__of__real__add1,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ one_one_real ) )
% 5.44/5.69 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_of_real_add1
% 5.44/5.69 thf(fact_7367_norm__of__real__add1,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ one_one_complex ) )
% 5.44/5.69 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_of_real_add1
% 5.44/5.69 thf(fact_7368_norm__of__real__addn,axiom,
% 5.44/5.69 ! [X: real,B: num] :
% 5.44/5.69 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( numeral_numeral_real @ B ) ) )
% 5.44/5.69 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_of_real_addn
% 5.44/5.69 thf(fact_7369_norm__of__real__addn,axiom,
% 5.44/5.69 ! [X: real,B: num] :
% 5.44/5.69 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( numera6690914467698888265omplex @ B ) ) )
% 5.44/5.69 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_of_real_addn
% 5.44/5.69 thf(fact_7370_arccos__0,axiom,
% 5.44/5.69 ( ( arccos @ zero_zero_real )
% 5.44/5.69 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_0
% 5.44/5.69 thf(fact_7371_arcsin__1,axiom,
% 5.44/5.69 ( ( arcsin @ one_one_real )
% 5.44/5.69 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_1
% 5.44/5.69 thf(fact_7372_sum__zero__power_H,axiom,
% 5.44/5.69 ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 5.44/5.69 ( ( ( ( finite_finite_nat @ A2 )
% 5.44/5.69 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.69 => ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.44/5.69 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.44/5.69 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.69 => ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = zero_zero_complex ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_zero_power'
% 5.44/5.69 thf(fact_7373_sum__zero__power_H,axiom,
% 5.44/5.69 ! [A2: set_nat,C: nat > real,D: nat > real] :
% 5.44/5.69 ( ( ( ( finite_finite_nat @ A2 )
% 5.44/5.69 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.69 => ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.44/5.69 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.44/5.69 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.69 => ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_zero_power'
% 5.44/5.69 thf(fact_7374_cos__of__real__pi__half,axiom,
% 5.44/5.69 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 = zero_zero_real ) ).
% 5.44/5.69
% 5.44/5.69 % cos_of_real_pi_half
% 5.44/5.69 thf(fact_7375_cos__of__real__pi__half,axiom,
% 5.44/5.69 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.44/5.69 = zero_zero_complex ) ).
% 5.44/5.69
% 5.44/5.69 % cos_of_real_pi_half
% 5.44/5.69 thf(fact_7376_sin__of__real__pi__half,axiom,
% 5.44/5.69 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 = one_one_real ) ).
% 5.44/5.69
% 5.44/5.69 % sin_of_real_pi_half
% 5.44/5.69 thf(fact_7377_sin__of__real__pi__half,axiom,
% 5.44/5.69 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.44/5.69 = one_one_complex ) ).
% 5.44/5.69
% 5.44/5.69 % sin_of_real_pi_half
% 5.44/5.69 thf(fact_7378_arcsin__minus__1,axiom,
% 5.44/5.69 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.44/5.69 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_minus_1
% 5.44/5.69 thf(fact_7379_norm__sum,axiom,
% 5.44/5.69 ! [F: nat > complex,A2: set_nat] :
% 5.44/5.69 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 5.44/5.69 @ ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_sum
% 5.44/5.69 thf(fact_7380_norm__sum,axiom,
% 5.44/5.69 ! [F: complex > complex,A2: set_complex] :
% 5.44/5.69 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.44/5.69 @ ( groups5808333547571424918x_real
% 5.44/5.69 @ ^ [I5: complex] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_sum
% 5.44/5.69 thf(fact_7381_norm__sum,axiom,
% 5.44/5.69 ! [F: nat > real,A2: set_nat] :
% 5.44/5.69 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.44/5.69 @ ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( real_V7735802525324610683m_real @ ( F @ I5 ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_sum
% 5.44/5.69 thf(fact_7382_sum__norm__le,axiom,
% 5.44/5.69 ! [S: set_real,F: real > complex,G: real > real] :
% 5.44/5.69 ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ S )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S ) ) @ ( groups8097168146408367636l_real @ G @ S ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_norm_le
% 5.44/5.69 thf(fact_7383_sum__norm__le,axiom,
% 5.44/5.69 ! [S: set_int,F: int > complex,G: int > real] :
% 5.44/5.69 ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S ) ) @ ( groups8778361861064173332t_real @ G @ S ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_norm_le
% 5.44/5.69 thf(fact_7384_sum__norm__le,axiom,
% 5.44/5.69 ! [S: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 5.44/5.69 ( ! [X5: product_prod_nat_nat] :
% 5.44/5.69 ( ( member8440522571783428010at_nat @ X5 @ S )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S ) ) @ ( groups4567486121110086003t_real @ G @ S ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_norm_le
% 5.44/5.69 thf(fact_7385_sum__norm__le,axiom,
% 5.44/5.69 ! [S: set_nat,F: nat > complex,G: nat > real] :
% 5.44/5.69 ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S ) ) @ ( groups6591440286371151544t_real @ G @ S ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_norm_le
% 5.44/5.69 thf(fact_7386_sum__norm__le,axiom,
% 5.44/5.69 ! [S: set_complex,F: complex > complex,G: complex > real] :
% 5.44/5.69 ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S ) ) @ ( groups5808333547571424918x_real @ G @ S ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_norm_le
% 5.44/5.69 thf(fact_7387_sum__norm__le,axiom,
% 5.44/5.69 ! [S: set_nat,F: nat > real,G: nat > real] :
% 5.44/5.69 ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S ) ) @ ( groups6591440286371151544t_real @ G @ S ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_norm_le
% 5.44/5.69 thf(fact_7388_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.44/5.69 ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7389_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.44/5.69 ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7390_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.44/5.69 ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7391_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.44/5.69 ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7392_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_real,F: real > int,G: real > int] :
% 5.44/5.69 ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7393_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.44/5.69 ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7394_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_nat,F: nat > nat,G: nat > nat] :
% 5.44/5.69 ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K5 ) @ ( groups3542108847815614940at_nat @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7395_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_nat,F: nat > real,G: nat > real] :
% 5.44/5.69 ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ K5 ) @ ( groups6591440286371151544t_real @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7396_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_int,F: int > int,G: int > int] :
% 5.44/5.69 ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7397_sum__mono,axiom,
% 5.44/5.69 ! [K5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat,G: product_prod_nat_nat > nat] :
% 5.44/5.69 ( ! [I4: product_prod_nat_nat] :
% 5.44/5.69 ( ( member8440522571783428010at_nat @ I4 @ K5 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups977919841031483927at_nat @ F @ K5 ) @ ( groups977919841031483927at_nat @ G @ K5 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono
% 5.44/5.69 thf(fact_7398_sum__product,axiom,
% 5.44/5.69 ! [F: nat > nat,A2: set_nat,G: nat > nat,B2: set_nat] :
% 5.44/5.69 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B2 ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] :
% 5.44/5.69 ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.44/5.69 @ B2 )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_product
% 5.44/5.69 thf(fact_7399_sum__product,axiom,
% 5.44/5.69 ! [F: complex > complex,A2: set_complex,G: complex > complex,B2: set_complex] :
% 5.44/5.69 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B2 ) )
% 5.44/5.69 = ( groups7754918857620584856omplex
% 5.44/5.69 @ ^ [I5: complex] :
% 5.44/5.69 ( groups7754918857620584856omplex
% 5.44/5.69 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.44/5.69 @ B2 )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_product
% 5.44/5.69 thf(fact_7400_sum__product,axiom,
% 5.44/5.69 ! [F: nat > real,A2: set_nat,G: nat > real,B2: set_nat] :
% 5.44/5.69 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B2 ) )
% 5.44/5.69 = ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] :
% 5.44/5.69 ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [J3: nat] : ( times_times_real @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.44/5.69 @ B2 )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_product
% 5.44/5.69 thf(fact_7401_sum__product,axiom,
% 5.44/5.69 ! [F: int > int,A2: set_int,G: int > int,B2: set_int] :
% 5.44/5.69 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B2 ) )
% 5.44/5.69 = ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [I5: int] :
% 5.44/5.69 ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [J3: int] : ( times_times_int @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.44/5.69 @ B2 )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_product
% 5.44/5.69 thf(fact_7402_sum__distrib__right,axiom,
% 5.44/5.69 ! [F: nat > nat,A2: set_nat,R: nat] :
% 5.44/5.69 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
% 5.44/5.69 = ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [N: nat] : ( times_times_nat @ ( F @ N ) @ R )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_distrib_right
% 5.44/5.69 thf(fact_7403_sum__distrib__right,axiom,
% 5.44/5.69 ! [F: complex > complex,A2: set_complex,R: complex] :
% 5.44/5.69 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 5.44/5.69 = ( groups7754918857620584856omplex
% 5.44/5.69 @ ^ [N: complex] : ( times_times_complex @ ( F @ N ) @ R )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_distrib_right
% 5.44/5.69 thf(fact_7404_sum__distrib__right,axiom,
% 5.44/5.69 ! [F: nat > real,A2: set_nat,R: real] :
% 5.44/5.69 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 5.44/5.69 = ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ R )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_distrib_right
% 5.44/5.69 thf(fact_7405_sum__distrib__right,axiom,
% 5.44/5.69 ! [F: int > int,A2: set_int,R: int] :
% 5.44/5.69 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R )
% 5.44/5.69 = ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [N: int] : ( times_times_int @ ( F @ N ) @ R )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_distrib_right
% 5.44/5.69 thf(fact_7406_sum__distrib__left,axiom,
% 5.44/5.69 ! [R: nat,F: nat > nat,A2: set_nat] :
% 5.44/5.69 ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [N: nat] : ( times_times_nat @ R @ ( F @ N ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_distrib_left
% 5.44/5.69 thf(fact_7407_sum__distrib__left,axiom,
% 5.44/5.69 ! [R: complex,F: complex > complex,A2: set_complex] :
% 5.44/5.69 ( ( times_times_complex @ R @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.44/5.69 = ( groups7754918857620584856omplex
% 5.44/5.69 @ ^ [N: complex] : ( times_times_complex @ R @ ( F @ N ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_distrib_left
% 5.44/5.69 thf(fact_7408_sum__distrib__left,axiom,
% 5.44/5.69 ! [R: real,F: nat > real,A2: set_nat] :
% 5.44/5.69 ( ( times_times_real @ R @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.44/5.69 = ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [N: nat] : ( times_times_real @ R @ ( F @ N ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_distrib_left
% 5.44/5.69 thf(fact_7409_sum__distrib__left,axiom,
% 5.44/5.69 ! [R: int,F: int > int,A2: set_int] :
% 5.44/5.69 ( ( times_times_int @ R @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.44/5.69 = ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [N: int] : ( times_times_int @ R @ ( F @ N ) )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_distrib_left
% 5.44/5.69 thf(fact_7410_sum_Odistrib,axiom,
% 5.44/5.69 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.distrib
% 5.44/5.69 thf(fact_7411_sum_Odistrib,axiom,
% 5.44/5.69 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.44/5.69 ( ( groups7754918857620584856omplex
% 5.44/5.69 @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.distrib
% 5.44/5.69 thf(fact_7412_sum_Odistrib,axiom,
% 5.44/5.69 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.44/5.69 ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.distrib
% 5.44/5.69 thf(fact_7413_sum_Odistrib,axiom,
% 5.44/5.69 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.44/5.69 ( ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.44/5.69 @ A2 )
% 5.44/5.69 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.distrib
% 5.44/5.69 thf(fact_7414_sum__divide__distrib,axiom,
% 5.44/5.69 ! [F: complex > complex,A2: set_complex,R: complex] :
% 5.44/5.69 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 5.44/5.69 = ( groups7754918857620584856omplex
% 5.44/5.69 @ ^ [N: complex] : ( divide1717551699836669952omplex @ ( F @ N ) @ R )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_divide_distrib
% 5.44/5.69 thf(fact_7415_sum__divide__distrib,axiom,
% 5.44/5.69 ! [F: nat > real,A2: set_nat,R: real] :
% 5.44/5.69 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 5.44/5.69 = ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ R )
% 5.44/5.69 @ A2 ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_divide_distrib
% 5.44/5.69 thf(fact_7416_mod__sum__eq,axiom,
% 5.44/5.69 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.44/5.69 ( ( modulo_modulo_nat
% 5.44/5.69 @ ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( modulo_modulo_nat @ ( F @ I5 ) @ A )
% 5.44/5.69 @ A2 )
% 5.44/5.69 @ A )
% 5.44/5.69 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.44/5.69
% 5.44/5.69 % mod_sum_eq
% 5.44/5.69 thf(fact_7417_mod__sum__eq,axiom,
% 5.44/5.69 ! [F: int > int,A: int,A2: set_int] :
% 5.44/5.69 ( ( modulo_modulo_int
% 5.44/5.69 @ ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [I5: int] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 5.44/5.69 @ A2 )
% 5.44/5.69 @ A )
% 5.44/5.69 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.44/5.69
% 5.44/5.69 % mod_sum_eq
% 5.44/5.69 thf(fact_7418_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > extended_enat] :
% 5.44/5.69 ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( groups7108830773950497114d_enat @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7419_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > extended_enat] :
% 5.44/5.69 ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( groups2800946370649118462d_enat @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7420_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > extended_enat] :
% 5.44/5.69 ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( groups4225252721152677374d_enat @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7421_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > extended_enat] :
% 5.44/5.69 ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( groups1752964319039525884d_enat @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7422_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > real] :
% 5.44/5.69 ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7423_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > real] :
% 5.44/5.69 ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7424_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > real] :
% 5.44/5.69 ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7425_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > nat] :
% 5.44/5.69 ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7426_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > nat] :
% 5.44/5.69 ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7427_sum__nonneg,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > nat] :
% 5.44/5.69 ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg
% 5.44/5.69 thf(fact_7428_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > extended_enat] :
% 5.44/5.69 ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups7108830773950497114d_enat @ F @ A2 ) @ zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7429_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > extended_enat] :
% 5.44/5.69 ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups2800946370649118462d_enat @ F @ A2 ) @ zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7430_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > extended_enat] :
% 5.44/5.69 ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups4225252721152677374d_enat @ F @ A2 ) @ zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7431_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > extended_enat] :
% 5.44/5.69 ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ A2 ) @ zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7432_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > real] :
% 5.44/5.69 ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7433_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > real] :
% 5.44/5.69 ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7434_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > real] :
% 5.44/5.69 ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7435_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > nat] :
% 5.44/5.69 ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7436_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > nat] :
% 5.44/5.69 ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7437_sum__nonpos,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > nat] :
% 5.44/5.69 ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonpos
% 5.44/5.69 thf(fact_7438_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: real > nat,I6: set_real,G: real > nat,I2: real] :
% 5.44/5.69 ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 5.44/5.69 = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_real @ I2 @ I6 )
% 5.44/5.69 => ( ( finite_finite_real @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7439_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: int > nat,I6: set_int,G: int > nat,I2: int] :
% 5.44/5.69 ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_int @ I2 @ I6 )
% 5.44/5.69 => ( ( finite_finite_int @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7440_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: complex > nat,I6: set_complex,G: complex > nat,I2: complex] :
% 5.44/5.69 ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_complex @ I2 @ I6 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7441_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: real > int,I6: set_real,G: real > int,I2: real] :
% 5.44/5.69 ( ( ( groups1932886352136224148al_int @ F @ I6 )
% 5.44/5.69 = ( groups1932886352136224148al_int @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_real @ I2 @ I6 )
% 5.44/5.69 => ( ( finite_finite_real @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7442_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: nat > int,I6: set_nat,G: nat > int,I2: nat] :
% 5.44/5.69 ( ( ( groups3539618377306564664at_int @ F @ I6 )
% 5.44/5.69 = ( groups3539618377306564664at_int @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_nat @ I2 @ I6 )
% 5.44/5.69 => ( ( finite_finite_nat @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7443_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: complex > int,I6: set_complex,G: complex > int,I2: complex] :
% 5.44/5.69 ( ( ( groups5690904116761175830ex_int @ F @ I6 )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_complex @ I2 @ I6 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7444_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: nat > nat,I6: set_nat,G: nat > nat,I2: nat] :
% 5.44/5.69 ( ( ( groups3542108847815614940at_nat @ F @ I6 )
% 5.44/5.69 = ( groups3542108847815614940at_nat @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_nat @ I2 @ I6 )
% 5.44/5.69 => ( ( finite_finite_nat @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7445_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: nat > real,I6: set_nat,G: nat > real,I2: nat] :
% 5.44/5.69 ( ( ( groups6591440286371151544t_real @ F @ I6 )
% 5.44/5.69 = ( groups6591440286371151544t_real @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_nat @ I2 @ I6 )
% 5.44/5.69 => ( ( finite_finite_nat @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7446_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: int > int,I6: set_int,G: int > int,I2: int] :
% 5.44/5.69 ( ( ( groups4538972089207619220nt_int @ F @ I6 )
% 5.44/5.69 = ( groups4538972089207619220nt_int @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member_int @ I2 @ I6 )
% 5.44/5.69 => ( ( finite_finite_int @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7447_sum__mono__inv,axiom,
% 5.44/5.69 ! [F: product_prod_nat_nat > nat,I6: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,I2: product_prod_nat_nat] :
% 5.44/5.69 ( ( ( groups977919841031483927at_nat @ F @ I6 )
% 5.44/5.69 = ( groups977919841031483927at_nat @ G @ I6 ) )
% 5.44/5.69 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.69 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.44/5.69 => ( ( member8440522571783428010at_nat @ I2 @ I6 )
% 5.44/5.69 => ( ( finite6177210948735845034at_nat @ I6 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = ( G @ I2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono_inv
% 5.44/5.69 thf(fact_7448_sum__cong__Suc,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.44/5.69 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 5.44/5.69 => ( ( F @ ( suc @ X5 ) )
% 5.44/5.69 = ( G @ ( suc @ X5 ) ) ) )
% 5.44/5.69 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.44/5.69 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_cong_Suc
% 5.44/5.69 thf(fact_7449_sum__cong__Suc,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.44/5.69 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 5.44/5.69 => ( ( F @ ( suc @ X5 ) )
% 5.44/5.69 = ( G @ ( suc @ X5 ) ) ) )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.44/5.69 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_cong_Suc
% 5.44/5.69 thf(fact_7450_complex__of__real__mult__Complex,axiom,
% 5.44/5.69 ! [R: real,X: real,Y: real] :
% 5.44/5.69 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y ) )
% 5.44/5.69 = ( complex2 @ ( times_times_real @ R @ X ) @ ( times_times_real @ R @ Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % complex_of_real_mult_Complex
% 5.44/5.69 thf(fact_7451_Complex__mult__complex__of__real,axiom,
% 5.44/5.69 ! [X: real,Y: real,R: real] :
% 5.44/5.69 ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 5.44/5.69 = ( complex2 @ ( times_times_real @ X @ R ) @ ( times_times_real @ Y @ R ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % Complex_mult_complex_of_real
% 5.44/5.69 thf(fact_7452_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.44/5.69 ! [G: nat > nat,M: nat,N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.shift_bounds_cl_Suc_ivl
% 5.44/5.69 thf(fact_7453_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.44/5.69 ! [G: nat > real,M: nat,N2: nat] :
% 5.44/5.69 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.shift_bounds_cl_Suc_ivl
% 5.44/5.69 thf(fact_7454_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.44/5.69 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.shift_bounds_cl_nat_ivl
% 5.44/5.69 thf(fact_7455_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.44/5.69 ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 5.44/5.69 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.44/5.69 = ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.shift_bounds_cl_nat_ivl
% 5.44/5.69 thf(fact_7456_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_nat,T: set_nat,G: nat > extended_enat,I2: nat > nat,F: nat > extended_enat] :
% 5.44/5.69 ( ( finite_finite_nat @ S3 )
% 5.44/5.69 => ( ( finite_finite_nat @ T )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ T )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: nat] :
% 5.44/5.69 ( ( member_nat @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups7108830773950497114d_enat @ F @ S3 ) @ ( groups7108830773950497114d_enat @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7457_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_nat,T: set_complex,G: complex > extended_enat,I2: complex > nat,F: nat > extended_enat] :
% 5.44/5.69 ( ( finite_finite_nat @ S3 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ T )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: complex] :
% 5.44/5.69 ( ( member_complex @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups7108830773950497114d_enat @ F @ S3 ) @ ( groups1752964319039525884d_enat @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7458_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_complex,T: set_nat,G: nat > extended_enat,I2: nat > complex,F: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ( finite_finite_nat @ T )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ T )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: nat] :
% 5.44/5.69 ( ( member_nat @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ S3 ) @ ( groups7108830773950497114d_enat @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7459_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_complex,T: set_complex,G: complex > extended_enat,I2: complex > complex,F: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ T )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: complex] :
% 5.44/5.69 ( ( member_complex @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ S3 ) @ ( groups1752964319039525884d_enat @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7460_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_complex,T: set_complex,G: complex > real,I2: complex > complex,F: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ T )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: complex] :
% 5.44/5.69 ( ( member_complex @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_less_eq_real @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S3 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7461_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_complex,T: set_complex,G: complex > nat,I2: complex > complex,F: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ T )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: complex] :
% 5.44/5.69 ( ( member_complex @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_less_eq_nat @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ S3 ) @ ( groups5693394587270226106ex_nat @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7462_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_nat,T: set_nat,G: nat > int,I2: nat > nat,F: nat > int] :
% 5.44/5.69 ( ( finite_finite_nat @ S3 )
% 5.44/5.69 => ( ( finite_finite_nat @ T )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ T )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: nat] :
% 5.44/5.69 ( ( member_nat @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ S3 ) @ ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7463_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_nat,T: set_complex,G: complex > int,I2: complex > nat,F: nat > int] :
% 5.44/5.69 ( ( finite_finite_nat @ S3 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ T )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: complex] :
% 5.44/5.69 ( ( member_complex @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ S3 ) @ ( groups5690904116761175830ex_int @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7464_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_complex,T: set_nat,G: nat > int,I2: nat > complex,F: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ( finite_finite_nat @ T )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ T )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: nat] :
% 5.44/5.69 ( ( member_nat @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ S3 ) @ ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7465_sum__le__included,axiom,
% 5.44/5.69 ! [S3: set_complex,T: set_complex,G: complex > int,I2: complex > complex,F: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ T )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ T )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S3 )
% 5.44/5.69 => ? [Xa: complex] :
% 5.44/5.69 ( ( member_complex @ Xa @ T )
% 5.44/5.69 & ( ( I2 @ Xa )
% 5.44/5.69 = X5 )
% 5.44/5.69 & ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ Xa ) ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ S3 ) @ ( groups5690904116761175830ex_int @ G @ T ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_included
% 5.44/5.69 thf(fact_7466_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups2800946370649118462d_enat @ F @ A2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 = ( ! [X2: real] :
% 5.44/5.69 ( ( member_real @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7467_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups4225252721152677374d_enat @ F @ A2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 = ( ! [X2: int] :
% 5.44/5.69 ( ( member_int @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7468_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > extended_enat] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups7108830773950497114d_enat @ F @ A2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 = ( ! [X2: nat] :
% 5.44/5.69 ( ( member_nat @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7469_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups1752964319039525884d_enat @ F @ A2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 = ( ! [X2: complex] :
% 5.44/5.69 ( ( member_complex @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7470_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 5.44/5.69 = zero_zero_real )
% 5.44/5.69 = ( ! [X2: real] :
% 5.44/5.69 ( ( member_real @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7471_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 5.44/5.69 = zero_zero_real )
% 5.44/5.69 = ( ! [X2: int] :
% 5.44/5.69 ( ( member_int @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7472_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 5.44/5.69 = zero_zero_real )
% 5.44/5.69 = ( ! [X2: complex] :
% 5.44/5.69 ( ( member_complex @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_zero_real ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7473_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 5.44/5.69 = zero_zero_nat )
% 5.44/5.69 = ( ! [X2: real] :
% 5.44/5.69 ( ( member_real @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_zero_nat ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7474_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.44/5.69 = zero_zero_nat )
% 5.44/5.69 = ( ! [X2: int] :
% 5.44/5.69 ( ( member_int @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_zero_nat ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7475_sum__nonneg__eq__0__iff,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.44/5.69 = zero_zero_nat )
% 5.44/5.69 = ( ! [X2: complex] :
% 5.44/5.69 ( ( member_complex @ X2 @ A2 )
% 5.44/5.69 => ( ( F @ X2 )
% 5.44/5.69 = zero_zero_nat ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_eq_0_iff
% 5.44/5.69 thf(fact_7476_sum__strict__mono__ex1,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ? [X3: complex] :
% 5.44/5.69 ( ( member_complex @ X3 @ A2 )
% 5.44/5.69 & ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.44/5.69 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono_ex1
% 5.44/5.69 thf(fact_7477_sum__strict__mono__ex1,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ? [X3: complex] :
% 5.44/5.69 ( ( member_complex @ X3 @ A2 )
% 5.44/5.69 & ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono_ex1
% 5.44/5.69 thf(fact_7478_sum__strict__mono__ex1,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ? [X3: nat] :
% 5.44/5.69 ( ( member_nat @ X3 @ A2 )
% 5.44/5.69 & ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.44/5.69 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono_ex1
% 5.44/5.69 thf(fact_7479_sum__strict__mono__ex1,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ? [X3: complex] :
% 5.44/5.69 ( ( member_complex @ X3 @ A2 )
% 5.44/5.69 & ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.44/5.69 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono_ex1
% 5.44/5.69 thf(fact_7480_sum__strict__mono__ex1,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ? [X3: nat] :
% 5.44/5.69 ( ( member_nat @ X3 @ A2 )
% 5.44/5.69 & ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono_ex1
% 5.44/5.69 thf(fact_7481_sum__strict__mono__ex1,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ? [X3: nat] :
% 5.44/5.69 ( ( member_nat @ X3 @ A2 )
% 5.44/5.69 & ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.44/5.69 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono_ex1
% 5.44/5.69 thf(fact_7482_sum__strict__mono__ex1,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > int,G: int > int] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_eq_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ? [X3: int] :
% 5.44/5.69 ( ( member_int @ X3 @ A2 )
% 5.44/5.69 & ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.44/5.69 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono_ex1
% 5.44/5.69 thf(fact_7483_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: extended_enat > extended_enat > $o,S: set_nat,H2: nat > extended_enat,G: nat > extended_enat] :
% 5.44/5.69 ( ( R2 @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat )
% 5.44/5.69 => ( ! [X15: extended_enat,Y15: extended_enat,X23: extended_enat,Y23: extended_enat] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_p3455044024723400733d_enat @ X15 @ Y15 ) @ ( plus_p3455044024723400733d_enat @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite_finite_nat @ S )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups7108830773950497114d_enat @ H2 @ S ) @ ( groups7108830773950497114d_enat @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7484_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: extended_enat > extended_enat > $o,S: set_complex,H2: complex > extended_enat,G: complex > extended_enat] :
% 5.44/5.69 ( ( R2 @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat )
% 5.44/5.69 => ( ! [X15: extended_enat,Y15: extended_enat,X23: extended_enat,Y23: extended_enat] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_p3455044024723400733d_enat @ X15 @ Y15 ) @ ( plus_p3455044024723400733d_enat @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups1752964319039525884d_enat @ H2 @ S ) @ ( groups1752964319039525884d_enat @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7485_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: complex > complex > $o,S: set_nat,H2: nat > complex,G: nat > complex] :
% 5.44/5.69 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.44/5.69 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite_finite_nat @ S )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups2073611262835488442omplex @ H2 @ S ) @ ( groups2073611262835488442omplex @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7486_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: real > real > $o,S: set_complex,H2: complex > real,G: complex > real] :
% 5.44/5.69 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.44/5.69 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups5808333547571424918x_real @ H2 @ S ) @ ( groups5808333547571424918x_real @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7487_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: nat > nat > $o,S: set_complex,H2: complex > nat,G: complex > nat] :
% 5.44/5.69 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 5.44/5.69 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups5693394587270226106ex_nat @ H2 @ S ) @ ( groups5693394587270226106ex_nat @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7488_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: int > int > $o,S: set_nat,H2: nat > int,G: nat > int] :
% 5.44/5.69 ( ( R2 @ zero_zero_int @ zero_zero_int )
% 5.44/5.69 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite_finite_nat @ S )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups3539618377306564664at_int @ H2 @ S ) @ ( groups3539618377306564664at_int @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7489_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: int > int > $o,S: set_complex,H2: complex > int,G: complex > int] :
% 5.44/5.69 ( ( R2 @ zero_zero_int @ zero_zero_int )
% 5.44/5.69 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups5690904116761175830ex_int @ H2 @ S ) @ ( groups5690904116761175830ex_int @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7490_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: nat > nat > $o,S: set_nat,H2: nat > nat,G: nat > nat] :
% 5.44/5.69 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 5.44/5.69 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite_finite_nat @ S )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups3542108847815614940at_nat @ H2 @ S ) @ ( groups3542108847815614940at_nat @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7491_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: complex > complex > $o,S: set_complex,H2: complex > complex,G: complex > complex] :
% 5.44/5.69 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 5.44/5.69 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups7754918857620584856omplex @ H2 @ S ) @ ( groups7754918857620584856omplex @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7492_sum_Orelated,axiom,
% 5.44/5.69 ! [R2: real > real > $o,S: set_nat,H2: nat > real,G: nat > real] :
% 5.44/5.69 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 5.44/5.69 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.44/5.69 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.69 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.69 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.44/5.69 => ( ( finite_finite_nat @ S )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ S )
% 5.44/5.69 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( R2 @ ( groups6591440286371151544t_real @ H2 @ S ) @ ( groups6591440286371151544t_real @ G @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.related
% 5.44/5.69 thf(fact_7493_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > extended_enat,G: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_complex )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ ( groups1752964319039525884d_enat @ F @ A2 ) @ ( groups1752964319039525884d_enat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7494_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_nat,F: nat > extended_enat,G: nat > extended_enat] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_nat )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ A2 )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ ( groups7108830773950497114d_enat @ F @ A2 ) @ ( groups7108830773950497114d_enat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7495_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > extended_enat,G: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_int )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ ( groups4225252721152677374d_enat @ F @ A2 ) @ ( groups4225252721152677374d_enat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7496_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > extended_enat,G: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_real )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ ( groups2800946370649118462d_enat @ F @ A2 ) @ ( groups2800946370649118462d_enat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7497_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_complex )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7498_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > real,G: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_int )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7499_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > real,G: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_real )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7500_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_complex )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7501_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_int )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7502_sum__strict__mono,axiom,
% 5.44/5.69 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( A2 != bot_bot_set_real )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ A2 )
% 5.44/5.69 => ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono
% 5.44/5.69 thf(fact_7503_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( groups5754745047067104278omplex @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups5754745047067104278omplex @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7504_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > complex] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups3049146728041665814omplex @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( groups3049146728041665814omplex @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups3049146728041665814omplex @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups3049146728041665814omplex @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7505_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_nat,X: nat,G: nat > complex] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ( ( member_nat @ X @ A2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.69 = ( groups2073611262835488442omplex @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_nat @ X @ A2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups2073611262835488442omplex @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7506_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7507_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7508_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7509_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( groups1935376822645274424al_nat @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7510_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7511_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_complex,X: complex,G: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7512_sum_Oinsert__if,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > int] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( groups1932886352136224148al_int @ G @ A2 ) ) )
% 5.44/5.69 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_int @ ( G @ X ) @ ( groups1932886352136224148al_int @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_if
% 5.44/5.69 thf(fact_7513_nonzero__of__real__divide,axiom,
% 5.44/5.69 ! [Y: real,X: real] :
% 5.44/5.69 ( ( Y != zero_zero_real )
% 5.44/5.69 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.69 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % nonzero_of_real_divide
% 5.44/5.69 thf(fact_7514_nonzero__of__real__divide,axiom,
% 5.44/5.69 ! [Y: real,X: real] :
% 5.44/5.69 ( ( Y != zero_zero_real )
% 5.44/5.69 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % nonzero_of_real_divide
% 5.44/5.69 thf(fact_7515_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_real,F: real > extended_enat,B2: extended_enat,I2: real] :
% 5.44/5.69 ( ( finite_finite_real @ S3 )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups2800946370649118462d_enat @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_real @ I2 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7516_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_int,F: int > extended_enat,B2: extended_enat,I2: int] :
% 5.44/5.69 ( ( finite_finite_int @ S3 )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups4225252721152677374d_enat @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_int @ I2 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7517_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_nat,F: nat > extended_enat,B2: extended_enat,I2: nat] :
% 5.44/5.69 ( ( finite_finite_nat @ S3 )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups7108830773950497114d_enat @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_nat @ I2 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7518_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_complex,F: complex > extended_enat,B2: extended_enat,I2: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups1752964319039525884d_enat @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_complex @ I2 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7519_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_real,F: real > real,B2: real,I2: real] :
% 5.44/5.69 ( ( finite_finite_real @ S3 )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups8097168146408367636l_real @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_real @ I2 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7520_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_int,F: int > real,B2: real,I2: int] :
% 5.44/5.69 ( ( finite_finite_int @ S3 )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups8778361861064173332t_real @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_int @ I2 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7521_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_complex,F: complex > real,B2: real,I2: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups5808333547571424918x_real @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_complex @ I2 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7522_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_real,F: real > nat,B2: nat,I2: real] :
% 5.44/5.69 ( ( finite_finite_real @ S3 )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups1935376822645274424al_nat @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_real @ I2 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7523_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_int,F: int > nat,B2: nat,I2: int] :
% 5.44/5.69 ( ( finite_finite_int @ S3 )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups4541462559716669496nt_nat @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_int @ I2 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7524_sum__nonneg__leq__bound,axiom,
% 5.44/5.69 ! [S3: set_complex,F: complex > nat,B2: nat,I2: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups5693394587270226106ex_nat @ F @ S3 )
% 5.44/5.69 = B2 )
% 5.44/5.69 => ( ( member_complex @ I2 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_leq_bound
% 5.44/5.69 thf(fact_7525_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_real,F: real > extended_enat,I2: real] :
% 5.44/5.69 ( ( finite_finite_real @ S3 )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups2800946370649118462d_enat @ F @ S3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 => ( ( member_real @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7526_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_int,F: int > extended_enat,I2: int] :
% 5.44/5.69 ( ( finite_finite_int @ S3 )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups4225252721152677374d_enat @ F @ S3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 => ( ( member_int @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7527_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_nat,F: nat > extended_enat,I2: nat] :
% 5.44/5.69 ( ( finite_finite_nat @ S3 )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups7108830773950497114d_enat @ F @ S3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 => ( ( member_nat @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7528_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_complex,F: complex > extended_enat,I2: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ S3 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups1752964319039525884d_enat @ F @ S3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 => ( ( member_complex @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7529_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_real,F: real > real,I2: real] :
% 5.44/5.69 ( ( finite_finite_real @ S3 )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups8097168146408367636l_real @ F @ S3 )
% 5.44/5.69 = zero_zero_real )
% 5.44/5.69 => ( ( member_real @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_zero_real ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7530_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_int,F: int > real,I2: int] :
% 5.44/5.69 ( ( finite_finite_int @ S3 )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups8778361861064173332t_real @ F @ S3 )
% 5.44/5.69 = zero_zero_real )
% 5.44/5.69 => ( ( member_int @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_zero_real ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7531_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_complex,F: complex > real,I2: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups5808333547571424918x_real @ F @ S3 )
% 5.44/5.69 = zero_zero_real )
% 5.44/5.69 => ( ( member_complex @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_zero_real ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7532_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_real,F: real > nat,I2: real] :
% 5.44/5.69 ( ( finite_finite_real @ S3 )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups1935376822645274424al_nat @ F @ S3 )
% 5.44/5.69 = zero_zero_nat )
% 5.44/5.69 => ( ( member_real @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_zero_nat ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7533_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_int,F: int > nat,I2: int] :
% 5.44/5.69 ( ( finite_finite_int @ S3 )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups4541462559716669496nt_nat @ F @ S3 )
% 5.44/5.69 = zero_zero_nat )
% 5.44/5.69 => ( ( member_int @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_zero_nat ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7534_sum__nonneg__0,axiom,
% 5.44/5.69 ! [S3: set_complex,F: complex > nat,I2: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S3 )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ S3 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups5693394587270226106ex_nat @ F @ S3 )
% 5.44/5.69 = zero_zero_nat )
% 5.44/5.69 => ( ( member_complex @ I2 @ S3 )
% 5.44/5.69 => ( ( F @ I2 )
% 5.44/5.69 = zero_zero_nat ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_nonneg_0
% 5.44/5.69 thf(fact_7535_sum__power__add,axiom,
% 5.44/5.69 ! [X: complex,M: nat,I6: set_nat] :
% 5.44/5.69 ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I6 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_power_add
% 5.44/5.69 thf(fact_7536_sum__power__add,axiom,
% 5.44/5.69 ! [X: int,M: nat,I6: set_nat] :
% 5.44/5.69 ( ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [I5: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I6 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_power_add
% 5.44/5.69 thf(fact_7537_sum__power__add,axiom,
% 5.44/5.69 ! [X: real,M: nat,I6: set_nat] :
% 5.44/5.69 ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I6 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_power_add
% 5.44/5.69 thf(fact_7538_Complex__add__complex__of__real,axiom,
% 5.44/5.69 ! [X: real,Y: real,R: real] :
% 5.44/5.69 ( ( plus_plus_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 5.44/5.69 = ( complex2 @ ( plus_plus_real @ X @ R ) @ Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % Complex_add_complex_of_real
% 5.44/5.69 thf(fact_7539_complex__of__real__add__Complex,axiom,
% 5.44/5.69 ! [R: real,X: real,Y: real] :
% 5.44/5.69 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y ) )
% 5.44/5.69 = ( complex2 @ ( plus_plus_real @ R @ X ) @ Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % complex_of_real_add_Complex
% 5.44/5.69 thf(fact_7540_sum_OatLeastAtMost__rev,axiom,
% 5.44/5.69 ! [G: nat > nat,N2: nat,M: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeastAtMost_rev
% 5.44/5.69 thf(fact_7541_sum_OatLeastAtMost__rev,axiom,
% 5.44/5.69 ! [G: nat > real,N2: nat,M: nat] :
% 5.44/5.69 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.44/5.69 = ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeastAtMost_rev
% 5.44/5.69 thf(fact_7542_arccos__le__arccos,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_le_arccos
% 5.44/5.69 thf(fact_7543_arccos__eq__iff,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.69 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.44/5.69 => ( ( ( arccos @ X )
% 5.44/5.69 = ( arccos @ Y ) )
% 5.44/5.69 = ( X = Y ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_eq_iff
% 5.44/5.69 thf(fact_7544_arccos__le__mono,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.44/5.69 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_le_mono
% 5.44/5.69 thf(fact_7545_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_real,I2: real,F: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ I6 )
% 5.44/5.69 => ( ( member_real @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups2800946370649118462d_enat @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7546_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_int,I2: int,F: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ I6 )
% 5.44/5.69 => ( ( member_int @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups4225252721152677374d_enat @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7547_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_nat,I2: nat,F: nat > extended_enat] :
% 5.44/5.69 ( ( finite_finite_nat @ I6 )
% 5.44/5.69 => ( ( member_nat @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups7108830773950497114d_enat @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7548_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_complex,I2: complex,F: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.69 => ( ( member_complex @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups1752964319039525884d_enat @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7549_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_real,I2: real,F: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ I6 )
% 5.44/5.69 => ( ( member_real @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7550_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_int,I2: int,F: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ I6 )
% 5.44/5.69 => ( ( member_int @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7551_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_complex,I2: complex,F: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.69 => ( ( member_complex @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7552_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_real,I2: real,F: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ I6 )
% 5.44/5.69 => ( ( member_real @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7553_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_int,I2: int,F: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ I6 )
% 5.44/5.69 => ( ( member_int @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7554_sum__pos2,axiom,
% 5.44/5.69 ! [I6: set_complex,I2: complex,F: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.69 => ( ( member_complex @ I2 @ I6 )
% 5.44/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos2
% 5.44/5.69 thf(fact_7555_arcsin__le__arcsin,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_le_arcsin
% 5.44/5.69 thf(fact_7556_arcsin__minus,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.69 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 5.44/5.69 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_minus
% 5.44/5.69 thf(fact_7557_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_complex,F: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_complex )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups1752964319039525884d_enat @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7558_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_nat,F: nat > extended_enat] :
% 5.44/5.69 ( ( finite_finite_nat @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_nat )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups7108830773950497114d_enat @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7559_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_int,F: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_int )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups4225252721152677374d_enat @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7560_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_real,F: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_real )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( groups2800946370649118462d_enat @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7561_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_complex,F: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_complex )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7562_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_int,F: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_int )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7563_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_real,F: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_real )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7564_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_complex,F: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_complex )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7565_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_int,F: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_int )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7566_sum__pos,axiom,
% 5.44/5.69 ! [I6: set_real,F: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ I6 )
% 5.44/5.69 => ( ( I6 != bot_bot_set_real )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.44/5.69 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_pos
% 5.44/5.69 thf(fact_7567_arcsin__eq__iff,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.44/5.69 => ( ( ( arcsin @ X )
% 5.44/5.69 = ( arcsin @ Y ) )
% 5.44/5.69 = ( X = Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_eq_iff
% 5.44/5.69 thf(fact_7568_arcsin__le__mono,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.44/5.69 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_le_mono
% 5.44/5.69 thf(fact_7569_norm__less__p1,axiom,
% 5.44/5.69 ! [X: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X ) ) @ one_one_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_less_p1
% 5.44/5.69 thf(fact_7570_norm__less__p1,axiom,
% 5.44/5.69 ! [X: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X ) ) @ one_one_complex ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_less_p1
% 5.44/5.69 thf(fact_7571_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_int,S: set_int,G: int > extended_enat,H2: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups4225252721152677374d_enat @ G @ T3 )
% 5.44/5.69 = ( groups4225252721152677374d_enat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7572_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > extended_enat,H2: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups1752964319039525884d_enat @ G @ T3 )
% 5.44/5.69 = ( groups1752964319039525884d_enat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7573_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_int,S: set_int,G: int > complex,H2: int > complex] :
% 5.44/5.69 ( ( finite_finite_int @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups3049146728041665814omplex @ G @ T3 )
% 5.44/5.69 = ( groups3049146728041665814omplex @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7574_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_int,S: set_int,G: int > real,H2: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups8778361861064173332t_real @ G @ T3 )
% 5.44/5.69 = ( groups8778361861064173332t_real @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7575_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > real,H2: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.44/5.69 = ( groups5808333547571424918x_real @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7576_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_int,S: set_int,G: int > nat,H2: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat @ G @ T3 )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7577_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > nat,H2: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7578_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > int,H2: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7579_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > extended_enat,H2: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups2800946370649118462d_enat @ G @ T3 )
% 5.44/5.69 = ( groups2800946370649118462d_enat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7580_sum_Omono__neutral__cong__right,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > complex,H2: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ T3 )
% 5.44/5.69 = ( groups5754745047067104278omplex @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_right
% 5.44/5.69 thf(fact_7581_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_int,S: set_int,H2: int > extended_enat,G: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups4225252721152677374d_enat @ G @ S )
% 5.44/5.69 = ( groups4225252721152677374d_enat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7582_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,H2: complex > extended_enat,G: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups1752964319039525884d_enat @ G @ S )
% 5.44/5.69 = ( groups1752964319039525884d_enat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7583_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_int,S: set_int,H2: int > complex,G: int > complex] :
% 5.44/5.69 ( ( finite_finite_int @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups3049146728041665814omplex @ G @ S )
% 5.44/5.69 = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7584_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_int,S: set_int,H2: int > real,G: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups8778361861064173332t_real @ G @ S )
% 5.44/5.69 = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7585_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,H2: complex > real,G: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ S )
% 5.44/5.69 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7586_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_int,S: set_int,H2: int > nat,G: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat @ G @ S )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7587_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,H2: complex > nat,G: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ S )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7588_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,H2: complex > int,G: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ G @ S )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7589_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,H2: real > extended_enat,G: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups2800946370649118462d_enat @ G @ S )
% 5.44/5.69 = ( groups2800946370649118462d_enat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7590_sum_Omono__neutral__cong__left,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,H2: real > complex,G: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( H2 @ X5 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ S )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = ( H2 @ X5 ) ) )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ S )
% 5.44/5.69 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_cong_left
% 5.44/5.69 thf(fact_7591_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( groups1752964319039525884d_enat @ G @ T3 )
% 5.44/5.69 = ( groups1752964319039525884d_enat @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7592_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.44/5.69 = ( groups5808333547571424918x_real @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7593_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7594_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7595_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( groups2800946370649118462d_enat @ G @ T3 )
% 5.44/5.69 = ( groups2800946370649118462d_enat @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7596_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ T3 )
% 5.44/5.69 = ( groups5754745047067104278omplex @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7597_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ G @ T3 )
% 5.44/5.69 = ( groups8097168146408367636l_real @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7598_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 5.44/5.69 = ( groups1935376822645274424al_nat @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7599_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > int] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ G @ T3 )
% 5.44/5.69 = ( groups1932886352136224148al_int @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7600_sum_Omono__neutral__right,axiom,
% 5.44/5.69 ! [T3: set_nat,S: set_nat,G: nat > extended_enat] :
% 5.44/5.69 ( ( finite_finite_nat @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_nat @ S @ T3 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( groups7108830773950497114d_enat @ G @ T3 )
% 5.44/5.69 = ( groups7108830773950497114d_enat @ G @ S ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_right
% 5.44/5.69 thf(fact_7601_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( groups1752964319039525884d_enat @ G @ S )
% 5.44/5.69 = ( groups1752964319039525884d_enat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7602_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ S )
% 5.44/5.69 = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7603_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ S )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7604_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_complex,S: set_complex,G: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ G @ S )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7605_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( groups2800946370649118462d_enat @ G @ S )
% 5.44/5.69 = ( groups2800946370649118462d_enat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7606_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ S )
% 5.44/5.69 = ( groups5754745047067104278omplex @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7607_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ G @ S )
% 5.44/5.69 = ( groups8097168146408367636l_real @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7608_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat @ G @ S )
% 5.44/5.69 = ( groups1935376822645274424al_nat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7609_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_real,S: set_real,G: real > int] :
% 5.44/5.69 ( ( finite_finite_real @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ G @ S )
% 5.44/5.69 = ( groups1932886352136224148al_int @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7610_sum_Omono__neutral__left,axiom,
% 5.44/5.69 ! [T3: set_nat,S: set_nat,G: nat > extended_enat] :
% 5.44/5.69 ( ( finite_finite_nat @ T3 )
% 5.44/5.69 => ( ( ord_less_eq_set_nat @ S @ T3 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ T3 @ S ) )
% 5.44/5.69 => ( ( G @ X5 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( groups7108830773950497114d_enat @ G @ S )
% 5.44/5.69 = ( groups7108830773950497114d_enat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.mono_neutral_left
% 5.44/5.69 thf(fact_7611_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_int,A2: set_int,B2: set_int,G: int > extended_enat,H2: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: int] :
% 5.44/5.69 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( ( groups4225252721152677374d_enat @ G @ C4 )
% 5.44/5.69 = ( groups4225252721152677374d_enat @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups4225252721152677374d_enat @ G @ A2 )
% 5.44/5.69 = ( groups4225252721152677374d_enat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7612_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > extended_enat,H2: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: complex] :
% 5.44/5.69 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( ( groups1752964319039525884d_enat @ G @ C4 )
% 5.44/5.69 = ( groups1752964319039525884d_enat @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups1752964319039525884d_enat @ G @ A2 )
% 5.44/5.69 = ( groups1752964319039525884d_enat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7613_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 5.44/5.69 ( ( finite_finite_int @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: int] :
% 5.44/5.69 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ( ( groups3049146728041665814omplex @ G @ C4 )
% 5.44/5.69 = ( groups3049146728041665814omplex @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups3049146728041665814omplex @ G @ A2 )
% 5.44/5.69 = ( groups3049146728041665814omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7614_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: int] :
% 5.44/5.69 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ( ( groups8778361861064173332t_real @ G @ C4 )
% 5.44/5.69 = ( groups8778361861064173332t_real @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.44/5.69 = ( groups8778361861064173332t_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7615_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: complex] :
% 5.44/5.69 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 5.44/5.69 = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.44/5.69 = ( groups5808333547571424918x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7616_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: int] :
% 5.44/5.69 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7617_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: complex] :
% 5.44/5.69 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7618_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: complex] :
% 5.44/5.69 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ( ( groups5690904116761175830ex_int @ G @ C4 )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7619_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_real,A2: set_real,B2: set_real,G: real > extended_enat,H2: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: real] :
% 5.44/5.69 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [B3: real] :
% 5.44/5.69 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( ( groups2800946370649118462d_enat @ G @ C4 )
% 5.44/5.69 = ( groups2800946370649118462d_enat @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups2800946370649118462d_enat @ G @ A2 )
% 5.44/5.69 = ( groups2800946370649118462d_enat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7620_sum_Osame__carrierI,axiom,
% 5.44/5.69 ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: real] :
% 5.44/5.69 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ! [B3: real] :
% 5.44/5.69 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 5.44/5.69 = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.44/5.69 = ( groups5754745047067104278omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrierI
% 5.44/5.69 thf(fact_7621_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_int,A2: set_int,B2: set_int,G: int > extended_enat,H2: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: int] :
% 5.44/5.69 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( ( groups4225252721152677374d_enat @ G @ A2 )
% 5.44/5.69 = ( groups4225252721152677374d_enat @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups4225252721152677374d_enat @ G @ C4 )
% 5.44/5.69 = ( groups4225252721152677374d_enat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7622_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > extended_enat,H2: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: complex] :
% 5.44/5.69 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( ( groups1752964319039525884d_enat @ G @ A2 )
% 5.44/5.69 = ( groups1752964319039525884d_enat @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups1752964319039525884d_enat @ G @ C4 )
% 5.44/5.69 = ( groups1752964319039525884d_enat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7623_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 5.44/5.69 ( ( finite_finite_int @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: int] :
% 5.44/5.69 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 5.44/5.69 = ( groups3049146728041665814omplex @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups3049146728041665814omplex @ G @ C4 )
% 5.44/5.69 = ( groups3049146728041665814omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7624_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: int] :
% 5.44/5.69 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.44/5.69 = ( groups8778361861064173332t_real @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups8778361861064173332t_real @ G @ C4 )
% 5.44/5.69 = ( groups8778361861064173332t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7625_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: complex] :
% 5.44/5.69 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_real ) )
% 5.44/5.69 => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.44/5.69 = ( groups5808333547571424918x_real @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups5808333547571424918x_real @ G @ C4 )
% 5.44/5.69 = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7626_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: int] :
% 5.44/5.69 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups4541462559716669496nt_nat @ G @ C4 )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7627_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: complex] :
% 5.44/5.69 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_nat ) )
% 5.44/5.69 => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7628_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: complex] :
% 5.44/5.69 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_int ) )
% 5.44/5.69 => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups5690904116761175830ex_int @ G @ C4 )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7629_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_real,A2: set_real,B2: set_real,G: real > extended_enat,H2: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: real] :
% 5.44/5.69 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ! [B3: real] :
% 5.44/5.69 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_z5237406670263579293d_enat ) )
% 5.44/5.69 => ( ( ( groups2800946370649118462d_enat @ G @ A2 )
% 5.44/5.69 = ( groups2800946370649118462d_enat @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups2800946370649118462d_enat @ G @ C4 )
% 5.44/5.69 = ( groups2800946370649118462d_enat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7630_sum_Osame__carrier,axiom,
% 5.44/5.69 ! [C4: set_real,A2: set_real,B2: set_real,G: real > complex,H2: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.69 => ( ! [A3: real] :
% 5.44/5.69 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.44/5.69 => ( ( G @ A3 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ! [B3: real] :
% 5.44/5.69 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 5.44/5.69 => ( ( H2 @ B3 )
% 5.44/5.69 = zero_zero_complex ) )
% 5.44/5.69 => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.44/5.69 = ( groups5754745047067104278omplex @ H2 @ B2 ) )
% 5.44/5.69 = ( ( groups5754745047067104278omplex @ G @ C4 )
% 5.44/5.69 = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.same_carrier
% 5.44/5.69 thf(fact_7631_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 5.44/5.69 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.44/5.69 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5808333547571424918x_real @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7632_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 5.44/5.69 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.44/5.69 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5693394587270226106ex_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7633_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 5.44/5.69 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.44/5.69 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups5690904116761175830ex_int @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7634_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,G: real > complex] :
% 5.44/5.69 ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.69 => ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.44/5.69 = ( plus_plus_complex @ ( groups5754745047067104278omplex @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups5754745047067104278omplex @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7635_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,G: real > real] :
% 5.44/5.69 ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.69 => ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.44/5.69 = ( plus_plus_real @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups8097168146408367636l_real @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7636_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,G: real > nat] :
% 5.44/5.69 ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.69 => ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.44/5.69 = ( plus_plus_nat @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1935376822645274424al_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7637_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,G: real > int] :
% 5.44/5.69 ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.69 => ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 5.44/5.69 = ( plus_plus_int @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1932886352136224148al_int @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7638_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_nat,A2: set_nat,G: nat > complex] :
% 5.44/5.69 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.69 => ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.44/5.69 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2073611262835488442omplex @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7639_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_nat,A2: set_nat,G: nat > int] :
% 5.44/5.69 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.69 => ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 5.44/5.69 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7640_sum_Osubset__diff,axiom,
% 5.44/5.69 ! [B2: set_nat,A2: set_nat,G: nat > nat] :
% 5.44/5.69 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.69 => ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 5.44/5.69 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.subset_diff
% 5.44/5.69 thf(fact_7641_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_complex,B2: set_complex,F: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7642_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_complex,B2: set_complex,F: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7643_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_real,B2: set_real,F: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_complex @ ( groups5754745047067104278omplex @ F @ A2 ) @ ( groups5754745047067104278omplex @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7644_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_real,B2: set_real,F: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7645_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_real,B2: set_real,F: real > int] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7646_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_nat,B2: set_nat,F: nat > complex] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ A2 ) @ ( groups2073611262835488442omplex @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7647_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_nat,B2: set_nat,F: nat > int] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.69 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7648_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_complex,B2: set_complex,F: complex > complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.69 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7649_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_nat,B2: set_nat,F: nat > real] :
% 5.44/5.69 ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7650_sum__diff,axiom,
% 5.44/5.69 ! [A2: set_int,B2: set_int,F: int > int] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 5.44/5.69 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B2 ) )
% 5.44/5.69 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff
% 5.44/5.69 thf(fact_7651_sum__shift__lb__Suc0__0,axiom,
% 5.44/5.69 ! [F: nat > extended_enat,K: nat] :
% 5.44/5.69 ( ( ( F @ zero_zero_nat )
% 5.44/5.69 = zero_z5237406670263579293d_enat )
% 5.44/5.69 => ( ( groups7108830773950497114d_enat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.44/5.69 = ( groups7108830773950497114d_enat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_shift_lb_Suc0_0
% 5.44/5.69 thf(fact_7652_sum__shift__lb__Suc0__0,axiom,
% 5.44/5.69 ! [F: nat > complex,K: nat] :
% 5.44/5.69 ( ( ( F @ zero_zero_nat )
% 5.44/5.69 = zero_zero_complex )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.44/5.69 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_shift_lb_Suc0_0
% 5.44/5.69 thf(fact_7653_sum__shift__lb__Suc0__0,axiom,
% 5.44/5.69 ! [F: nat > int,K: nat] :
% 5.44/5.69 ( ( ( F @ zero_zero_nat )
% 5.44/5.69 = zero_zero_int )
% 5.44/5.69 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.44/5.69 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_shift_lb_Suc0_0
% 5.44/5.69 thf(fact_7654_sum__shift__lb__Suc0__0,axiom,
% 5.44/5.69 ! [F: nat > nat,K: nat] :
% 5.44/5.69 ( ( ( F @ zero_zero_nat )
% 5.44/5.69 = zero_zero_nat )
% 5.44/5.69 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_shift_lb_Suc0_0
% 5.44/5.69 thf(fact_7655_sum__shift__lb__Suc0__0,axiom,
% 5.44/5.69 ! [F: nat > real,K: nat] :
% 5.44/5.69 ( ( ( F @ zero_zero_nat )
% 5.44/5.69 = zero_zero_real )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.44/5.69 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_shift_lb_Suc0_0
% 5.44/5.69 thf(fact_7656_sum_OatLeast0__atMost__Suc,axiom,
% 5.44/5.69 ! [G: nat > complex,N2: nat] :
% 5.44/5.69 ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeast0_atMost_Suc
% 5.44/5.69 thf(fact_7657_sum_OatLeast0__atMost__Suc,axiom,
% 5.44/5.69 ! [G: nat > int,N2: nat] :
% 5.44/5.69 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeast0_atMost_Suc
% 5.44/5.69 thf(fact_7658_sum_OatLeast0__atMost__Suc,axiom,
% 5.44/5.69 ! [G: nat > nat,N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeast0_atMost_Suc
% 5.44/5.69 thf(fact_7659_sum_OatLeast0__atMost__Suc,axiom,
% 5.44/5.69 ! [G: nat > real,N2: nat] :
% 5.44/5.69 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeast0_atMost_Suc
% 5.44/5.69 thf(fact_7660_sum_Onat__ivl__Suc_H,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > complex] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ ( suc @ N2 ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.nat_ivl_Suc'
% 5.44/5.69 thf(fact_7661_sum_Onat__ivl__Suc_H,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > int] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.69 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.nat_ivl_Suc'
% 5.44/5.69 thf(fact_7662_sum_Onat__ivl__Suc_H,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.69 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.nat_ivl_Suc'
% 5.44/5.69 thf(fact_7663_sum_Onat__ivl__Suc_H,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > real] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.nat_ivl_Suc'
% 5.44/5.69 thf(fact_7664_sum_OatLeast__Suc__atMost,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > complex] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ M ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeast_Suc_atMost
% 5.44/5.69 thf(fact_7665_sum_OatLeast__Suc__atMost,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > int] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeast_Suc_atMost
% 5.44/5.69 thf(fact_7666_sum_OatLeast__Suc__atMost,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeast_Suc_atMost
% 5.44/5.69 thf(fact_7667_sum_OatLeast__Suc__atMost,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > real] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.atLeast_Suc_atMost
% 5.44/5.69 thf(fact_7668_sum_OSuc__reindex__ivl,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > complex] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ M )
% 5.44/5.69 @ ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.Suc_reindex_ivl
% 5.44/5.69 thf(fact_7669_sum_OSuc__reindex__ivl,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > int] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_int @ ( G @ M )
% 5.44/5.69 @ ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.Suc_reindex_ivl
% 5.44/5.69 thf(fact_7670_sum_OSuc__reindex__ivl,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ M )
% 5.44/5.69 @ ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.Suc_reindex_ivl
% 5.44/5.69 thf(fact_7671_sum_OSuc__reindex__ivl,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > real] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ M )
% 5.44/5.69 @ ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.Suc_reindex_ivl
% 5.44/5.69 thf(fact_7672_sum__Suc__diff,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > complex] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.69 => ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( minus_minus_complex @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( minus_minus_complex @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_Suc_diff
% 5.44/5.69 thf(fact_7673_sum__Suc__diff,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > int] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.69 => ( ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_Suc_diff
% 5.44/5.69 thf(fact_7674_sum__Suc__diff,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > real] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.69 => ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_Suc_diff
% 5.44/5.69 thf(fact_7675_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_int,A2: set_int,F: int > extended_enat] :
% 5.44/5.69 ( ( finite_finite_int @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups4225252721152677374d_enat @ F @ A2 ) @ ( groups4225252721152677374d_enat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7676_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,F: complex > extended_enat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups1752964319039525884d_enat @ F @ A2 ) @ ( groups1752964319039525884d_enat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7677_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_int,A2: set_int,F: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7678_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7679_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_int,A2: set_int,F: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: int] :
% 5.44/5.69 ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7680_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7681_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: complex] :
% 5.44/5.69 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7682_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,F: real > extended_enat] :
% 5.44/5.69 ( ( finite_finite_real @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: real] :
% 5.44/5.69 ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( groups2800946370649118462d_enat @ F @ A2 ) @ ( groups2800946370649118462d_enat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7683_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,F: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: real] :
% 5.44/5.69 ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7684_sum__mono2,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,F: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.69 => ( ! [B3: real] :
% 5.44/5.69 ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_mono2
% 5.44/5.69 thf(fact_7685_arccos__lbound,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_lbound
% 5.44/5.69 thf(fact_7686_arccos__less__arccos,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_less_arccos
% 5.44/5.69 thf(fact_7687_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7688_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_complex,X: complex,G: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7689_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_complex,X: complex,G: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( member_complex @ X @ A2 )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.44/5.69 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7690_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > complex] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups3049146728041665814omplex @ G @ A2 )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups3049146728041665814omplex @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7691_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7692_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_int,X: int,G: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( member_int @ X @ A2 )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7693_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups5754745047067104278omplex @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7694_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7695_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7696_sum_Oremove,axiom,
% 5.44/5.69 ! [A2: set_real,X: real,G: real > int] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( member_real @ X @ A2 )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 5.44/5.69 = ( plus_plus_int @ ( G @ X ) @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.remove
% 5.44/5.69 thf(fact_7697_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_complex,G: complex > real,X: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7698_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_complex,G: complex > nat,X: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7699_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_complex,G: complex > int,X: complex] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7700_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_int,G: int > complex,X: int] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( groups3049146728041665814omplex @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups3049146728041665814omplex @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7701_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_int,G: int > real,X: int] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7702_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_int,G: int > nat,X: int] :
% 5.44/5.69 ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7703_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_real,G: real > complex,X: real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( groups5754745047067104278omplex @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_complex @ ( G @ X ) @ ( groups5754745047067104278omplex @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7704_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_real,G: real > real,X: real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7705_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_real,G: real > nat,X: real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7706_sum_Oinsert__remove,axiom,
% 5.44/5.69 ! [A2: set_real,G: real > int,X: real] :
% 5.44/5.69 ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ( groups1932886352136224148al_int @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.69 = ( plus_plus_int @ ( G @ X ) @ ( groups1932886352136224148al_int @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.insert_remove
% 5.44/5.69 thf(fact_7707_arccos__less__mono,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.44/5.69 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_less_mono
% 5.44/5.69 thf(fact_7708_arccos__ubound,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_ubound
% 5.44/5.69 thf(fact_7709_arccos__cos,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ pi )
% 5.44/5.69 => ( ( arccos @ ( cos_real @ X ) )
% 5.44/5.69 = X ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_cos
% 5.44/5.69 thf(fact_7710_arcsin__less__arcsin,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_less_arcsin
% 5.44/5.69 thf(fact_7711_arcsin__less__mono,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.44/5.69 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.44/5.69 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_less_mono
% 5.44/5.69 thf(fact_7712_cos__arccos__abs,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.44/5.69 => ( ( cos_real @ ( arccos @ Y ) )
% 5.44/5.69 = Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_arccos_abs
% 5.44/5.69 thf(fact_7713_norm__of__real__diff,axiom,
% 5.44/5.69 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_of_real_diff
% 5.44/5.69 thf(fact_7714_norm__of__real__diff,axiom,
% 5.44/5.69 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % norm_of_real_diff
% 5.44/5.69 thf(fact_7715_arccos__cos__eq__abs,axiom,
% 5.44/5.69 ! [Theta: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.44/5.69 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.44/5.69 = ( abs_abs_real @ Theta ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_cos_eq_abs
% 5.44/5.69 thf(fact_7716_sum_Oub__add__nat,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > complex,P5: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 5.44/5.69 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.ub_add_nat
% 5.44/5.69 thf(fact_7717_sum_Oub__add__nat,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > int,P5: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.44/5.69 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 5.44/5.69 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.ub_add_nat
% 5.44/5.69 thf(fact_7718_sum_Oub__add__nat,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > nat,P5: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.44/5.69 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 5.44/5.69 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.ub_add_nat
% 5.44/5.69 thf(fact_7719_sum_Oub__add__nat,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,G: nat > real,P5: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 5.44/5.69 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.ub_add_nat
% 5.44/5.69 thf(fact_7720_sum__le__suminf,axiom,
% 5.44/5.69 ! [F: nat > int,I6: set_nat] :
% 5.44/5.69 ( ( summable_int @ F )
% 5.44/5.69 => ( ( finite_finite_nat @ I6 )
% 5.44/5.69 => ( ! [N4: nat] :
% 5.44/5.69 ( ( member_nat @ N4 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N4 ) ) )
% 5.44/5.69 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I6 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_suminf
% 5.44/5.69 thf(fact_7721_sum__le__suminf,axiom,
% 5.44/5.69 ! [F: nat > nat,I6: set_nat] :
% 5.44/5.69 ( ( summable_nat @ F )
% 5.44/5.69 => ( ( finite_finite_nat @ I6 )
% 5.44/5.69 => ( ! [N4: nat] :
% 5.44/5.69 ( ( member_nat @ N4 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N4 ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I6 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_suminf
% 5.44/5.69 thf(fact_7722_sum__le__suminf,axiom,
% 5.44/5.69 ! [F: nat > real,I6: set_nat] :
% 5.44/5.69 ( ( summable_real @ F )
% 5.44/5.69 => ( ( finite_finite_nat @ I6 )
% 5.44/5.69 => ( ! [N4: nat] :
% 5.44/5.69 ( ( member_nat @ N4 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N4 ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I6 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_le_suminf
% 5.44/5.69 thf(fact_7723_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_complex,A: complex,B: complex > real,C: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.69 => ( ( ( member_complex @ A @ S )
% 5.44/5.69 => ( ( groups5808333547571424918x_real
% 5.44/5.69 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_complex @ A @ S )
% 5.44/5.69 => ( ( groups5808333547571424918x_real
% 5.44/5.69 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7724_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.69 => ( ( ( member_complex @ A @ S )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat
% 5.44/5.69 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_complex @ A @ S )
% 5.44/5.69 => ( ( groups5693394587270226106ex_nat
% 5.44/5.69 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7725_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_complex,A: complex,B: complex > int,C: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.69 => ( ( ( member_complex @ A @ S )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int
% 5.44/5.69 @ ^ [K3: complex] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_complex @ A @ S )
% 5.44/5.69 => ( ( groups5690904116761175830ex_int
% 5.44/5.69 @ ^ [K3: complex] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7726_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_int,A: int,B: int > complex,C: int > complex] :
% 5.44/5.69 ( ( finite_finite_int @ S )
% 5.44/5.69 => ( ( ( member_int @ A @ S )
% 5.44/5.69 => ( ( groups3049146728041665814omplex
% 5.44/5.69 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_complex @ ( B @ A ) @ ( groups3049146728041665814omplex @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_int @ A @ S )
% 5.44/5.69 => ( ( groups3049146728041665814omplex
% 5.44/5.69 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups3049146728041665814omplex @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7727_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_int,A: int,B: int > real,C: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ S )
% 5.44/5.69 => ( ( ( member_int @ A @ S )
% 5.44/5.69 => ( ( groups8778361861064173332t_real
% 5.44/5.69 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_int @ A @ S )
% 5.44/5.69 => ( ( groups8778361861064173332t_real
% 5.44/5.69 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7728_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_int,A: int,B: int > nat,C: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ S )
% 5.44/5.69 => ( ( ( member_int @ A @ S )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat
% 5.44/5.69 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_int @ A @ S )
% 5.44/5.69 => ( ( groups4541462559716669496nt_nat
% 5.44/5.69 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7729_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_real,A: real,B: real > complex,C: real > complex] :
% 5.44/5.69 ( ( finite_finite_real @ S )
% 5.44/5.69 => ( ( ( member_real @ A @ S )
% 5.44/5.69 => ( ( groups5754745047067104278omplex
% 5.44/5.69 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_complex @ ( B @ A ) @ ( groups5754745047067104278omplex @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_real @ A @ S )
% 5.44/5.69 => ( ( groups5754745047067104278omplex
% 5.44/5.69 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups5754745047067104278omplex @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7730_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_real,A: real,B: real > real,C: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ S )
% 5.44/5.69 => ( ( ( member_real @ A @ S )
% 5.44/5.69 => ( ( groups8097168146408367636l_real
% 5.44/5.69 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_real @ A @ S )
% 5.44/5.69 => ( ( groups8097168146408367636l_real
% 5.44/5.69 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7731_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_real,A: real,B: real > nat,C: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ S )
% 5.44/5.69 => ( ( ( member_real @ A @ S )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat
% 5.44/5.69 @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_nat @ ( B @ A ) @ ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_real @ A @ S )
% 5.44/5.69 => ( ( groups1935376822645274424al_nat
% 5.44/5.69 @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7732_sum_Odelta__remove,axiom,
% 5.44/5.69 ! [S: set_real,A: real,B: real > int,C: real > int] :
% 5.44/5.69 ( ( finite_finite_real @ S )
% 5.44/5.69 => ( ( ( member_real @ A @ S )
% 5.44/5.69 => ( ( groups1932886352136224148al_int
% 5.44/5.69 @ ^ [K3: real] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( plus_plus_int @ ( B @ A ) @ ( groups1932886352136224148al_int @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.44/5.69 & ( ~ ( member_real @ A @ S )
% 5.44/5.69 => ( ( groups1932886352136224148al_int
% 5.44/5.69 @ ^ [K3: real] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.69 @ S )
% 5.44/5.69 = ( groups1932886352136224148al_int @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.delta_remove
% 5.44/5.69 thf(fact_7733_set__encode__def,axiom,
% 5.44/5.69 ( nat_set_encode
% 5.44/5.69 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % set_encode_def
% 5.44/5.69 thf(fact_7734_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_int,A2: set_int,B: int,F: int > real] :
% 5.44/5.69 ( ( finite_finite_int @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.69 => ( ( member_int @ B @ ( minus_minus_set_int @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7735_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.69 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7736_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_int,A2: set_int,B: int,F: int > nat] :
% 5.44/5.69 ( ( finite_finite_int @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.69 => ( ( member_int @ B @ ( minus_minus_set_int @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7737_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.69 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7738_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_complex,A2: set_complex,B: complex,F: complex > int] :
% 5.44/5.69 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.69 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.69 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7739_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,B: real,F: real > real] :
% 5.44/5.69 ( ( finite_finite_real @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.69 => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7740_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,B: real,F: real > nat] :
% 5.44/5.69 ( ( finite_finite_real @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.69 => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7741_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_real,A2: set_real,B: real,F: real > int] :
% 5.44/5.69 ( ( finite_finite_real @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.69 => ( ( member_real @ B @ ( minus_minus_set_real @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7742_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_nat,A2: set_nat,B: nat,F: nat > int] :
% 5.44/5.69 ( ( finite_finite_nat @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.69 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7743_sum__strict__mono2,axiom,
% 5.44/5.69 ! [B2: set_nat,A2: set_nat,B: nat,F: nat > nat] :
% 5.44/5.69 ( ( finite_finite_nat @ B2 )
% 5.44/5.69 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.69 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 5.44/5.69 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ B2 )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B2 ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_strict_mono2
% 5.44/5.69 thf(fact_7744_member__le__sum,axiom,
% 5.44/5.69 ! [I2: complex,A2: set_complex,F: complex > extended_enat] :
% 5.44/5.69 ( ( member_complex @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ I2 ) @ ( groups1752964319039525884d_enat @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7745_member__le__sum,axiom,
% 5.44/5.69 ! [I2: complex,A2: set_complex,F: complex > real] :
% 5.44/5.69 ( ( member_complex @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7746_member__le__sum,axiom,
% 5.44/5.69 ! [I2: int,A2: set_int,F: int > extended_enat] :
% 5.44/5.69 ( ( member_int @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ I2 ) @ ( groups4225252721152677374d_enat @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7747_member__le__sum,axiom,
% 5.44/5.69 ! [I2: int,A2: set_int,F: int > real] :
% 5.44/5.69 ( ( member_int @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7748_member__le__sum,axiom,
% 5.44/5.69 ! [I2: real,A2: set_real,F: real > extended_enat] :
% 5.44/5.69 ( ( member_real @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ I2 ) @ ( groups2800946370649118462d_enat @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7749_member__le__sum,axiom,
% 5.44/5.69 ! [I2: real,A2: set_real,F: real > real] :
% 5.44/5.69 ( ( member_real @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ord_less_eq_real @ ( F @ I2 ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7750_member__le__sum,axiom,
% 5.44/5.69 ! [I2: nat,A2: set_nat,F: nat > extended_enat] :
% 5.44/5.69 ( ( member_nat @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: nat] :
% 5.44/5.69 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite_finite_nat @ A2 )
% 5.44/5.69 => ( ord_le2932123472753598470d_enat @ ( F @ I2 ) @ ( groups7108830773950497114d_enat @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7751_member__le__sum,axiom,
% 5.44/5.69 ! [I2: complex,A2: set_complex,F: complex > nat] :
% 5.44/5.69 ( ( member_complex @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: complex] :
% 5.44/5.69 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7752_member__le__sum,axiom,
% 5.44/5.69 ! [I2: int,A2: set_int,F: int > nat] :
% 5.44/5.69 ( ( member_int @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: int] :
% 5.44/5.69 ( ( member_int @ X5 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite_finite_int @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7753_member__le__sum,axiom,
% 5.44/5.69 ! [I2: real,A2: set_real,F: real > nat] :
% 5.44/5.69 ( ( member_real @ I2 @ A2 )
% 5.44/5.69 => ( ! [X5: real] :
% 5.44/5.69 ( ( member_real @ X5 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 5.44/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.69 => ( ( finite_finite_real @ A2 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % member_le_sum
% 5.44/5.69 thf(fact_7754_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 5.44/5.69 ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups8097168146408367636l_real @ X @ I6 )
% 5.44/5.69 = one_one_real )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_real
% 5.44/5.69 @ ( abs_abs_real
% 5.44/5.69 @ ( minus_minus_real
% 5.44/5.69 @ ( groups8097168146408367636l_real
% 5.44/5.69 @ ^ [I5: real] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7755_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 5.44/5.69 ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups8778361861064173332t_real @ X @ I6 )
% 5.44/5.69 = one_one_real )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_real
% 5.44/5.69 @ ( abs_abs_real
% 5.44/5.69 @ ( minus_minus_real
% 5.44/5.69 @ ( groups8778361861064173332t_real
% 5.44/5.69 @ ^ [I5: int] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7756_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 5.44/5.69 ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups5808333547571424918x_real @ X @ I6 )
% 5.44/5.69 = one_one_real )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_real
% 5.44/5.69 @ ( abs_abs_real
% 5.44/5.69 @ ( minus_minus_real
% 5.44/5.69 @ ( groups5808333547571424918x_real
% 5.44/5.69 @ ^ [I5: complex] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7757_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat > real,A: product_prod_nat_nat > real,B: real,Delta: real] :
% 5.44/5.69 ( ! [I4: product_prod_nat_nat] :
% 5.44/5.69 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups4567486121110086003t_real @ X @ I6 )
% 5.44/5.69 = one_one_real )
% 5.44/5.69 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.69 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_real
% 5.44/5.69 @ ( abs_abs_real
% 5.44/5.69 @ ( minus_minus_real
% 5.44/5.69 @ ( groups4567486121110086003t_real
% 5.44/5.69 @ ^ [I5: product_prod_nat_nat] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7758_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_nat,X: nat > int,A: nat > int,B: int,Delta: int] :
% 5.44/5.69 ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups3539618377306564664at_int @ X @ I6 )
% 5.44/5.69 = one_one_int )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_int
% 5.44/5.69 @ ( abs_abs_int
% 5.44/5.69 @ ( minus_minus_int
% 5.44/5.69 @ ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7759_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_real,X: real > int,A: real > int,B: int,Delta: int] :
% 5.44/5.69 ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups1932886352136224148al_int @ X @ I6 )
% 5.44/5.69 = one_one_int )
% 5.44/5.69 => ( ! [I4: real] :
% 5.44/5.69 ( ( member_real @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_int
% 5.44/5.69 @ ( abs_abs_int
% 5.44/5.69 @ ( minus_minus_int
% 5.44/5.69 @ ( groups1932886352136224148al_int
% 5.44/5.69 @ ^ [I5: real] : ( times_times_int @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7760_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_complex,X: complex > int,A: complex > int,B: int,Delta: int] :
% 5.44/5.69 ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups5690904116761175830ex_int @ X @ I6 )
% 5.44/5.69 = one_one_int )
% 5.44/5.69 => ( ! [I4: complex] :
% 5.44/5.69 ( ( member_complex @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_int
% 5.44/5.69 @ ( abs_abs_int
% 5.44/5.69 @ ( minus_minus_int
% 5.44/5.69 @ ( groups5690904116761175830ex_int
% 5.44/5.69 @ ^ [I5: complex] : ( times_times_int @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7761_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat > int,A: product_prod_nat_nat > int,B: int,Delta: int] :
% 5.44/5.69 ( ! [I4: product_prod_nat_nat] :
% 5.44/5.69 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups975429370522433651at_int @ X @ I6 )
% 5.44/5.69 = one_one_int )
% 5.44/5.69 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.69 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_int
% 5.44/5.69 @ ( abs_abs_int
% 5.44/5.69 @ ( minus_minus_int
% 5.44/5.69 @ ( groups975429370522433651at_int
% 5.44/5.69 @ ^ [I5: product_prod_nat_nat] : ( times_times_int @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7762_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_nat,X: nat > real,A: nat > real,B: real,Delta: real] :
% 5.44/5.69 ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups6591440286371151544t_real @ X @ I6 )
% 5.44/5.69 = one_one_real )
% 5.44/5.69 => ( ! [I4: nat] :
% 5.44/5.69 ( ( member_nat @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_real
% 5.44/5.69 @ ( abs_abs_real
% 5.44/5.69 @ ( minus_minus_real
% 5.44/5.69 @ ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7763_convex__sum__bound__le,axiom,
% 5.44/5.69 ! [I6: set_int,X: int > int,A: int > int,B: int,Delta: int] :
% 5.44/5.69 ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I4 ) ) )
% 5.44/5.69 => ( ( ( groups4538972089207619220nt_int @ X @ I6 )
% 5.44/5.69 = one_one_int )
% 5.44/5.69 => ( ! [I4: int] :
% 5.44/5.69 ( ( member_int @ I4 @ I6 )
% 5.44/5.69 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.44/5.69 => ( ord_less_eq_int
% 5.44/5.69 @ ( abs_abs_int
% 5.44/5.69 @ ( minus_minus_int
% 5.44/5.69 @ ( groups4538972089207619220nt_int
% 5.44/5.69 @ ^ [I5: int] : ( times_times_int @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.44/5.69 @ I6 )
% 5.44/5.69 @ B ) )
% 5.44/5.69 @ Delta ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % convex_sum_bound_le
% 5.44/5.69 thf(fact_7764_arccos__lt__bounded,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.44/5.69 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_lt_bounded
% 5.44/5.69 thf(fact_7765_arccos__bounded,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.44/5.69 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_bounded
% 5.44/5.69 thf(fact_7766_sin__arccos__nonzero,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.69 => ( ( sin_real @ ( arccos @ X ) )
% 5.44/5.69 != zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sin_arccos_nonzero
% 5.44/5.69 thf(fact_7767_cos__int__times__real,axiom,
% 5.44/5.69 ! [M: int,X: real] :
% 5.44/5.69 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 5.44/5.69 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_int_times_real
% 5.44/5.69 thf(fact_7768_cos__int__times__real,axiom,
% 5.44/5.69 ! [M: int,X: real] :
% 5.44/5.69 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 5.44/5.69 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_int_times_real
% 5.44/5.69 thf(fact_7769_sin__int__times__real,axiom,
% 5.44/5.69 ! [M: int,X: real] :
% 5.44/5.69 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 5.44/5.69 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sin_int_times_real
% 5.44/5.69 thf(fact_7770_sin__int__times__real,axiom,
% 5.44/5.69 ! [M: int,X: real] :
% 5.44/5.69 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 5.44/5.69 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sin_int_times_real
% 5.44/5.69 thf(fact_7771_arccos__cos2,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.44/5.69 => ( ( arccos @ ( cos_real @ X ) )
% 5.44/5.69 = ( uminus_uminus_real @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_cos2
% 5.44/5.69 thf(fact_7772_arccos__minus,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.69 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.44/5.69 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_minus
% 5.44/5.69 thf(fact_7773_cos__arcsin__nonzero,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.69 => ( ( cos_real @ ( arcsin @ X ) )
% 5.44/5.69 != zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_arcsin_nonzero
% 5.44/5.69 thf(fact_7774_sum__natinterval__diff,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > complex] :
% 5.44/5.69 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.44/5.69 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = zero_zero_complex ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_natinterval_diff
% 5.44/5.69 thf(fact_7775_sum__natinterval__diff,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > int] :
% 5.44/5.69 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.44/5.69 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = zero_zero_int ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_natinterval_diff
% 5.44/5.69 thf(fact_7776_sum__natinterval__diff,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > real] :
% 5.44/5.69 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.44/5.69 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = zero_zero_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_natinterval_diff
% 5.44/5.69 thf(fact_7777_sum__telescope_H_H,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > complex] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.44/5.69 = ( minus_minus_complex @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_telescope''
% 5.44/5.69 thf(fact_7778_sum__telescope_H_H,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > int] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.44/5.69 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_telescope''
% 5.44/5.69 thf(fact_7779_sum__telescope_H_H,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,F: nat > real] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.44/5.69 = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_telescope''
% 5.44/5.69 thf(fact_7780_summable__partial__sum__bound,axiom,
% 5.44/5.69 ! [F: nat > complex,E: real] :
% 5.44/5.69 ( ( summable_complex @ F )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.44/5.69 => ~ ! [N8: nat] :
% 5.44/5.69 ~ ! [M2: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ N8 @ M2 )
% 5.44/5.69 => ! [N9: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N9 ) ) ) @ E ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % summable_partial_sum_bound
% 5.44/5.69 thf(fact_7781_summable__partial__sum__bound,axiom,
% 5.44/5.69 ! [F: nat > real,E: real] :
% 5.44/5.69 ( ( summable_real @ F )
% 5.44/5.69 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.44/5.69 => ~ ! [N8: nat] :
% 5.44/5.69 ~ ! [M2: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ N8 @ M2 )
% 5.44/5.69 => ! [N9: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N9 ) ) ) @ E ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % summable_partial_sum_bound
% 5.44/5.69 thf(fact_7782_mask__eq__sum__exp,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 5.44/5.69 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.69 @ ( collect_nat
% 5.44/5.69 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % mask_eq_sum_exp
% 5.44/5.69 thf(fact_7783_mask__eq__sum__exp,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 5.44/5.69 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.69 @ ( collect_nat
% 5.44/5.69 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % mask_eq_sum_exp
% 5.44/5.69 thf(fact_7784_sum__gp__multiplied,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,X: complex] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.44/5.69 = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_gp_multiplied
% 5.44/5.69 thf(fact_7785_sum__gp__multiplied,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,X: int] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.44/5.69 = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_gp_multiplied
% 5.44/5.69 thf(fact_7786_sum__gp__multiplied,axiom,
% 5.44/5.69 ! [M: nat,N2: nat,X: real] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.69 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.44/5.69 = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_gp_multiplied
% 5.44/5.69 thf(fact_7787_sum_Oin__pairs,axiom,
% 5.44/5.69 ! [G: nat > complex,M: nat,N2: nat] :
% 5.44/5.69 ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.69 = ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.in_pairs
% 5.44/5.69 thf(fact_7788_sum_Oin__pairs,axiom,
% 5.44/5.69 ! [G: nat > int,M: nat,N2: nat] :
% 5.44/5.69 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.69 = ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.in_pairs
% 5.44/5.69 thf(fact_7789_sum_Oin__pairs,axiom,
% 5.44/5.69 ! [G: nat > nat,M: nat,N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.in_pairs
% 5.44/5.69 thf(fact_7790_sum_Oin__pairs,axiom,
% 5.44/5.69 ! [G: nat > real,M: nat,N2: nat] :
% 5.44/5.69 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.69 = ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.in_pairs
% 5.44/5.69 thf(fact_7791_arccos,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.44/5.69 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.44/5.69 & ( ( cos_real @ ( arccos @ Y ) )
% 5.44/5.69 = Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos
% 5.44/5.69 thf(fact_7792_arccos__minus__abs,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.69 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.44/5.69 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_minus_abs
% 5.44/5.69 thf(fact_7793_cos__sin__eq,axiom,
% 5.44/5.69 ( cos_real
% 5.44/5.69 = ( ^ [X2: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_sin_eq
% 5.44/5.69 thf(fact_7794_cos__sin__eq,axiom,
% 5.44/5.69 ( cos_complex
% 5.44/5.69 = ( ^ [X2: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % cos_sin_eq
% 5.44/5.69 thf(fact_7795_sin__cos__eq,axiom,
% 5.44/5.69 ( sin_real
% 5.44/5.69 = ( ^ [X2: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sin_cos_eq
% 5.44/5.69 thf(fact_7796_sin__cos__eq,axiom,
% 5.44/5.69 ( sin_complex
% 5.44/5.69 = ( ^ [X2: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sin_cos_eq
% 5.44/5.69 thf(fact_7797_mask__eq__sum__exp__nat,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.69 @ ( collect_nat
% 5.44/5.69 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % mask_eq_sum_exp_nat
% 5.44/5.69 thf(fact_7798_gauss__sum__nat,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [X2: nat] : X2
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.69 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % gauss_sum_nat
% 5.44/5.69 thf(fact_7799_minus__sin__cos__eq,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( uminus_uminus_real @ ( sin_real @ X ) )
% 5.44/5.69 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % minus_sin_cos_eq
% 5.44/5.69 thf(fact_7800_minus__sin__cos__eq,axiom,
% 5.44/5.69 ! [X: complex] :
% 5.44/5.69 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X ) )
% 5.44/5.69 = ( cos_complex @ ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % minus_sin_cos_eq
% 5.44/5.69 thf(fact_7801_double__arith__series,axiom,
% 5.44/5.69 ! [A: extended_enat,D: extended_enat,N2: nat] :
% 5.44/5.69 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 5.44/5.69 @ ( groups7108830773950497114d_enat
% 5.44/5.69 @ ^ [I5: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ D ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_arith_series
% 5.44/5.69 thf(fact_7802_double__arith__series,axiom,
% 5.44/5.69 ! [A: int,D: int,N2: nat] :
% 5.44/5.69 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.44/5.69 @ ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_arith_series
% 5.44/5.69 thf(fact_7803_double__arith__series,axiom,
% 5.44/5.69 ! [A: complex,D: complex,N2: nat] :
% 5.44/5.69 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.44/5.69 @ ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ D ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_arith_series
% 5.44/5.69 thf(fact_7804_double__arith__series,axiom,
% 5.44/5.69 ! [A: code_integer,D: code_integer,N2: nat] :
% 5.44/5.69 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.44/5.69 @ ( groups7501900531339628137nteger
% 5.44/5.69 @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_arith_series
% 5.44/5.69 thf(fact_7805_double__arith__series,axiom,
% 5.44/5.69 ! [A: nat,D: nat,N2: nat] :
% 5.44/5.69 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.44/5.69 @ ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_arith_series
% 5.44/5.69 thf(fact_7806_double__arith__series,axiom,
% 5.44/5.69 ! [A: real,D: real,N2: nat] :
% 5.44/5.69 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.44/5.69 @ ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ D ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_arith_series
% 5.44/5.69 thf(fact_7807_double__gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum
% 5.44/5.69 thf(fact_7808_double__gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum
% 5.44/5.69 thf(fact_7809_double__gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum
% 5.44/5.69 thf(fact_7810_double__gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum
% 5.44/5.69 thf(fact_7811_double__gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum
% 5.44/5.69 thf(fact_7812_double__gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.69 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum
% 5.44/5.69 thf(fact_7813_arith__series__nat,axiom,
% 5.44/5.69 ! [A: nat,D: nat,N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I5 @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.69 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arith_series_nat
% 5.44/5.69 thf(fact_7814_Sum__Icc__nat,axiom,
% 5.44/5.69 ! [M: nat,N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [X2: nat] : X2
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.69 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % Sum_Icc_nat
% 5.44/5.69 thf(fact_7815_arccos__le__pi2,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_le_pi2
% 5.44/5.69 thf(fact_7816_arcsin__lt__bounded,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.44/5.69 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_lt_bounded
% 5.44/5.69 thf(fact_7817_arcsin__lbound,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_lbound
% 5.44/5.69 thf(fact_7818_arcsin__ubound,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_ubound
% 5.44/5.69 thf(fact_7819_arcsin__bounded,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.44/5.69 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_bounded
% 5.44/5.69 thf(fact_7820_arcsin__sin,axiom,
% 5.44/5.69 ! [X: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( arcsin @ ( sin_real @ X ) )
% 5.44/5.69 = X ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_sin
% 5.44/5.69 thf(fact_7821_arith__series,axiom,
% 5.44/5.69 ! [A: int,D: int,N2: nat] :
% 5.44/5.69 ( ( groups3539618377306564664at_int
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.69 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arith_series
% 5.44/5.69 thf(fact_7822_arith__series,axiom,
% 5.44/5.69 ! [A: code_integer,D: code_integer,N2: nat] :
% 5.44/5.69 ( ( groups7501900531339628137nteger
% 5.44/5.69 @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.69 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arith_series
% 5.44/5.69 thf(fact_7823_arith__series,axiom,
% 5.44/5.69 ! [A: nat,D: nat,N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 5.44/5.69 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.69 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arith_series
% 5.44/5.69 thf(fact_7824_gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.69 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % gauss_sum
% 5.44/5.69 thf(fact_7825_gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.69 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % gauss_sum
% 5.44/5.69 thf(fact_7826_gauss__sum,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.69 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % gauss_sum
% 5.44/5.69 thf(fact_7827_double__gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.44/5.69 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7828_double__gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.44/5.69 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7829_double__gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.44/5.69 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7830_double__gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.44/5.69 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7831_double__gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.44/5.69 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7832_double__gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.44/5.69 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % double_gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7833_sum__gp__offset,axiom,
% 5.44/5.69 ! [X: complex,M: nat,N2: nat] :
% 5.44/5.69 ( ( ( X = one_one_complex )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 5.44/5.69 & ( ( X != one_one_complex )
% 5.44/5.69 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.44/5.69 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_gp_offset
% 5.44/5.69 thf(fact_7834_sum__gp__offset,axiom,
% 5.44/5.69 ! [X: real,M: nat,N2: nat] :
% 5.44/5.69 ( ( ( X = one_one_real )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 5.44/5.69 & ( ( X != one_one_real )
% 5.44/5.69 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.44/5.69 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_gp_offset
% 5.44/5.69 thf(fact_7835_arcsin,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.44/5.69 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.44/5.69 = Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin
% 5.44/5.69 thf(fact_7836_arcsin__pi,axiom,
% 5.44/5.69 ! [Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.44/5.69 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.44/5.69 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.44/5.69 = Y ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_pi
% 5.44/5.69 thf(fact_7837_arcsin__le__iff,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 5.44/5.69 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arcsin_le_iff
% 5.44/5.69 thf(fact_7838_le__arcsin__iff,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.69 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.69 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.69 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 5.44/5.69 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % le_arcsin_iff
% 5.44/5.69 thf(fact_7839_arccos__cos__eq__abs__2pi,axiom,
% 5.44/5.69 ! [Theta: real] :
% 5.44/5.69 ~ ! [K2: int] :
% 5.44/5.69 ( ( arccos @ ( cos_real @ Theta ) )
% 5.44/5.69 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arccos_cos_eq_abs_2pi
% 5.44/5.69 thf(fact_7840_gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.44/5.69 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7841_gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.44/5.69 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7842_gauss__sum__from__Suc__0,axiom,
% 5.44/5.69 ! [N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.44/5.69 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % gauss_sum_from_Suc_0
% 5.44/5.69 thf(fact_7843_arsinh__def,axiom,
% 5.44/5.69 ( arsinh_real
% 5.44/5.69 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % arsinh_def
% 5.44/5.69 thf(fact_7844_lemma__termdiff2,axiom,
% 5.44/5.69 ! [H2: complex,Z: complex,N2: nat] :
% 5.44/5.69 ( ( H2 != zero_zero_complex )
% 5.44/5.69 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.44/5.69 = ( times_times_complex @ H2
% 5.44/5.69 @ ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [P4: nat] :
% 5.44/5.69 ( groups2073611262835488442omplex
% 5.44/5.69 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.44/5.69 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.44/5.69 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lemma_termdiff2
% 5.44/5.69 thf(fact_7845_lemma__termdiff2,axiom,
% 5.44/5.69 ! [H2: real,Z: real,N2: nat] :
% 5.44/5.69 ( ( H2 != zero_zero_real )
% 5.44/5.69 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.44/5.69 = ( times_times_real @ H2
% 5.44/5.69 @ ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [P4: nat] :
% 5.44/5.69 ( groups6591440286371151544t_real
% 5.44/5.69 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.44/5.69 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P4 ) ) )
% 5.44/5.69 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lemma_termdiff2
% 5.44/5.69 thf(fact_7846_geometric__deriv__sums,axiom,
% 5.44/5.69 ! [Z: real] :
% 5.44/5.69 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.44/5.69 => ( sums_real
% 5.44/5.69 @ ^ [N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) )
% 5.44/5.69 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % geometric_deriv_sums
% 5.44/5.69 thf(fact_7847_geometric__deriv__sums,axiom,
% 5.44/5.69 ! [Z: complex] :
% 5.44/5.69 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.44/5.69 => ( sums_complex
% 5.44/5.69 @ ^ [N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) )
% 5.44/5.69 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % geometric_deriv_sums
% 5.44/5.69 thf(fact_7848_monoI1,axiom,
% 5.44/5.69 ! [X8: nat > real] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_real @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) )
% 5.44/5.69 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI1
% 5.44/5.69 thf(fact_7849_monoI1,axiom,
% 5.44/5.69 ! [X8: nat > set_real] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_set_real @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) )
% 5.44/5.69 => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI1
% 5.44/5.69 thf(fact_7850_monoI1,axiom,
% 5.44/5.69 ! [X8: nat > set_nat] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_set_nat @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) )
% 5.44/5.69 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI1
% 5.44/5.69 thf(fact_7851_monoI1,axiom,
% 5.44/5.69 ! [X8: nat > num] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_num @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) )
% 5.44/5.69 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI1
% 5.44/5.69 thf(fact_7852_monoI1,axiom,
% 5.44/5.69 ! [X8: nat > nat] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) )
% 5.44/5.69 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI1
% 5.44/5.69 thf(fact_7853_monoI1,axiom,
% 5.44/5.69 ! [X8: nat > int] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_int @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) )
% 5.44/5.69 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI1
% 5.44/5.69 thf(fact_7854_monoI2,axiom,
% 5.44/5.69 ! [X8: nat > real] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_real @ ( X8 @ N4 ) @ ( X8 @ M5 ) ) )
% 5.44/5.69 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI2
% 5.44/5.69 thf(fact_7855_monoI2,axiom,
% 5.44/5.69 ! [X8: nat > set_real] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_set_real @ ( X8 @ N4 ) @ ( X8 @ M5 ) ) )
% 5.44/5.69 => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI2
% 5.44/5.69 thf(fact_7856_monoI2,axiom,
% 5.44/5.69 ! [X8: nat > set_nat] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_set_nat @ ( X8 @ N4 ) @ ( X8 @ M5 ) ) )
% 5.44/5.69 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI2
% 5.44/5.69 thf(fact_7857_monoI2,axiom,
% 5.44/5.69 ! [X8: nat > num] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_num @ ( X8 @ N4 ) @ ( X8 @ M5 ) ) )
% 5.44/5.69 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI2
% 5.44/5.69 thf(fact_7858_monoI2,axiom,
% 5.44/5.69 ! [X8: nat > nat] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_nat @ ( X8 @ N4 ) @ ( X8 @ M5 ) ) )
% 5.44/5.69 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI2
% 5.44/5.69 thf(fact_7859_monoI2,axiom,
% 5.44/5.69 ! [X8: nat > int] :
% 5.44/5.69 ( ! [M5: nat,N4: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.44/5.69 => ( ord_less_eq_int @ ( X8 @ N4 ) @ ( X8 @ M5 ) ) )
% 5.44/5.69 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoI2
% 5.44/5.69 thf(fact_7860_monoseq__def,axiom,
% 5.44/5.69 ( topolo6980174941875973593q_real
% 5.44/5.69 = ( ^ [X4: nat > real] :
% 5.44/5.69 ( ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_real @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.44/5.69 | ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_real @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoseq_def
% 5.44/5.69 thf(fact_7861_monoseq__def,axiom,
% 5.44/5.69 ( topolo2489691266198938127t_real
% 5.44/5.69 = ( ^ [X4: nat > set_real] :
% 5.44/5.69 ( ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_set_real @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.44/5.69 | ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_set_real @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoseq_def
% 5.44/5.69 thf(fact_7862_monoseq__def,axiom,
% 5.44/5.69 ( topolo7278393974255667507et_nat
% 5.44/5.69 = ( ^ [X4: nat > set_nat] :
% 5.44/5.69 ( ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_set_nat @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.44/5.69 | ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_set_nat @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoseq_def
% 5.44/5.69 thf(fact_7863_monoseq__def,axiom,
% 5.44/5.69 ( topolo1459490580787246023eq_num
% 5.44/5.69 = ( ^ [X4: nat > num] :
% 5.44/5.69 ( ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_num @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.44/5.69 | ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_num @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoseq_def
% 5.44/5.69 thf(fact_7864_monoseq__def,axiom,
% 5.44/5.69 ( topolo4902158794631467389eq_nat
% 5.44/5.69 = ( ^ [X4: nat > nat] :
% 5.44/5.69 ( ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_nat @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.44/5.69 | ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_nat @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoseq_def
% 5.44/5.69 thf(fact_7865_monoseq__def,axiom,
% 5.44/5.69 ( topolo4899668324122417113eq_int
% 5.44/5.69 = ( ^ [X4: nat > int] :
% 5.44/5.69 ( ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_int @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.44/5.69 | ! [M6: nat,N: nat] :
% 5.44/5.69 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.69 => ( ord_less_eq_int @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % monoseq_def
% 5.44/5.69 thf(fact_7866_lessThan__iff,axiom,
% 5.44/5.69 ! [I2: extended_enat,K: extended_enat] :
% 5.44/5.69 ( ( member_Extended_enat @ I2 @ ( set_or8419480210114673929d_enat @ K ) )
% 5.44/5.69 = ( ord_le72135733267957522d_enat @ I2 @ K ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_iff
% 5.44/5.69 thf(fact_7867_lessThan__iff,axiom,
% 5.44/5.69 ! [I2: num,K: num] :
% 5.44/5.69 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 5.44/5.69 = ( ord_less_num @ I2 @ K ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_iff
% 5.44/5.69 thf(fact_7868_lessThan__iff,axiom,
% 5.44/5.69 ! [I2: int,K: int] :
% 5.44/5.69 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 5.44/5.69 = ( ord_less_int @ I2 @ K ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_iff
% 5.44/5.69 thf(fact_7869_lessThan__iff,axiom,
% 5.44/5.69 ! [I2: nat,K: nat] :
% 5.44/5.69 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 5.44/5.69 = ( ord_less_nat @ I2 @ K ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_iff
% 5.44/5.69 thf(fact_7870_lessThan__iff,axiom,
% 5.44/5.69 ! [I2: real,K: real] :
% 5.44/5.69 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 5.44/5.69 = ( ord_less_real @ I2 @ K ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_iff
% 5.44/5.69 thf(fact_7871_lessThan__subset__iff,axiom,
% 5.44/5.69 ! [X: num,Y: num] :
% 5.44/5.69 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 5.44/5.69 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_subset_iff
% 5.44/5.69 thf(fact_7872_lessThan__subset__iff,axiom,
% 5.44/5.69 ! [X: int,Y: int] :
% 5.44/5.69 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 5.44/5.69 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_subset_iff
% 5.44/5.69 thf(fact_7873_lessThan__subset__iff,axiom,
% 5.44/5.69 ! [X: nat,Y: nat] :
% 5.44/5.69 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.44/5.69 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_subset_iff
% 5.44/5.69 thf(fact_7874_lessThan__subset__iff,axiom,
% 5.44/5.69 ! [X: real,Y: real] :
% 5.44/5.69 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 5.44/5.69 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_subset_iff
% 5.44/5.69 thf(fact_7875_sum_OlessThan__Suc,axiom,
% 5.44/5.69 ! [G: nat > complex,N2: nat] :
% 5.44/5.69 ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.lessThan_Suc
% 5.44/5.69 thf(fact_7876_sum_OlessThan__Suc,axiom,
% 5.44/5.69 ! [G: nat > int,N2: nat] :
% 5.44/5.69 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.lessThan_Suc
% 5.44/5.69 thf(fact_7877_sum_OlessThan__Suc,axiom,
% 5.44/5.69 ! [G: nat > nat,N2: nat] :
% 5.44/5.69 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.lessThan_Suc
% 5.44/5.69 thf(fact_7878_sum_OlessThan__Suc,axiom,
% 5.44/5.69 ! [G: nat > real,N2: nat] :
% 5.44/5.69 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.69 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum.lessThan_Suc
% 5.44/5.69 thf(fact_7879_powser__sums__zero__iff,axiom,
% 5.44/5.69 ! [A: nat > complex,X: complex] :
% 5.44/5.69 ( ( sums_complex
% 5.44/5.69 @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 5.44/5.69 @ X )
% 5.44/5.69 = ( ( A @ zero_zero_nat )
% 5.44/5.69 = X ) ) ).
% 5.44/5.69
% 5.44/5.69 % powser_sums_zero_iff
% 5.44/5.69 thf(fact_7880_powser__sums__zero__iff,axiom,
% 5.44/5.69 ! [A: nat > real,X: real] :
% 5.44/5.69 ( ( sums_real
% 5.44/5.69 @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 5.44/5.69 @ X )
% 5.44/5.69 = ( ( A @ zero_zero_nat )
% 5.44/5.69 = X ) ) ).
% 5.44/5.69
% 5.44/5.69 % powser_sums_zero_iff
% 5.44/5.69 thf(fact_7881_sum__diff__distrib,axiom,
% 5.44/5.69 ! [Q: real > nat,P: real > nat,N2: real] :
% 5.44/5.69 ( ! [X5: real] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.44/5.69 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 5.44/5.69 = ( groups1935376822645274424al_nat
% 5.44/5.69 @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.44/5.69 @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff_distrib
% 5.44/5.69 thf(fact_7882_sum__diff__distrib,axiom,
% 5.44/5.69 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 5.44/5.69 ( ! [X5: nat] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.44/5.69 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.44/5.69 = ( groups3542108847815614940at_nat
% 5.44/5.69 @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.44/5.69 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sum_diff_distrib
% 5.44/5.69 thf(fact_7883_sums__le,axiom,
% 5.44/5.69 ! [F: nat > real,G: nat > real,S3: real,T: real] :
% 5.44/5.69 ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.44/5.69 => ( ( sums_real @ F @ S3 )
% 5.44/5.69 => ( ( sums_real @ G @ T )
% 5.44/5.69 => ( ord_less_eq_real @ S3 @ T ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_le
% 5.44/5.69 thf(fact_7884_sums__le,axiom,
% 5.44/5.69 ! [F: nat > nat,G: nat > nat,S3: nat,T: nat] :
% 5.44/5.69 ( ! [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.44/5.69 => ( ( sums_nat @ F @ S3 )
% 5.44/5.69 => ( ( sums_nat @ G @ T )
% 5.44/5.69 => ( ord_less_eq_nat @ S3 @ T ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_le
% 5.44/5.69 thf(fact_7885_sums__le,axiom,
% 5.44/5.69 ! [F: nat > int,G: nat > int,S3: int,T: int] :
% 5.44/5.69 ( ! [N4: nat] : ( ord_less_eq_int @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.44/5.69 => ( ( sums_int @ F @ S3 )
% 5.44/5.69 => ( ( sums_int @ G @ T )
% 5.44/5.69 => ( ord_less_eq_int @ S3 @ T ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_le
% 5.44/5.69 thf(fact_7886_sums__mult2,axiom,
% 5.44/5.69 ! [F: nat > complex,A: complex,C: complex] :
% 5.44/5.69 ( ( sums_complex @ F @ A )
% 5.44/5.69 => ( sums_complex
% 5.44/5.69 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C )
% 5.44/5.69 @ ( times_times_complex @ A @ C ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_mult2
% 5.44/5.69 thf(fact_7887_sums__mult2,axiom,
% 5.44/5.69 ! [F: nat > real,A: real,C: real] :
% 5.44/5.69 ( ( sums_real @ F @ A )
% 5.44/5.69 => ( sums_real
% 5.44/5.69 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C )
% 5.44/5.69 @ ( times_times_real @ A @ C ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_mult2
% 5.44/5.69 thf(fact_7888_sums__mult,axiom,
% 5.44/5.69 ! [F: nat > complex,A: complex,C: complex] :
% 5.44/5.69 ( ( sums_complex @ F @ A )
% 5.44/5.69 => ( sums_complex
% 5.44/5.69 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 5.44/5.69 @ ( times_times_complex @ C @ A ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_mult
% 5.44/5.69 thf(fact_7889_sums__mult,axiom,
% 5.44/5.69 ! [F: nat > real,A: real,C: real] :
% 5.44/5.69 ( ( sums_real @ F @ A )
% 5.44/5.69 => ( sums_real
% 5.44/5.69 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 5.44/5.69 @ ( times_times_real @ C @ A ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_mult
% 5.44/5.69 thf(fact_7890_sums__add,axiom,
% 5.44/5.69 ! [F: nat > complex,A: complex,G: nat > complex,B: complex] :
% 5.44/5.69 ( ( sums_complex @ F @ A )
% 5.44/5.69 => ( ( sums_complex @ G @ B )
% 5.44/5.69 => ( sums_complex
% 5.44/5.69 @ ^ [N: nat] : ( plus_plus_complex @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.69 @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_add
% 5.44/5.69 thf(fact_7891_sums__add,axiom,
% 5.44/5.69 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.44/5.69 ( ( sums_real @ F @ A )
% 5.44/5.69 => ( ( sums_real @ G @ B )
% 5.44/5.69 => ( sums_real
% 5.44/5.69 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.69 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_add
% 5.44/5.69 thf(fact_7892_sums__add,axiom,
% 5.44/5.69 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.44/5.69 ( ( sums_nat @ F @ A )
% 5.44/5.69 => ( ( sums_nat @ G @ B )
% 5.44/5.69 => ( sums_nat
% 5.44/5.69 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.69 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_add
% 5.44/5.69 thf(fact_7893_sums__add,axiom,
% 5.44/5.69 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.44/5.69 ( ( sums_int @ F @ A )
% 5.44/5.69 => ( ( sums_int @ G @ B )
% 5.44/5.69 => ( sums_int
% 5.44/5.69 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.69 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_add
% 5.44/5.69 thf(fact_7894_sums__divide,axiom,
% 5.44/5.69 ! [F: nat > real,A: real,C: real] :
% 5.44/5.69 ( ( sums_real @ F @ A )
% 5.44/5.69 => ( sums_real
% 5.44/5.69 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C )
% 5.44/5.69 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_divide
% 5.44/5.69 thf(fact_7895_sums__divide,axiom,
% 5.44/5.69 ! [F: nat > complex,A: complex,C: complex] :
% 5.44/5.69 ( ( sums_complex @ F @ A )
% 5.44/5.69 => ( sums_complex
% 5.44/5.69 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C )
% 5.44/5.69 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_divide
% 5.44/5.69 thf(fact_7896_lessThan__def,axiom,
% 5.44/5.69 ( set_or8419480210114673929d_enat
% 5.44/5.69 = ( ^ [U2: extended_enat] :
% 5.44/5.69 ( collec4429806609662206161d_enat
% 5.44/5.69 @ ^ [X2: extended_enat] : ( ord_le72135733267957522d_enat @ X2 @ U2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_def
% 5.44/5.69 thf(fact_7897_lessThan__def,axiom,
% 5.44/5.69 ( set_ord_lessThan_num
% 5.44/5.69 = ( ^ [U2: num] :
% 5.44/5.69 ( collect_num
% 5.44/5.69 @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_def
% 5.44/5.69 thf(fact_7898_lessThan__def,axiom,
% 5.44/5.69 ( set_ord_lessThan_int
% 5.44/5.69 = ( ^ [U2: int] :
% 5.44/5.69 ( collect_int
% 5.44/5.69 @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_def
% 5.44/5.69 thf(fact_7899_lessThan__def,axiom,
% 5.44/5.69 ( set_ord_lessThan_nat
% 5.44/5.69 = ( ^ [U2: nat] :
% 5.44/5.69 ( collect_nat
% 5.44/5.69 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_def
% 5.44/5.69 thf(fact_7900_lessThan__def,axiom,
% 5.44/5.69 ( set_or5984915006950818249n_real
% 5.44/5.69 = ( ^ [U2: real] :
% 5.44/5.69 ( collect_real
% 5.44/5.69 @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % lessThan_def
% 5.44/5.69 thf(fact_7901_sums__iff__shift,axiom,
% 5.44/5.69 ! [F: nat > complex,N2: nat,S3: complex] :
% 5.44/5.69 ( ( sums_complex
% 5.44/5.69 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.44/5.69 @ S3 )
% 5.44/5.69 = ( sums_complex @ F @ ( plus_plus_complex @ S3 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.69
% 5.44/5.69 % sums_iff_shift
% 5.44/5.69 thf(fact_7902_sums__iff__shift,axiom,
% 5.44/5.69 ! [F: nat > real,N2: nat,S3: real] :
% 5.44/5.69 ( ( sums_real
% 5.44/5.69 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.44/5.69 @ S3 )
% 5.44/5.69 = ( sums_real @ F @ ( plus_plus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_iff_shift
% 5.44/5.70 thf(fact_7903_sums__split__initial__segment,axiom,
% 5.44/5.70 ! [F: nat > complex,S3: complex,N2: nat] :
% 5.44/5.70 ( ( sums_complex @ F @ S3 )
% 5.44/5.70 => ( sums_complex
% 5.44/5.70 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.44/5.70 @ ( minus_minus_complex @ S3 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_split_initial_segment
% 5.44/5.70 thf(fact_7904_sums__split__initial__segment,axiom,
% 5.44/5.70 ! [F: nat > real,S3: real,N2: nat] :
% 5.44/5.70 ( ( sums_real @ F @ S3 )
% 5.44/5.70 => ( sums_real
% 5.44/5.70 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.44/5.70 @ ( minus_minus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_split_initial_segment
% 5.44/5.70 thf(fact_7905_sums__iff__shift_H,axiom,
% 5.44/5.70 ! [F: nat > complex,N2: nat,S3: complex] :
% 5.44/5.70 ( ( sums_complex
% 5.44/5.70 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.44/5.70 @ ( minus_minus_complex @ S3 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.44/5.70 = ( sums_complex @ F @ S3 ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_iff_shift'
% 5.44/5.70 thf(fact_7906_sums__iff__shift_H,axiom,
% 5.44/5.70 ! [F: nat > real,N2: nat,S3: real] :
% 5.44/5.70 ( ( sums_real
% 5.44/5.70 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.44/5.70 @ ( minus_minus_real @ S3 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.44/5.70 = ( sums_real @ F @ S3 ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_iff_shift'
% 5.44/5.70 thf(fact_7907_lessThan__strict__subset__iff,axiom,
% 5.44/5.70 ! [M: extended_enat,N2: extended_enat] :
% 5.44/5.70 ( ( ord_le2529575680413868914d_enat @ ( set_or8419480210114673929d_enat @ M ) @ ( set_or8419480210114673929d_enat @ N2 ) )
% 5.44/5.70 = ( ord_le72135733267957522d_enat @ M @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % lessThan_strict_subset_iff
% 5.44/5.70 thf(fact_7908_lessThan__strict__subset__iff,axiom,
% 5.44/5.70 ! [M: num,N2: num] :
% 5.44/5.70 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 5.44/5.70 = ( ord_less_num @ M @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % lessThan_strict_subset_iff
% 5.44/5.70 thf(fact_7909_lessThan__strict__subset__iff,axiom,
% 5.44/5.70 ! [M: int,N2: int] :
% 5.44/5.70 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 5.44/5.70 = ( ord_less_int @ M @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % lessThan_strict_subset_iff
% 5.44/5.70 thf(fact_7910_lessThan__strict__subset__iff,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % lessThan_strict_subset_iff
% 5.44/5.70 thf(fact_7911_lessThan__strict__subset__iff,axiom,
% 5.44/5.70 ! [M: real,N2: real] :
% 5.44/5.70 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 5.44/5.70 = ( ord_less_real @ M @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % lessThan_strict_subset_iff
% 5.44/5.70 thf(fact_7912_sums__mult2__iff,axiom,
% 5.44/5.70 ! [C: complex,F: nat > complex,D: complex] :
% 5.44/5.70 ( ( C != zero_zero_complex )
% 5.44/5.70 => ( ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C )
% 5.44/5.70 @ ( times_times_complex @ D @ C ) )
% 5.44/5.70 = ( sums_complex @ F @ D ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_mult2_iff
% 5.44/5.70 thf(fact_7913_sums__mult2__iff,axiom,
% 5.44/5.70 ! [C: real,F: nat > real,D: real] :
% 5.44/5.70 ( ( C != zero_zero_real )
% 5.44/5.70 => ( ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C )
% 5.44/5.70 @ ( times_times_real @ D @ C ) )
% 5.44/5.70 = ( sums_real @ F @ D ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_mult2_iff
% 5.44/5.70 thf(fact_7914_sums__mult__iff,axiom,
% 5.44/5.70 ! [C: complex,F: nat > complex,D: complex] :
% 5.44/5.70 ( ( C != zero_zero_complex )
% 5.44/5.70 => ( ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 5.44/5.70 @ ( times_times_complex @ C @ D ) )
% 5.44/5.70 = ( sums_complex @ F @ D ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_mult_iff
% 5.44/5.70 thf(fact_7915_sums__mult__iff,axiom,
% 5.44/5.70 ! [C: real,F: nat > real,D: real] :
% 5.44/5.70 ( ( C != zero_zero_real )
% 5.44/5.70 => ( ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 5.44/5.70 @ ( times_times_real @ C @ D ) )
% 5.44/5.70 = ( sums_real @ F @ D ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_mult_iff
% 5.44/5.70 thf(fact_7916_lessThan__Suc,axiom,
% 5.44/5.70 ! [K: nat] :
% 5.44/5.70 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.44/5.70 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % lessThan_Suc
% 5.44/5.70 thf(fact_7917_sum__subtractf__nat,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.44/5.70 ( ! [X5: real] :
% 5.44/5.70 ( ( member_real @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ( groups1935376822645274424al_nat
% 5.44/5.70 @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.70 @ A2 )
% 5.44/5.70 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_subtractf_nat
% 5.44/5.70 thf(fact_7918_sum__subtractf__nat,axiom,
% 5.44/5.70 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ( groups4541462559716669496nt_nat
% 5.44/5.70 @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.70 @ A2 )
% 5.44/5.70 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_subtractf_nat
% 5.44/5.70 thf(fact_7919_sum__subtractf__nat,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.44/5.70 ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ( groups5693394587270226106ex_nat
% 5.44/5.70 @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.70 @ A2 )
% 5.44/5.70 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_subtractf_nat
% 5.44/5.70 thf(fact_7920_sum__subtractf__nat,axiom,
% 5.44/5.70 ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 5.44/5.70 ( ! [X5: product_prod_nat_nat] :
% 5.44/5.70 ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ( groups977919841031483927at_nat
% 5.44/5.70 @ ^ [X2: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.70 @ A2 )
% 5.44/5.70 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_subtractf_nat
% 5.44/5.70 thf(fact_7921_sum__subtractf__nat,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ( groups3542108847815614940at_nat
% 5.44/5.70 @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.70 @ A2 )
% 5.44/5.70 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_subtractf_nat
% 5.44/5.70 thf(fact_7922_sum__eq__Suc0__iff,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > nat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.44/5.70 = ( suc @ zero_zero_nat ) )
% 5.44/5.70 = ( ? [X2: complex] :
% 5.44/5.70 ( ( member_complex @ X2 @ A2 )
% 5.44/5.70 & ( ( F @ X2 )
% 5.44/5.70 = ( suc @ zero_zero_nat ) )
% 5.44/5.70 & ! [Y3: complex] :
% 5.44/5.70 ( ( member_complex @ Y3 @ A2 )
% 5.44/5.70 => ( ( X2 != Y3 )
% 5.44/5.70 => ( ( F @ Y3 )
% 5.44/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_eq_Suc0_iff
% 5.44/5.70 thf(fact_7923_sum__eq__Suc0__iff,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > nat] :
% 5.44/5.70 ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.44/5.70 = ( suc @ zero_zero_nat ) )
% 5.44/5.70 = ( ? [X2: nat] :
% 5.44/5.70 ( ( member_nat @ X2 @ A2 )
% 5.44/5.70 & ( ( F @ X2 )
% 5.44/5.70 = ( suc @ zero_zero_nat ) )
% 5.44/5.70 & ! [Y3: nat] :
% 5.44/5.70 ( ( member_nat @ Y3 @ A2 )
% 5.44/5.70 => ( ( X2 != Y3 )
% 5.44/5.70 => ( ( F @ Y3 )
% 5.44/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_eq_Suc0_iff
% 5.44/5.70 thf(fact_7924_sum__SucD,axiom,
% 5.44/5.70 ! [F: nat > nat,A2: set_nat,N2: nat] :
% 5.44/5.70 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.44/5.70 = ( suc @ N2 ) )
% 5.44/5.70 => ? [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 & ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_SucD
% 5.44/5.70 thf(fact_7925_sum__eq__1__iff,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > nat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.44/5.70 = one_one_nat )
% 5.44/5.70 = ( ? [X2: complex] :
% 5.44/5.70 ( ( member_complex @ X2 @ A2 )
% 5.44/5.70 & ( ( F @ X2 )
% 5.44/5.70 = one_one_nat )
% 5.44/5.70 & ! [Y3: complex] :
% 5.44/5.70 ( ( member_complex @ Y3 @ A2 )
% 5.44/5.70 => ( ( X2 != Y3 )
% 5.44/5.70 => ( ( F @ Y3 )
% 5.44/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_eq_1_iff
% 5.44/5.70 thf(fact_7926_sum__eq__1__iff,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > nat] :
% 5.44/5.70 ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.44/5.70 = one_one_nat )
% 5.44/5.70 = ( ? [X2: nat] :
% 5.44/5.70 ( ( member_nat @ X2 @ A2 )
% 5.44/5.70 & ( ( F @ X2 )
% 5.44/5.70 = one_one_nat )
% 5.44/5.70 & ! [Y3: nat] :
% 5.44/5.70 ( ( member_nat @ Y3 @ A2 )
% 5.44/5.70 => ( ( X2 != Y3 )
% 5.44/5.70 => ( ( F @ Y3 )
% 5.44/5.70 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_eq_1_iff
% 5.44/5.70 thf(fact_7927_sums__mult__D,axiom,
% 5.44/5.70 ! [C: real,F: nat > real,A: real] :
% 5.44/5.70 ( ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 5.44/5.70 @ A )
% 5.44/5.70 => ( ( C != zero_zero_real )
% 5.44/5.70 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_mult_D
% 5.44/5.70 thf(fact_7928_sums__mult__D,axiom,
% 5.44/5.70 ! [C: complex,F: nat > complex,A: complex] :
% 5.44/5.70 ( ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 5.44/5.70 @ A )
% 5.44/5.70 => ( ( C != zero_zero_complex )
% 5.44/5.70 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_mult_D
% 5.44/5.70 thf(fact_7929_sums__Suc__imp,axiom,
% 5.44/5.70 ! [F: nat > complex,S3: complex] :
% 5.44/5.70 ( ( ( F @ zero_zero_nat )
% 5.44/5.70 = zero_zero_complex )
% 5.44/5.70 => ( ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.44/5.70 @ S3 )
% 5.44/5.70 => ( sums_complex @ F @ S3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_Suc_imp
% 5.44/5.70 thf(fact_7930_sums__Suc__imp,axiom,
% 5.44/5.70 ! [F: nat > real,S3: real] :
% 5.44/5.70 ( ( ( F @ zero_zero_nat )
% 5.44/5.70 = zero_zero_real )
% 5.44/5.70 => ( ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.44/5.70 @ S3 )
% 5.44/5.70 => ( sums_real @ F @ S3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_Suc_imp
% 5.44/5.70 thf(fact_7931_sums__Suc,axiom,
% 5.44/5.70 ! [F: nat > complex,L2: complex] :
% 5.44/5.70 ( ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.44/5.70 @ L2 )
% 5.44/5.70 => ( sums_complex @ F @ ( plus_plus_complex @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_Suc
% 5.44/5.70 thf(fact_7932_sums__Suc,axiom,
% 5.44/5.70 ! [F: nat > real,L2: real] :
% 5.44/5.70 ( ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.44/5.70 @ L2 )
% 5.44/5.70 => ( sums_real @ F @ ( plus_plus_real @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_Suc
% 5.44/5.70 thf(fact_7933_sums__Suc,axiom,
% 5.44/5.70 ! [F: nat > nat,L2: nat] :
% 5.44/5.70 ( ( sums_nat
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.44/5.70 @ L2 )
% 5.44/5.70 => ( sums_nat @ F @ ( plus_plus_nat @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_Suc
% 5.44/5.70 thf(fact_7934_sums__Suc,axiom,
% 5.44/5.70 ! [F: nat > int,L2: int] :
% 5.44/5.70 ( ( sums_int
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.44/5.70 @ L2 )
% 5.44/5.70 => ( sums_int @ F @ ( plus_plus_int @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_Suc
% 5.44/5.70 thf(fact_7935_sums__Suc__iff,axiom,
% 5.44/5.70 ! [F: nat > complex,S3: complex] :
% 5.44/5.70 ( ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.44/5.70 @ S3 )
% 5.44/5.70 = ( sums_complex @ F @ ( plus_plus_complex @ S3 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_Suc_iff
% 5.44/5.70 thf(fact_7936_sums__Suc__iff,axiom,
% 5.44/5.70 ! [F: nat > real,S3: real] :
% 5.44/5.70 ( ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.44/5.70 @ S3 )
% 5.44/5.70 = ( sums_real @ F @ ( plus_plus_real @ S3 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_Suc_iff
% 5.44/5.70 thf(fact_7937_sums__zero__iff__shift,axiom,
% 5.44/5.70 ! [N2: nat,F: nat > complex,S3: complex] :
% 5.44/5.70 ( ! [I4: nat] :
% 5.44/5.70 ( ( ord_less_nat @ I4 @ N2 )
% 5.44/5.70 => ( ( F @ I4 )
% 5.44/5.70 = zero_zero_complex ) )
% 5.44/5.70 => ( ( sums_complex
% 5.44/5.70 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.44/5.70 @ S3 )
% 5.44/5.70 = ( sums_complex @ F @ S3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_zero_iff_shift
% 5.44/5.70 thf(fact_7938_sums__zero__iff__shift,axiom,
% 5.44/5.70 ! [N2: nat,F: nat > real,S3: real] :
% 5.44/5.70 ( ! [I4: nat] :
% 5.44/5.70 ( ( ord_less_nat @ I4 @ N2 )
% 5.44/5.70 => ( ( F @ I4 )
% 5.44/5.70 = zero_zero_real ) )
% 5.44/5.70 => ( ( sums_real
% 5.44/5.70 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.44/5.70 @ S3 )
% 5.44/5.70 = ( sums_real @ F @ S3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_zero_iff_shift
% 5.44/5.70 thf(fact_7939_lessThan__nat__numeral,axiom,
% 5.44/5.70 ! [K: num] :
% 5.44/5.70 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.44/5.70 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % lessThan_nat_numeral
% 5.44/5.70 thf(fact_7940_sum_Onat__diff__reindex,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups3542108847815614940at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.nat_diff_reindex
% 5.44/5.70 thf(fact_7941_sum_Onat__diff__reindex,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.nat_diff_reindex
% 5.44/5.70 thf(fact_7942_sum__nth__roots,axiom,
% 5.44/5.70 ! [N2: nat,C: complex] :
% 5.44/5.70 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.44/5.70 => ( ( groups7754918857620584856omplex
% 5.44/5.70 @ ^ [X2: complex] : X2
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [Z5: complex] :
% 5.44/5.70 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.70 = C ) ) )
% 5.44/5.70 = zero_zero_complex ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_nth_roots
% 5.44/5.70 thf(fact_7943_powser__sums__if,axiom,
% 5.44/5.70 ! [M: nat,Z: complex] :
% 5.44/5.70 ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( if_complex @ ( N = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N ) )
% 5.44/5.70 @ ( power_power_complex @ Z @ M ) ) ).
% 5.44/5.70
% 5.44/5.70 % powser_sums_if
% 5.44/5.70 thf(fact_7944_powser__sums__if,axiom,
% 5.44/5.70 ! [M: nat,Z: real] :
% 5.44/5.70 ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( if_real @ ( N = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N ) )
% 5.44/5.70 @ ( power_power_real @ Z @ M ) ) ).
% 5.44/5.70
% 5.44/5.70 % powser_sums_if
% 5.44/5.70 thf(fact_7945_powser__sums__if,axiom,
% 5.44/5.70 ! [M: nat,Z: int] :
% 5.44/5.70 ( sums_int
% 5.44/5.70 @ ^ [N: nat] : ( times_times_int @ ( if_int @ ( N = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N ) )
% 5.44/5.70 @ ( power_power_int @ Z @ M ) ) ).
% 5.44/5.70
% 5.44/5.70 % powser_sums_if
% 5.44/5.70 thf(fact_7946_powser__sums__zero,axiom,
% 5.44/5.70 ! [A: nat > complex] :
% 5.44/5.70 ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 5.44/5.70 @ ( A @ zero_zero_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % powser_sums_zero
% 5.44/5.70 thf(fact_7947_powser__sums__zero,axiom,
% 5.44/5.70 ! [A: nat > real] :
% 5.44/5.70 ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 5.44/5.70 @ ( A @ zero_zero_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % powser_sums_zero
% 5.44/5.70 thf(fact_7948_sum__diff__nat,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.70 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 5.44/5.70 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_diff_nat
% 5.44/5.70 thf(fact_7949_sum__diff__nat,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,F: real > nat] :
% 5.44/5.70 ( ( finite_finite_real @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.70 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ B2 ) )
% 5.44/5.70 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_diff_nat
% 5.44/5.70 thf(fact_7950_sum__diff__nat,axiom,
% 5.44/5.70 ! [B2: set_nat,A2: set_nat,F: nat > nat] :
% 5.44/5.70 ( ( finite_finite_nat @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.70 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 5.44/5.70 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_diff_nat
% 5.44/5.70 thf(fact_7951_sums__If__finite__set_H,axiom,
% 5.44/5.70 ! [G: nat > complex,S: complex,A2: set_nat,S5: complex,F: nat > complex] :
% 5.44/5.70 ( ( sums_complex @ G @ S )
% 5.44/5.70 => ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( S5
% 5.44/5.70 = ( plus_plus_complex @ S
% 5.44/5.70 @ ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [N: nat] : ( minus_minus_complex @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.70 @ A2 ) ) )
% 5.44/5.70 => ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( if_complex @ ( member_nat @ N @ A2 ) @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.70 @ S5 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_If_finite_set'
% 5.44/5.70 thf(fact_7952_sums__If__finite__set_H,axiom,
% 5.44/5.70 ! [G: nat > real,S: real,A2: set_nat,S5: real,F: nat > real] :
% 5.44/5.70 ( ( sums_real @ G @ S )
% 5.44/5.70 => ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( S5
% 5.44/5.70 = ( plus_plus_real @ S
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.70 @ A2 ) ) )
% 5.44/5.70 => ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( if_real @ ( member_nat @ N @ A2 ) @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.70 @ S5 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_If_finite_set'
% 5.44/5.70 thf(fact_7953_suminf__le__const,axiom,
% 5.44/5.70 ! [F: nat > int,X: int] :
% 5.44/5.70 ( ( summable_int @ F )
% 5.44/5.70 => ( ! [N4: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N4 ) ) @ X )
% 5.44/5.70 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % suminf_le_const
% 5.44/5.70 thf(fact_7954_suminf__le__const,axiom,
% 5.44/5.70 ! [F: nat > nat,X: nat] :
% 5.44/5.70 ( ( summable_nat @ F )
% 5.44/5.70 => ( ! [N4: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N4 ) ) @ X )
% 5.44/5.70 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % suminf_le_const
% 5.44/5.70 thf(fact_7955_suminf__le__const,axiom,
% 5.44/5.70 ! [F: nat > real,X: real] :
% 5.44/5.70 ( ( summable_real @ F )
% 5.44/5.70 => ( ! [N4: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N4 ) ) @ X )
% 5.44/5.70 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % suminf_le_const
% 5.44/5.70 thf(fact_7956_sum_OlessThan__Suc__shift,axiom,
% 5.44/5.70 ! [G: nat > complex,N2: nat] :
% 5.44/5.70 ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.lessThan_Suc_shift
% 5.44/5.70 thf(fact_7957_sum_OlessThan__Suc__shift,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat] :
% 5.44/5.70 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.lessThan_Suc_shift
% 5.44/5.70 thf(fact_7958_sum_OlessThan__Suc__shift,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups3542108847815614940at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.lessThan_Suc_shift
% 5.44/5.70 thf(fact_7959_sum_OlessThan__Suc__shift,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.lessThan_Suc_shift
% 5.44/5.70 thf(fact_7960_sum__lessThan__telescope_H,axiom,
% 5.44/5.70 ! [F: nat > complex,M: nat] :
% 5.44/5.70 ( ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [N: nat] : ( minus_minus_complex @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( minus_minus_complex @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_lessThan_telescope'
% 5.44/5.70 thf(fact_7961_sum__lessThan__telescope_H,axiom,
% 5.44/5.70 ! [F: nat > int,M: nat] :
% 5.44/5.70 ( ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_lessThan_telescope'
% 5.44/5.70 thf(fact_7962_sum__lessThan__telescope_H,axiom,
% 5.44/5.70 ! [F: nat > real,M: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_lessThan_telescope'
% 5.44/5.70 thf(fact_7963_sum__lessThan__telescope,axiom,
% 5.44/5.70 ! [F: nat > complex,M: nat] :
% 5.44/5.70 ( ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [N: nat] : ( minus_minus_complex @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( minus_minus_complex @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_lessThan_telescope
% 5.44/5.70 thf(fact_7964_sum__lessThan__telescope,axiom,
% 5.44/5.70 ! [F: nat > int,M: nat] :
% 5.44/5.70 ( ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_lessThan_telescope
% 5.44/5.70 thf(fact_7965_sum__lessThan__telescope,axiom,
% 5.44/5.70 ! [F: nat > real,M: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [N: nat] : ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_lessThan_telescope
% 5.44/5.70 thf(fact_7966_sumr__diff__mult__const2,axiom,
% 5.44/5.70 ! [F: nat > int,N2: nat,R: int] :
% 5.44/5.70 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ R ) )
% 5.44/5.70 = ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ R )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sumr_diff_mult_const2
% 5.44/5.70 thf(fact_7967_sumr__diff__mult__const2,axiom,
% 5.44/5.70 ! [F: nat > complex,N2: nat,R: complex] :
% 5.44/5.70 ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ R ) )
% 5.44/5.70 = ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [I5: nat] : ( minus_minus_complex @ ( F @ I5 ) @ R )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sumr_diff_mult_const2
% 5.44/5.70 thf(fact_7968_sumr__diff__mult__const2,axiom,
% 5.44/5.70 ! [F: nat > code_integer,N2: nat,R: code_integer] :
% 5.44/5.70 ( ( minus_8373710615458151222nteger @ ( groups7501900531339628137nteger @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ R ) )
% 5.44/5.70 = ( groups7501900531339628137nteger
% 5.44/5.70 @ ^ [I5: nat] : ( minus_8373710615458151222nteger @ ( F @ I5 ) @ R )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sumr_diff_mult_const2
% 5.44/5.70 thf(fact_7969_sumr__diff__mult__const2,axiom,
% 5.44/5.70 ! [F: nat > real,N2: nat,R: real] :
% 5.44/5.70 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ R ) )
% 5.44/5.70 = ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ R )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sumr_diff_mult_const2
% 5.44/5.70 thf(fact_7970_summableI__nonneg__bounded,axiom,
% 5.44/5.70 ! [F: nat > int,X: int] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N4 ) )
% 5.44/5.70 => ( ! [N4: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N4 ) ) @ X )
% 5.44/5.70 => ( summable_int @ F ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % summableI_nonneg_bounded
% 5.44/5.70 thf(fact_7971_summableI__nonneg__bounded,axiom,
% 5.44/5.70 ! [F: nat > nat,X: nat] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N4 ) )
% 5.44/5.70 => ( ! [N4: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N4 ) ) @ X )
% 5.44/5.70 => ( summable_nat @ F ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % summableI_nonneg_bounded
% 5.44/5.70 thf(fact_7972_summableI__nonneg__bounded,axiom,
% 5.44/5.70 ! [F: nat > real,X: real] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N4 ) )
% 5.44/5.70 => ( ! [N4: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N4 ) ) @ X )
% 5.44/5.70 => ( summable_real @ F ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % summableI_nonneg_bounded
% 5.44/5.70 thf(fact_7973_sum_OatLeast1__atMost__eq,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.44/5.70 = ( groups3542108847815614940at_nat
% 5.44/5.70 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.atLeast1_atMost_eq
% 5.44/5.70 thf(fact_7974_sum_OatLeast1__atMost__eq,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.44/5.70 = ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.atLeast1_atMost_eq
% 5.44/5.70 thf(fact_7975_sum__roots__unity,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.44/5.70 => ( ( groups7754918857620584856omplex
% 5.44/5.70 @ ^ [X2: complex] : X2
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [Z5: complex] :
% 5.44/5.70 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.70 = one_one_complex ) ) )
% 5.44/5.70 = zero_zero_complex ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_roots_unity
% 5.44/5.70 thf(fact_7976_one__diff__power__eq,axiom,
% 5.44/5.70 ! [X: complex,N2: nat] :
% 5.44/5.70 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_diff_power_eq
% 5.44/5.70 thf(fact_7977_one__diff__power__eq,axiom,
% 5.44/5.70 ! [X: int,N2: nat] :
% 5.44/5.70 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 5.44/5.70 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_diff_power_eq
% 5.44/5.70 thf(fact_7978_one__diff__power__eq,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_diff_power_eq
% 5.44/5.70 thf(fact_7979_power__diff__1__eq,axiom,
% 5.44/5.70 ! [X: complex,N2: nat] :
% 5.44/5.70 ( ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ one_one_complex )
% 5.44/5.70 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_diff_1_eq
% 5.44/5.70 thf(fact_7980_power__diff__1__eq,axiom,
% 5.44/5.70 ! [X: int,N2: nat] :
% 5.44/5.70 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ one_one_int )
% 5.44/5.70 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_diff_1_eq
% 5.44/5.70 thf(fact_7981_power__diff__1__eq,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ one_one_real )
% 5.44/5.70 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_diff_1_eq
% 5.44/5.70 thf(fact_7982_geometric__sum,axiom,
% 5.44/5.70 ! [X: complex,N2: nat] :
% 5.44/5.70 ( ( X != one_one_complex )
% 5.44/5.70 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % geometric_sum
% 5.44/5.70 thf(fact_7983_geometric__sum,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( X != one_one_real )
% 5.44/5.70 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % geometric_sum
% 5.44/5.70 thf(fact_7984_suminf__split__initial__segment,axiom,
% 5.44/5.70 ! [F: nat > complex,K: nat] :
% 5.44/5.70 ( ( summable_complex @ F )
% 5.44/5.70 => ( ( suminf_complex @ F )
% 5.44/5.70 = ( plus_plus_complex
% 5.44/5.70 @ ( suminf_complex
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.44/5.70 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % suminf_split_initial_segment
% 5.44/5.70 thf(fact_7985_suminf__split__initial__segment,axiom,
% 5.44/5.70 ! [F: nat > real,K: nat] :
% 5.44/5.70 ( ( summable_real @ F )
% 5.44/5.70 => ( ( suminf_real @ F )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( suminf_real
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.44/5.70 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % suminf_split_initial_segment
% 5.44/5.70 thf(fact_7986_suminf__minus__initial__segment,axiom,
% 5.44/5.70 ! [F: nat > complex,K: nat] :
% 5.44/5.70 ( ( summable_complex @ F )
% 5.44/5.70 => ( ( suminf_complex
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.44/5.70 = ( minus_minus_complex @ ( suminf_complex @ F ) @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % suminf_minus_initial_segment
% 5.44/5.70 thf(fact_7987_suminf__minus__initial__segment,axiom,
% 5.44/5.70 ! [F: nat > real,K: nat] :
% 5.44/5.70 ( ( summable_real @ F )
% 5.44/5.70 => ( ( suminf_real
% 5.44/5.70 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.44/5.70 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % suminf_minus_initial_segment
% 5.44/5.70 thf(fact_7988_sum__less__suminf,axiom,
% 5.44/5.70 ! [F: nat > int,N2: nat] :
% 5.44/5.70 ( ( summable_int @ F )
% 5.44/5.70 => ( ! [M5: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.44/5.70 => ( ord_less_int @ zero_zero_int @ ( F @ M5 ) ) )
% 5.44/5.70 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_less_suminf
% 5.44/5.70 thf(fact_7989_sum__less__suminf,axiom,
% 5.44/5.70 ! [F: nat > nat,N2: nat] :
% 5.44/5.70 ( ( summable_nat @ F )
% 5.44/5.70 => ( ! [M5: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.44/5.70 => ( ord_less_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 5.44/5.70 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_less_suminf
% 5.44/5.70 thf(fact_7990_sum__less__suminf,axiom,
% 5.44/5.70 ! [F: nat > real,N2: nat] :
% 5.44/5.70 ( ( summable_real @ F )
% 5.44/5.70 => ( ! [M5: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.44/5.70 => ( ord_less_real @ zero_zero_real @ ( F @ M5 ) ) )
% 5.44/5.70 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_less_suminf
% 5.44/5.70 thf(fact_7991_sum__gp__strict,axiom,
% 5.44/5.70 ! [X: complex,N2: nat] :
% 5.44/5.70 ( ( ( X = one_one_complex )
% 5.44/5.70 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.44/5.70 & ( ( X != one_one_complex )
% 5.44/5.70 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_gp_strict
% 5.44/5.70 thf(fact_7992_sum__gp__strict,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( ( X = one_one_real )
% 5.44/5.70 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.44/5.70 & ( ( X != one_one_real )
% 5.44/5.70 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_gp_strict
% 5.44/5.70 thf(fact_7993_lemma__termdiff1,axiom,
% 5.44/5.70 ! [Z: complex,H2: complex,M: nat] :
% 5.44/5.70 ( ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [P4: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ P4 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P4 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % lemma_termdiff1
% 5.44/5.70 thf(fact_7994_lemma__termdiff1,axiom,
% 5.44/5.70 ! [Z: int,H2: int,M: nat] :
% 5.44/5.70 ( ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [P4: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ P4 ) ) @ ( power_power_int @ Z @ M ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ Z @ P4 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % lemma_termdiff1
% 5.44/5.70 thf(fact_7995_lemma__termdiff1,axiom,
% 5.44/5.70 ! [Z: real,H2: real,M: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [P4: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ P4 ) ) @ ( power_power_real @ Z @ M ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) )
% 5.44/5.70 = ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ Z @ P4 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P4 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P4 ) ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % lemma_termdiff1
% 5.44/5.70 thf(fact_7996_diff__power__eq__sum,axiom,
% 5.44/5.70 ! [X: complex,N2: nat,Y: complex] :
% 5.44/5.70 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.44/5.70 @ ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [P4: nat] : ( times_times_complex @ ( power_power_complex @ X @ P4 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P4 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diff_power_eq_sum
% 5.44/5.70 thf(fact_7997_diff__power__eq__sum,axiom,
% 5.44/5.70 ! [X: int,N2: nat,Y: int] :
% 5.44/5.70 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.44/5.70 @ ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [P4: nat] : ( times_times_int @ ( power_power_int @ X @ P4 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P4 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diff_power_eq_sum
% 5.44/5.70 thf(fact_7998_diff__power__eq__sum,axiom,
% 5.44/5.70 ! [X: real,N2: nat,Y: real] :
% 5.44/5.70 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [P4: nat] : ( times_times_real @ ( power_power_real @ X @ P4 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P4 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diff_power_eq_sum
% 5.44/5.70 thf(fact_7999_power__diff__sumr2,axiom,
% 5.44/5.70 ! [X: complex,N2: nat,Y: complex] :
% 5.44/5.70 ( ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.44/5.70 @ ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_complex @ X @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_diff_sumr2
% 5.44/5.70 thf(fact_8000_power__diff__sumr2,axiom,
% 5.44/5.70 ! [X: int,N2: nat,Y: int] :
% 5.44/5.70 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.44/5.70 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.44/5.70 @ ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_int @ X @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_diff_sumr2
% 5.44/5.70 thf(fact_8001_power__diff__sumr2,axiom,
% 5.44/5.70 ! [X: real,N2: nat,Y: real] :
% 5.44/5.70 ( ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_real @ X @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_diff_sumr2
% 5.44/5.70 thf(fact_8002_geometric__sums,axiom,
% 5.44/5.70 ! [C: real] :
% 5.44/5.70 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.44/5.70 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % geometric_sums
% 5.44/5.70 thf(fact_8003_geometric__sums,axiom,
% 5.44/5.70 ! [C: complex] :
% 5.44/5.70 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.44/5.70 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % geometric_sums
% 5.44/5.70 thf(fact_8004_power__half__series,axiom,
% 5.44/5.70 ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N ) )
% 5.44/5.70 @ one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % power_half_series
% 5.44/5.70 thf(fact_8005_real__sum__nat__ivl__bounded2,axiom,
% 5.44/5.70 ! [N2: nat,F: nat > code_integer,K5: code_integer,K: nat] :
% 5.44/5.70 ( ! [P7: nat] :
% 5.44/5.70 ( ( ord_less_nat @ P7 @ N2 )
% 5.44/5.70 => ( ord_le3102999989581377725nteger @ ( F @ P7 ) @ K5 ) )
% 5.44/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ K5 )
% 5.44/5.70 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ K5 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % real_sum_nat_ivl_bounded2
% 5.44/5.70 thf(fact_8006_real__sum__nat__ivl__bounded2,axiom,
% 5.44/5.70 ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 5.44/5.70 ( ! [P7: nat] :
% 5.44/5.70 ( ( ord_less_nat @ P7 @ N2 )
% 5.44/5.70 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.44/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.44/5.70 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % real_sum_nat_ivl_bounded2
% 5.44/5.70 thf(fact_8007_real__sum__nat__ivl__bounded2,axiom,
% 5.44/5.70 ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 5.44/5.70 ( ! [P7: nat] :
% 5.44/5.70 ( ( ord_less_nat @ P7 @ N2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.44/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % real_sum_nat_ivl_bounded2
% 5.44/5.70 thf(fact_8008_real__sum__nat__ivl__bounded2,axiom,
% 5.44/5.70 ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 5.44/5.70 ( ! [P7: nat] :
% 5.44/5.70 ( ( ord_less_nat @ P7 @ N2 )
% 5.44/5.70 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % real_sum_nat_ivl_bounded2
% 5.44/5.70 thf(fact_8009_sum__less__suminf2,axiom,
% 5.44/5.70 ! [F: nat > int,N2: nat,I2: nat] :
% 5.44/5.70 ( ( summable_int @ F )
% 5.44/5.70 => ( ! [M5: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.44/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M5 ) ) )
% 5.44/5.70 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.44/5.70 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.44/5.70 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_less_suminf2
% 5.44/5.70 thf(fact_8010_sum__less__suminf2,axiom,
% 5.44/5.70 ! [F: nat > nat,N2: nat,I2: nat] :
% 5.44/5.70 ( ( summable_nat @ F )
% 5.44/5.70 => ( ! [M5: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.44/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 5.44/5.70 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.44/5.70 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.44/5.70 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_less_suminf2
% 5.44/5.70 thf(fact_8011_sum__less__suminf2,axiom,
% 5.44/5.70 ! [F: nat > real,N2: nat,I2: nat] :
% 5.44/5.70 ( ( summable_real @ F )
% 5.44/5.70 => ( ! [M5: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.44/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M5 ) ) )
% 5.44/5.70 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.44/5.70 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.44/5.70 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_less_suminf2
% 5.44/5.70 thf(fact_8012_one__diff__power__eq_H,axiom,
% 5.44/5.70 ! [X: complex,N2: nat] :
% 5.44/5.70 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 5.44/5.70 @ ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [I5: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_diff_power_eq'
% 5.44/5.70 thf(fact_8013_one__diff__power__eq_H,axiom,
% 5.44/5.70 ! [X: int,N2: nat] :
% 5.44/5.70 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 5.44/5.70 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 5.44/5.70 @ ( groups3539618377306564664at_int
% 5.44/5.70 @ ^ [I5: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_diff_power_eq'
% 5.44/5.70 thf(fact_8014_one__diff__power__eq_H,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [I5: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_diff_power_eq'
% 5.44/5.70 thf(fact_8015_sums__if_H,axiom,
% 5.44/5.70 ! [G: nat > real,X: real] :
% 5.44/5.70 ( ( sums_real @ G @ X )
% 5.44/5.70 => ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.70 @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_if'
% 5.44/5.70 thf(fact_8016_sums__if,axiom,
% 5.44/5.70 ! [G: nat > real,X: real,F: nat > real,Y: real] :
% 5.44/5.70 ( ( sums_real @ G @ X )
% 5.44/5.70 => ( ( sums_real @ F @ Y )
% 5.44/5.70 => ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( F @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.70 @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sums_if
% 5.44/5.70 thf(fact_8017_sum__split__even__odd,axiom,
% 5.44/5.70 ! [F: nat > real,G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( F @ I5 ) @ ( G @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [I5: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ one_one_nat ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_split_even_odd
% 5.44/5.70 thf(fact_8018_Sum__Icc__int,axiom,
% 5.44/5.70 ! [M: int,N2: int] :
% 5.44/5.70 ( ( ord_less_eq_int @ M @ N2 )
% 5.44/5.70 => ( ( groups4538972089207619220nt_int
% 5.44/5.70 @ ^ [X2: int] : X2
% 5.44/5.70 @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 5.44/5.70 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Sum_Icc_int
% 5.44/5.70 thf(fact_8019_sum__pos__lt__pair,axiom,
% 5.44/5.70 ! [F: nat > real,K: nat] :
% 5.44/5.70 ( ( summable_real @ F )
% 5.44/5.70 => ( ! [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 ) ) ) ) )
% 5.44/5.70 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_pos_lt_pair
% 5.44/5.70 thf(fact_8020_mono__SucI1,axiom,
% 5.44/5.70 ! [X8: nat > real] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_real @ ( X8 @ N4 ) @ ( X8 @ ( suc @ N4 ) ) )
% 5.44/5.70 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI1
% 5.44/5.70 thf(fact_8021_mono__SucI1,axiom,
% 5.44/5.70 ! [X8: nat > set_real] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_set_real @ ( X8 @ N4 ) @ ( X8 @ ( suc @ N4 ) ) )
% 5.44/5.70 => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI1
% 5.44/5.70 thf(fact_8022_mono__SucI1,axiom,
% 5.44/5.70 ! [X8: nat > set_nat] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_set_nat @ ( X8 @ N4 ) @ ( X8 @ ( suc @ N4 ) ) )
% 5.44/5.70 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI1
% 5.44/5.70 thf(fact_8023_mono__SucI1,axiom,
% 5.44/5.70 ! [X8: nat > num] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_num @ ( X8 @ N4 ) @ ( X8 @ ( suc @ N4 ) ) )
% 5.44/5.70 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI1
% 5.44/5.70 thf(fact_8024_mono__SucI1,axiom,
% 5.44/5.70 ! [X8: nat > nat] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_nat @ ( X8 @ N4 ) @ ( X8 @ ( suc @ N4 ) ) )
% 5.44/5.70 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI1
% 5.44/5.70 thf(fact_8025_mono__SucI1,axiom,
% 5.44/5.70 ! [X8: nat > int] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_int @ ( X8 @ N4 ) @ ( X8 @ ( suc @ N4 ) ) )
% 5.44/5.70 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI1
% 5.44/5.70 thf(fact_8026_mono__SucI2,axiom,
% 5.44/5.70 ! [X8: nat > real] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N4 ) ) @ ( X8 @ N4 ) )
% 5.44/5.70 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI2
% 5.44/5.70 thf(fact_8027_mono__SucI2,axiom,
% 5.44/5.70 ! [X8: nat > set_real] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_set_real @ ( X8 @ ( suc @ N4 ) ) @ ( X8 @ N4 ) )
% 5.44/5.70 => ( topolo2489691266198938127t_real @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI2
% 5.44/5.70 thf(fact_8028_mono__SucI2,axiom,
% 5.44/5.70 ! [X8: nat > set_nat] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_set_nat @ ( X8 @ ( suc @ N4 ) ) @ ( X8 @ N4 ) )
% 5.44/5.70 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI2
% 5.44/5.70 thf(fact_8029_mono__SucI2,axiom,
% 5.44/5.70 ! [X8: nat > num] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N4 ) ) @ ( X8 @ N4 ) )
% 5.44/5.70 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI2
% 5.44/5.70 thf(fact_8030_mono__SucI2,axiom,
% 5.44/5.70 ! [X8: nat > nat] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N4 ) ) @ ( X8 @ N4 ) )
% 5.44/5.70 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI2
% 5.44/5.70 thf(fact_8031_mono__SucI2,axiom,
% 5.44/5.70 ! [X8: nat > int] :
% 5.44/5.70 ( ! [N4: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N4 ) ) @ ( X8 @ N4 ) )
% 5.44/5.70 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.44/5.70
% 5.44/5.70 % mono_SucI2
% 5.44/5.70 thf(fact_8032_monoseq__Suc,axiom,
% 5.44/5.70 ( topolo6980174941875973593q_real
% 5.44/5.70 = ( ^ [X4: nat > real] :
% 5.44/5.70 ( ! [N: nat] : ( ord_less_eq_real @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.44/5.70 | ! [N: nat] : ( ord_less_eq_real @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % monoseq_Suc
% 5.44/5.70 thf(fact_8033_monoseq__Suc,axiom,
% 5.44/5.70 ( topolo2489691266198938127t_real
% 5.44/5.70 = ( ^ [X4: nat > set_real] :
% 5.44/5.70 ( ! [N: nat] : ( ord_less_eq_set_real @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.44/5.70 | ! [N: nat] : ( ord_less_eq_set_real @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % monoseq_Suc
% 5.44/5.70 thf(fact_8034_monoseq__Suc,axiom,
% 5.44/5.70 ( topolo7278393974255667507et_nat
% 5.44/5.70 = ( ^ [X4: nat > set_nat] :
% 5.44/5.70 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.44/5.70 | ! [N: nat] : ( ord_less_eq_set_nat @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % monoseq_Suc
% 5.44/5.70 thf(fact_8035_monoseq__Suc,axiom,
% 5.44/5.70 ( topolo1459490580787246023eq_num
% 5.44/5.70 = ( ^ [X4: nat > num] :
% 5.44/5.70 ( ! [N: nat] : ( ord_less_eq_num @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.44/5.70 | ! [N: nat] : ( ord_less_eq_num @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % monoseq_Suc
% 5.44/5.70 thf(fact_8036_monoseq__Suc,axiom,
% 5.44/5.70 ( topolo4902158794631467389eq_nat
% 5.44/5.70 = ( ^ [X4: nat > nat] :
% 5.44/5.70 ( ! [N: nat] : ( ord_less_eq_nat @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.44/5.70 | ! [N: nat] : ( ord_less_eq_nat @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % monoseq_Suc
% 5.44/5.70 thf(fact_8037_monoseq__Suc,axiom,
% 5.44/5.70 ( topolo4899668324122417113eq_int
% 5.44/5.70 = ( ^ [X4: nat > int] :
% 5.44/5.70 ( ! [N: nat] : ( ord_less_eq_int @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.44/5.70 | ! [N: nat] : ( ord_less_eq_int @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % monoseq_Suc
% 5.44/5.70 thf(fact_8038_sum__bounds__lt__plus1,axiom,
% 5.44/5.70 ! [F: nat > nat,Mm: nat] :
% 5.44/5.70 ( ( groups3542108847815614940at_nat
% 5.44/5.70 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.44/5.70 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_bounds_lt_plus1
% 5.44/5.70 thf(fact_8039_sum__bounds__lt__plus1,axiom,
% 5.44/5.70 ! [F: nat > real,Mm: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.44/5.70 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum_bounds_lt_plus1
% 5.44/5.70 thf(fact_8040_sumr__cos__zero__one,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % sumr_cos_zero_one
% 5.44/5.70 thf(fact_8041_diffs__equiv,axiom,
% 5.44/5.70 ! [C: nat > real,X: real] :
% 5.44/5.70 ( ( summable_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) )
% 5.44/5.70 => ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( C @ N ) ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.44/5.70 @ ( suminf_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diffs_equiv
% 5.44/5.70 thf(fact_8042_diffs__equiv,axiom,
% 5.44/5.70 ! [C: nat > complex,X: complex] :
% 5.44/5.70 ( ( summable_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) )
% 5.44/5.70 => ( sums_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( C @ N ) ) @ ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.44/5.70 @ ( suminf_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diffs_equiv
% 5.44/5.70 thf(fact_8043_sin__paired,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.44/5.70 @ ( sin_real @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % sin_paired
% 5.44/5.70 thf(fact_8044_fact__0,axiom,
% 5.44/5.70 ( ( semiri4449623510593786356d_enat @ zero_zero_nat )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ).
% 5.44/5.70
% 5.44/5.70 % fact_0
% 5.44/5.70 thf(fact_8045_fact__0,axiom,
% 5.44/5.70 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.44/5.70 = one_one_complex ) ).
% 5.44/5.70
% 5.44/5.70 % fact_0
% 5.44/5.70 thf(fact_8046_fact__0,axiom,
% 5.44/5.70 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.44/5.70 = one_one_int ) ).
% 5.44/5.70
% 5.44/5.70 % fact_0
% 5.44/5.70 thf(fact_8047_fact__0,axiom,
% 5.44/5.70 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % fact_0
% 5.44/5.70 thf(fact_8048_fact__0,axiom,
% 5.44/5.70 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.44/5.70 = one_one_nat ) ).
% 5.44/5.70
% 5.44/5.70 % fact_0
% 5.44/5.70 thf(fact_8049_fact__1,axiom,
% 5.44/5.70 ( ( semiri4449623510593786356d_enat @ one_one_nat )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ).
% 5.44/5.70
% 5.44/5.70 % fact_1
% 5.44/5.70 thf(fact_8050_fact__1,axiom,
% 5.44/5.70 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.44/5.70 = one_one_complex ) ).
% 5.44/5.70
% 5.44/5.70 % fact_1
% 5.44/5.70 thf(fact_8051_fact__1,axiom,
% 5.44/5.70 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.44/5.70 = one_one_int ) ).
% 5.44/5.70
% 5.44/5.70 % fact_1
% 5.44/5.70 thf(fact_8052_fact__1,axiom,
% 5.44/5.70 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % fact_1
% 5.44/5.70 thf(fact_8053_fact__1,axiom,
% 5.44/5.70 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.44/5.70 = one_one_nat ) ).
% 5.44/5.70
% 5.44/5.70 % fact_1
% 5.44/5.70 thf(fact_8054_cos__coeff__0,axiom,
% 5.44/5.70 ( ( cos_coeff @ zero_zero_nat )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % cos_coeff_0
% 5.44/5.70 thf(fact_8055_fact__Suc__0,axiom,
% 5.44/5.70 ( ( semiri4449623510593786356d_enat @ ( suc @ zero_zero_nat ) )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc_0
% 5.44/5.70 thf(fact_8056_fact__Suc__0,axiom,
% 5.44/5.70 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.44/5.70 = one_one_complex ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc_0
% 5.44/5.70 thf(fact_8057_fact__Suc__0,axiom,
% 5.44/5.70 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.44/5.70 = one_one_int ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc_0
% 5.44/5.70 thf(fact_8058_fact__Suc__0,axiom,
% 5.44/5.70 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc_0
% 5.44/5.70 thf(fact_8059_fact__Suc__0,axiom,
% 5.44/5.70 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.44/5.70 = one_one_nat ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc_0
% 5.44/5.70 thf(fact_8060_fact__Suc,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc
% 5.44/5.70 thf(fact_8061_fact__Suc,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( semiri5044797733671781792omplex @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc
% 5.44/5.70 thf(fact_8062_fact__Suc,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( semiri3624122377584611663nteger @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N2 ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc
% 5.44/5.70 thf(fact_8063_fact__Suc,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( semiri2265585572941072030t_real @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc
% 5.44/5.70 thf(fact_8064_fact__Suc,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_Suc
% 5.44/5.70 thf(fact_8065_fact__2,axiom,
% 5.44/5.70 ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.70 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_2
% 5.44/5.70 thf(fact_8066_fact__2,axiom,
% 5.44/5.70 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.70 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_2
% 5.44/5.70 thf(fact_8067_fact__2,axiom,
% 5.44/5.70 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.70 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_2
% 5.44/5.70 thf(fact_8068_fact__2,axiom,
% 5.44/5.70 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.70 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_2
% 5.44/5.70 thf(fact_8069_fact__2,axiom,
% 5.44/5.70 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.70 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_2
% 5.44/5.70 thf(fact_8070_fact__ge__zero,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_ge_zero
% 5.44/5.70 thf(fact_8071_fact__ge__zero,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_ge_zero
% 5.44/5.70 thf(fact_8072_fact__ge__zero,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_ge_zero
% 5.44/5.70 thf(fact_8073_fact__not__neg,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 5.44/5.70
% 5.44/5.70 % fact_not_neg
% 5.44/5.70 thf(fact_8074_fact__not__neg,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N2 ) @ zero_zero_real ) ).
% 5.44/5.70
% 5.44/5.70 % fact_not_neg
% 5.44/5.70 thf(fact_8075_fact__not__neg,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 5.44/5.70
% 5.44/5.70 % fact_not_neg
% 5.44/5.70 thf(fact_8076_fact__gt__zero,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_gt_zero
% 5.44/5.70 thf(fact_8077_fact__gt__zero,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_gt_zero
% 5.44/5.70 thf(fact_8078_fact__gt__zero,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_gt_zero
% 5.44/5.70 thf(fact_8079_fact__ge__1,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_ge_1
% 5.44/5.70 thf(fact_8080_fact__ge__1,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_ge_1
% 5.44/5.70 thf(fact_8081_fact__ge__1,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_ge_1
% 5.44/5.70 thf(fact_8082_fact__fact__dvd__fact,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_fact_dvd_fact
% 5.44/5.70 thf(fact_8083_fact__fact__dvd__fact,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_fact_dvd_fact
% 5.44/5.70 thf(fact_8084_fact__fact__dvd__fact,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_fact_dvd_fact
% 5.44/5.70 thf(fact_8085_fact__fact__dvd__fact,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_fact_dvd_fact
% 5.44/5.70 thf(fact_8086_fact__mono,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_mono
% 5.44/5.70 thf(fact_8087_fact__mono,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_mono
% 5.44/5.70 thf(fact_8088_fact__mono,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_mono
% 5.44/5.70 thf(fact_8089_fact__dvd,axiom,
% 5.44/5.70 ! [N2: nat,M: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.70 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_dvd
% 5.44/5.70 thf(fact_8090_fact__dvd,axiom,
% 5.44/5.70 ! [N2: nat,M: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_dvd
% 5.44/5.70 thf(fact_8091_fact__dvd,axiom,
% 5.44/5.70 ! [N2: nat,M: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.70 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_dvd
% 5.44/5.70 thf(fact_8092_fact__dvd,axiom,
% 5.44/5.70 ! [N2: nat,M: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.70 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_dvd
% 5.44/5.70 thf(fact_8093_choose__dvd,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % choose_dvd
% 5.44/5.70 thf(fact_8094_choose__dvd,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % choose_dvd
% 5.44/5.70 thf(fact_8095_choose__dvd,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % choose_dvd
% 5.44/5.70 thf(fact_8096_choose__dvd,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % choose_dvd
% 5.44/5.70 thf(fact_8097_fact__less__mono,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.70 => ( ( ord_less_nat @ M @ N2 )
% 5.44/5.70 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_less_mono
% 5.44/5.70 thf(fact_8098_fact__less__mono,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.70 => ( ( ord_less_nat @ M @ N2 )
% 5.44/5.70 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_less_mono
% 5.44/5.70 thf(fact_8099_fact__less__mono,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.70 => ( ( ord_less_nat @ M @ N2 )
% 5.44/5.70 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_less_mono
% 5.44/5.70 thf(fact_8100_fact__mod,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.44/5.70 = zero_zero_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_mod
% 5.44/5.70 thf(fact_8101_fact__mod,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.44/5.70 = zero_zero_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_mod
% 5.44/5.70 thf(fact_8102_fact__le__power,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_le3102999989581377725nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri4939895301339042750nteger @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_le_power
% 5.44/5.70 thf(fact_8103_fact__le__power,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_le_power
% 5.44/5.70 thf(fact_8104_fact__le__power,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_le_power
% 5.44/5.70 thf(fact_8105_fact__le__power,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_le_power
% 5.44/5.70 thf(fact_8106_diffs__def,axiom,
% 5.44/5.70 ( diffs_real
% 5.44/5.70 = ( ^ [C2: nat > real,N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diffs_def
% 5.44/5.70 thf(fact_8107_diffs__def,axiom,
% 5.44/5.70 ( diffs_int
% 5.44/5.70 = ( ^ [C2: nat > int,N: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diffs_def
% 5.44/5.70 thf(fact_8108_diffs__def,axiom,
% 5.44/5.70 ( diffs_complex
% 5.44/5.70 = ( ^ [C2: nat > complex,N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diffs_def
% 5.44/5.70 thf(fact_8109_diffs__def,axiom,
% 5.44/5.70 ( diffs_Code_integer
% 5.44/5.70 = ( ^ [C2: nat > code_integer,N: nat] : ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % diffs_def
% 5.44/5.70 thf(fact_8110_fact__numeral,axiom,
% 5.44/5.70 ! [K: num] :
% 5.44/5.70 ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ K ) )
% 5.44/5.70 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ K ) @ ( semiri4449623510593786356d_enat @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_numeral
% 5.44/5.70 thf(fact_8111_fact__numeral,axiom,
% 5.44/5.70 ! [K: num] :
% 5.44/5.70 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.44/5.70 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_numeral
% 5.44/5.70 thf(fact_8112_fact__numeral,axiom,
% 5.44/5.70 ! [K: num] :
% 5.44/5.70 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.44/5.70 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_numeral
% 5.44/5.70 thf(fact_8113_fact__numeral,axiom,
% 5.44/5.70 ! [K: num] :
% 5.44/5.70 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.44/5.70 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_numeral
% 5.44/5.70 thf(fact_8114_fact__numeral,axiom,
% 5.44/5.70 ! [K: num] :
% 5.44/5.70 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.44/5.70 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_numeral
% 5.44/5.70 thf(fact_8115_termdiff__converges__all,axiom,
% 5.44/5.70 ! [C: nat > complex,X: complex] :
% 5.44/5.70 ( ! [X5: complex] :
% 5.44/5.70 ( summable_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X5 @ N ) ) )
% 5.44/5.70 => ( summable_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % termdiff_converges_all
% 5.44/5.70 thf(fact_8116_termdiff__converges__all,axiom,
% 5.44/5.70 ! [C: nat > real,X: real] :
% 5.44/5.70 ( ! [X5: real] :
% 5.44/5.70 ( summable_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X5 @ N ) ) )
% 5.44/5.70 => ( summable_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % termdiff_converges_all
% 5.44/5.70 thf(fact_8117_square__fact__le__2__fact,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % square_fact_le_2_fact
% 5.44/5.70 thf(fact_8118_cos__coeff__def,axiom,
% 5.44/5.70 ( cos_coeff
% 5.44/5.70 = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ zero_zero_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % cos_coeff_def
% 5.44/5.70 thf(fact_8119_fact__num__eq__if,axiom,
% 5.44/5.70 ( semiri4449623510593786356d_enat
% 5.44/5.70 = ( ^ [M6: nat] : ( if_Extended_enat @ ( M6 = zero_zero_nat ) @ one_on7984719198319812577d_enat @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ M6 ) @ ( semiri4449623510593786356d_enat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_num_eq_if
% 5.44/5.70 thf(fact_8120_fact__num__eq__if,axiom,
% 5.44/5.70 ( semiri1406184849735516958ct_int
% 5.44/5.70 = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_num_eq_if
% 5.44/5.70 thf(fact_8121_fact__num__eq__if,axiom,
% 5.44/5.70 ( semiri5044797733671781792omplex
% 5.44/5.70 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_num_eq_if
% 5.44/5.70 thf(fact_8122_fact__num__eq__if,axiom,
% 5.44/5.70 ( semiri3624122377584611663nteger
% 5.44/5.70 = ( ^ [M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M6 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_num_eq_if
% 5.44/5.70 thf(fact_8123_fact__num__eq__if,axiom,
% 5.44/5.70 ( semiri2265585572941072030t_real
% 5.44/5.70 = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_num_eq_if
% 5.44/5.70 thf(fact_8124_fact__num__eq__if,axiom,
% 5.44/5.70 ( semiri1408675320244567234ct_nat
% 5.44/5.70 = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_num_eq_if
% 5.44/5.70 thf(fact_8125_fact__reduce,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ( ( semiri1406184849735516958ct_int @ N2 )
% 5.44/5.70 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_reduce
% 5.44/5.70 thf(fact_8126_fact__reduce,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ( ( semiri5044797733671781792omplex @ N2 )
% 5.44/5.70 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_reduce
% 5.44/5.70 thf(fact_8127_fact__reduce,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ( ( semiri3624122377584611663nteger @ N2 )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_reduce
% 5.44/5.70 thf(fact_8128_fact__reduce,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ( ( semiri2265585572941072030t_real @ N2 )
% 5.44/5.70 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_reduce
% 5.44/5.70 thf(fact_8129_fact__reduce,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 5.44/5.70 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_reduce
% 5.44/5.70 thf(fact_8130_Maclaurin__zero,axiom,
% 5.44/5.70 ! [X: real,N2: nat,Diff: nat > extended_enat > real] :
% 5.44/5.70 ( ( X = zero_zero_real )
% 5.44/5.70 => ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_z5237406670263579293d_enat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( Diff @ zero_zero_nat @ zero_z5237406670263579293d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_zero
% 5.44/5.70 thf(fact_8131_Maclaurin__zero,axiom,
% 5.44/5.70 ! [X: real,N2: nat,Diff: nat > complex > real] :
% 5.44/5.70 ( ( X = zero_zero_real )
% 5.44/5.70 => ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_zero
% 5.44/5.70 thf(fact_8132_Maclaurin__zero,axiom,
% 5.44/5.70 ! [X: real,N2: nat,Diff: nat > real > real] :
% 5.44/5.70 ( ( X = zero_zero_real )
% 5.44/5.70 => ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_zero
% 5.44/5.70 thf(fact_8133_Maclaurin__zero,axiom,
% 5.44/5.70 ! [X: real,N2: nat,Diff: nat > nat > real] :
% 5.44/5.70 ( ( X = zero_zero_real )
% 5.44/5.70 => ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_zero
% 5.44/5.70 thf(fact_8134_Maclaurin__zero,axiom,
% 5.44/5.70 ! [X: real,N2: nat,Diff: nat > int > real] :
% 5.44/5.70 ( ( X = zero_zero_real )
% 5.44/5.70 => ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_zero
% 5.44/5.70 thf(fact_8135_Maclaurin__lemma,axiom,
% 5.44/5.70 ! [H2: real,F: real > real,J: nat > real,N2: nat] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.44/5.70 => ? [B8: real] :
% 5.44/5.70 ( ( F @ H2 )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_lemma
% 5.44/5.70 thf(fact_8136_termdiff__converges,axiom,
% 5.44/5.70 ! [X: real,K5: real,C: nat > real] :
% 5.44/5.70 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ K5 )
% 5.44/5.70 => ( ! [X5: real] :
% 5.44/5.70 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X5 ) @ K5 )
% 5.44/5.70 => ( summable_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X5 @ N ) ) ) )
% 5.44/5.70 => ( summable_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % termdiff_converges
% 5.44/5.70 thf(fact_8137_termdiff__converges,axiom,
% 5.44/5.70 ! [X: complex,K5: real,C: nat > complex] :
% 5.44/5.70 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ K5 )
% 5.44/5.70 => ( ! [X5: complex] :
% 5.44/5.70 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X5 ) @ K5 )
% 5.44/5.70 => ( summable_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X5 @ N ) ) ) )
% 5.44/5.70 => ( summable_complex
% 5.44/5.70 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % termdiff_converges
% 5.44/5.70 thf(fact_8138_Maclaurin__exp__le,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ? [T4: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.44/5.70 & ( ( exp_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_exp_le
% 5.44/5.70 thf(fact_8139_Maclaurin__cos__expansion,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ? [T4: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.44/5.70 & ( ( cos_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_cos_expansion
% 5.44/5.70 thf(fact_8140_Maclaurin__cos__expansion2,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ? [T4: real] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.44/5.70 & ( ord_less_real @ T4 @ X )
% 5.44/5.70 & ( ( cos_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_cos_expansion2
% 5.44/5.70 thf(fact_8141_Maclaurin__minus__cos__expansion,axiom,
% 5.44/5.70 ! [N2: nat,X: real] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.70 => ? [T4: real] :
% 5.44/5.70 ( ( ord_less_real @ X @ T4 )
% 5.44/5.70 & ( ord_less_real @ T4 @ zero_zero_real )
% 5.44/5.70 & ( ( cos_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_minus_cos_expansion
% 5.44/5.70 thf(fact_8142_cos__paired,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( sums_real
% 5.44/5.70 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.44/5.70 @ ( cos_real @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % cos_paired
% 5.44/5.70 thf(fact_8143_Maclaurin__exp__lt,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( X != zero_zero_real )
% 5.44/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ? [T4: real] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T4 ) )
% 5.44/5.70 & ( ord_less_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.44/5.70 & ( ( exp_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_exp_lt
% 5.44/5.70 thf(fact_8144_Maclaurin__sin__expansion3,axiom,
% 5.44/5.70 ! [N2: nat,X: real] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.70 => ? [T4: real] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.44/5.70 & ( ord_less_real @ T4 @ X )
% 5.44/5.70 & ( ( sin_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_sin_expansion3
% 5.44/5.70 thf(fact_8145_Maclaurin__sin__expansion4,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.70 => ? [T4: real] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.44/5.70 & ( ord_less_eq_real @ T4 @ X )
% 5.44/5.70 & ( ( sin_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_sin_expansion4
% 5.44/5.70 thf(fact_8146_Maclaurin__sin__expansion2,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ? [T4: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.44/5.70 & ( ( sin_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_sin_expansion2
% 5.44/5.70 thf(fact_8147_Maclaurin__sin__expansion,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ? [T4: real] :
% 5.44/5.70 ( ( sin_real @ X )
% 5.44/5.70 = ( plus_plus_real
% 5.44/5.70 @ ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Maclaurin_sin_expansion
% 5.44/5.70 thf(fact_8148_fact__mono__nat,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_mono_nat
% 5.44/5.70 thf(fact_8149_fact__ge__self,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_ge_self
% 5.44/5.70 thf(fact_8150_fact__less__mono__nat,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.70 => ( ( ord_less_nat @ M @ N2 )
% 5.44/5.70 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_less_mono_nat
% 5.44/5.70 thf(fact_8151_fact__ge__Suc__0__nat,axiom,
% 5.44/5.70 ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_ge_Suc_0_nat
% 5.44/5.70 thf(fact_8152_dvd__fact,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.44/5.70 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % dvd_fact
% 5.44/5.70 thf(fact_8153_fact__diff__Suc,axiom,
% 5.44/5.70 ! [N2: nat,M: nat] :
% 5.44/5.70 ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.44/5.70 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 5.44/5.70 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_diff_Suc
% 5.44/5.70 thf(fact_8154_fact__div__fact__le__pow,axiom,
% 5.44/5.70 ! [R: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ R @ N2 )
% 5.44/5.70 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R ) ) ) @ ( power_power_nat @ N2 @ R ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_div_fact_le_pow
% 5.44/5.70 thf(fact_8155_sin__coeff__Suc,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( sin_coeff @ ( suc @ N2 ) )
% 5.44/5.70 = ( divide_divide_real @ ( cos_coeff @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sin_coeff_Suc
% 5.44/5.70 thf(fact_8156_cos__coeff__Suc,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( cos_coeff @ ( suc @ N2 ) )
% 5.44/5.70 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N2 ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % cos_coeff_Suc
% 5.44/5.70 thf(fact_8157_sin__coeff__def,axiom,
% 5.44/5.70 ( sin_coeff
% 5.44/5.70 = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sin_coeff_def
% 5.44/5.70 thf(fact_8158_floor__log__nat__eq__powr__iff,axiom,
% 5.44/5.70 ! [B: nat,K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.44/5.70 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.70 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.44/5.70 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.44/5.70 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.44/5.70 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_log_nat_eq_powr_iff
% 5.44/5.70 thf(fact_8159_pochhammer__double,axiom,
% 5.44/5.70 ! [Z: real,N2: nat] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_double
% 5.44/5.70 thf(fact_8160_pochhammer__double,axiom,
% 5.44/5.70 ! [Z: complex,N2: nat] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_double
% 5.44/5.70 thf(fact_8161_of__nat__code,axiom,
% 5.44/5.70 ( semiri4216267220026989637d_enat
% 5.44/5.70 = ( ^ [N: nat] :
% 5.44/5.70 ( semiri8563196900006977889d_enat
% 5.44/5.70 @ ^ [I5: extended_enat] : ( plus_p3455044024723400733d_enat @ I5 @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ N
% 5.44/5.70 @ zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % of_nat_code
% 5.44/5.70 thf(fact_8162_of__nat__code,axiom,
% 5.44/5.70 ( semiri5074537144036343181t_real
% 5.44/5.70 = ( ^ [N: nat] :
% 5.44/5.70 ( semiri7260567687927622513x_real
% 5.44/5.70 @ ^ [I5: real] : ( plus_plus_real @ I5 @ one_one_real )
% 5.44/5.70 @ N
% 5.44/5.70 @ zero_zero_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % of_nat_code
% 5.44/5.70 thf(fact_8163_of__nat__code,axiom,
% 5.44/5.70 ( semiri1314217659103216013at_int
% 5.44/5.70 = ( ^ [N: nat] :
% 5.44/5.70 ( semiri8420488043553186161ux_int
% 5.44/5.70 @ ^ [I5: int] : ( plus_plus_int @ I5 @ one_one_int )
% 5.44/5.70 @ N
% 5.44/5.70 @ zero_zero_int ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % of_nat_code
% 5.44/5.70 thf(fact_8164_of__nat__code,axiom,
% 5.44/5.70 ( semiri1316708129612266289at_nat
% 5.44/5.70 = ( ^ [N: nat] :
% 5.44/5.70 ( semiri8422978514062236437ux_nat
% 5.44/5.70 @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ one_one_nat )
% 5.44/5.70 @ N
% 5.44/5.70 @ zero_zero_nat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % of_nat_code
% 5.44/5.70 thf(fact_8165_of__nat__code,axiom,
% 5.44/5.70 ( semiri8010041392384452111omplex
% 5.44/5.70 = ( ^ [N: nat] :
% 5.44/5.70 ( semiri2816024913162550771omplex
% 5.44/5.70 @ ^ [I5: complex] : ( plus_plus_complex @ I5 @ one_one_complex )
% 5.44/5.70 @ N
% 5.44/5.70 @ zero_zero_complex ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % of_nat_code
% 5.44/5.70 thf(fact_8166_of__nat__code,axiom,
% 5.44/5.70 ( semiri4939895301339042750nteger
% 5.44/5.70 = ( ^ [N: nat] :
% 5.44/5.70 ( semiri4055485073559036834nteger
% 5.44/5.70 @ ^ [I5: code_integer] : ( plus_p5714425477246183910nteger @ I5 @ one_one_Code_integer )
% 5.44/5.70 @ N
% 5.44/5.70 @ zero_z3403309356797280102nteger ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % of_nat_code
% 5.44/5.70 thf(fact_8167_gchoose__row__sum__weighted,axiom,
% 5.44/5.70 ! [R: complex,M: nat] :
% 5.44/5.70 ( ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.44/5.70 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R @ ( suc @ M ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gchoose_row_sum_weighted
% 5.44/5.70 thf(fact_8168_gchoose__row__sum__weighted,axiom,
% 5.44/5.70 ! [R: real,M: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.44/5.70 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R @ ( suc @ M ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gchoose_row_sum_weighted
% 5.44/5.70 thf(fact_8169_of__int__floor__cancel,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = X )
% 5.44/5.70 = ( ? [N: int] :
% 5.44/5.70 ( X
% 5.44/5.70 = ( ring_1_of_int_real @ N ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % of_int_floor_cancel
% 5.44/5.70 thf(fact_8170_gbinomial__0_I2_J,axiom,
% 5.44/5.70 ! [K: nat] :
% 5.44/5.70 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.44/5.70 = zero_zero_complex ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_0(2)
% 5.44/5.70 thf(fact_8171_gbinomial__0_I2_J,axiom,
% 5.44/5.70 ! [K: nat] :
% 5.44/5.70 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.44/5.70 = zero_zero_real ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_0(2)
% 5.44/5.70 thf(fact_8172_gbinomial__0_I2_J,axiom,
% 5.44/5.70 ! [K: nat] :
% 5.44/5.70 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.44/5.70 = zero_zero_nat ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_0(2)
% 5.44/5.70 thf(fact_8173_gbinomial__0_I2_J,axiom,
% 5.44/5.70 ! [K: nat] :
% 5.44/5.70 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.44/5.70 = zero_zero_int ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_0(2)
% 5.44/5.70 thf(fact_8174_floor__numeral,axiom,
% 5.44/5.70 ! [V: num] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.44/5.70 = ( numeral_numeral_int @ V ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_numeral
% 5.44/5.70 thf(fact_8175_gbinomial__0_I1_J,axiom,
% 5.44/5.70 ! [A: complex] :
% 5.44/5.70 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.44/5.70 = one_one_complex ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_0(1)
% 5.44/5.70 thf(fact_8176_gbinomial__0_I1_J,axiom,
% 5.44/5.70 ! [A: real] :
% 5.44/5.70 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_0(1)
% 5.44/5.70 thf(fact_8177_gbinomial__0_I1_J,axiom,
% 5.44/5.70 ! [A: nat] :
% 5.44/5.70 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.44/5.70 = one_one_nat ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_0(1)
% 5.44/5.70 thf(fact_8178_gbinomial__0_I1_J,axiom,
% 5.44/5.70 ! [A: int] :
% 5.44/5.70 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.44/5.70 = one_one_int ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_0(1)
% 5.44/5.70 thf(fact_8179_floor__one,axiom,
% 5.44/5.70 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.44/5.70 = one_one_int ) ).
% 5.44/5.70
% 5.44/5.70 % floor_one
% 5.44/5.70 thf(fact_8180_pochhammer__0,axiom,
% 5.44/5.70 ! [A: extended_enat] :
% 5.44/5.70 ( ( comm_s3181272606743183617d_enat @ A @ zero_zero_nat )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0
% 5.44/5.70 thf(fact_8181_pochhammer__0,axiom,
% 5.44/5.70 ! [A: complex] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.44/5.70 = one_one_complex ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0
% 5.44/5.70 thf(fact_8182_pochhammer__0,axiom,
% 5.44/5.70 ! [A: real] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0
% 5.44/5.70 thf(fact_8183_pochhammer__0,axiom,
% 5.44/5.70 ! [A: nat] :
% 5.44/5.70 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.44/5.70 = one_one_nat ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0
% 5.44/5.70 thf(fact_8184_pochhammer__0,axiom,
% 5.44/5.70 ! [A: int] :
% 5.44/5.70 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.44/5.70 = one_one_int ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0
% 5.44/5.70 thf(fact_8185_zero__le__floor,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % zero_le_floor
% 5.44/5.70 thf(fact_8186_floor__less__zero,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 5.44/5.70 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_less_zero
% 5.44/5.70 thf(fact_8187_numeral__le__floor,axiom,
% 5.44/5.70 ! [V: num,X: real] :
% 5.44/5.70 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % numeral_le_floor
% 5.44/5.70 thf(fact_8188_zero__less__floor,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % zero_less_floor
% 5.44/5.70 thf(fact_8189_floor__le__zero,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 5.44/5.70 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_le_zero
% 5.44/5.70 thf(fact_8190_floor__less__numeral,axiom,
% 5.44/5.70 ! [X: real,V: num] :
% 5.44/5.70 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.70 = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_less_numeral
% 5.44/5.70 thf(fact_8191_one__le__floor,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_le_floor
% 5.44/5.70 thf(fact_8192_floor__less__one,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.44/5.70 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_less_one
% 5.44/5.70 thf(fact_8193_floor__neg__numeral,axiom,
% 5.44/5.70 ! [V: num] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.70 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_neg_numeral
% 5.44/5.70 thf(fact_8194_floor__diff__numeral,axiom,
% 5.44/5.70 ! [X: real,V: num] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.44/5.70 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_diff_numeral
% 5.44/5.70 thf(fact_8195_floor__diff__one,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.44/5.70 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_diff_one
% 5.44/5.70 thf(fact_8196_floor__numeral__power,axiom,
% 5.44/5.70 ! [X: num,N2: nat] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.44/5.70 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_numeral_power
% 5.44/5.70 thf(fact_8197_floor__divide__eq__div__numeral,axiom,
% 5.44/5.70 ! [A: num,B: num] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.44/5.70 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_divide_eq_div_numeral
% 5.44/5.70 thf(fact_8198_numeral__less__floor,axiom,
% 5.44/5.70 ! [V: num,X: real] :
% 5.44/5.70 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % numeral_less_floor
% 5.44/5.70 thf(fact_8199_floor__le__numeral,axiom,
% 5.44/5.70 ! [X: real,V: num] :
% 5.44/5.70 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.44/5.70 = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_le_numeral
% 5.44/5.70 thf(fact_8200_one__less__floor,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_less_floor
% 5.44/5.70 thf(fact_8201_floor__le__one,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.44/5.70 = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_le_one
% 5.44/5.70 thf(fact_8202_neg__numeral__le__floor,axiom,
% 5.44/5.70 ! [V: num,X: real] :
% 5.44/5.70 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % neg_numeral_le_floor
% 5.44/5.70 thf(fact_8203_floor__less__neg__numeral,axiom,
% 5.44/5.70 ! [X: real,V: num] :
% 5.44/5.70 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.70 = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_less_neg_numeral
% 5.44/5.70 thf(fact_8204_floor__one__divide__eq__div__numeral,axiom,
% 5.44/5.70 ! [B: num] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.44/5.70 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_one_divide_eq_div_numeral
% 5.44/5.70 thf(fact_8205_floor__minus__divide__eq__div__numeral,axiom,
% 5.44/5.70 ! [A: num,B: num] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.44/5.70 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_minus_divide_eq_div_numeral
% 5.44/5.70 thf(fact_8206_neg__numeral__less__floor,axiom,
% 5.44/5.70 ! [V: num,X: real] :
% 5.44/5.70 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % neg_numeral_less_floor
% 5.44/5.70 thf(fact_8207_floor__le__neg__numeral,axiom,
% 5.44/5.70 ! [X: real,V: num] :
% 5.44/5.70 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.44/5.70 = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_le_neg_numeral
% 5.44/5.70 thf(fact_8208_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.44/5.70 ! [B: num] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.44/5.70 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_minus_one_divide_eq_div_numeral
% 5.44/5.70 thf(fact_8209_floor__mono,axiom,
% 5.44/5.70 ! [X: real,Y: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.70 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_mono
% 5.44/5.70 thf(fact_8210_of__int__floor__le,axiom,
% 5.44/5.70 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X ) ).
% 5.44/5.70
% 5.44/5.70 % of_int_floor_le
% 5.44/5.70 thf(fact_8211_floor__less__cancel,axiom,
% 5.44/5.70 ! [X: real,Y: real] :
% 5.44/5.70 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) )
% 5.44/5.70 => ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_less_cancel
% 5.44/5.70 thf(fact_8212_pochhammer__pos,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.70 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_pos
% 5.44/5.70 thf(fact_8213_pochhammer__pos,axiom,
% 5.44/5.70 ! [X: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.44/5.70 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_pos
% 5.44/5.70 thf(fact_8214_pochhammer__pos,axiom,
% 5.44/5.70 ! [X: int,N2: nat] :
% 5.44/5.70 ( ( ord_less_int @ zero_zero_int @ X )
% 5.44/5.70 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_pos
% 5.44/5.70 thf(fact_8215_pochhammer__eq__0__mono,axiom,
% 5.44/5.70 ! [A: complex,N2: nat,M: nat] :
% 5.44/5.70 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.44/5.70 = zero_zero_complex )
% 5.44/5.70 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.70 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.44/5.70 = zero_zero_complex ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_eq_0_mono
% 5.44/5.70 thf(fact_8216_pochhammer__eq__0__mono,axiom,
% 5.44/5.70 ! [A: real,N2: nat,M: nat] :
% 5.44/5.70 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.44/5.70 = zero_zero_real )
% 5.44/5.70 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.70 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.44/5.70 = zero_zero_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_eq_0_mono
% 5.44/5.70 thf(fact_8217_pochhammer__neq__0__mono,axiom,
% 5.44/5.70 ! [A: complex,M: nat,N2: nat] :
% 5.44/5.70 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.44/5.70 != zero_zero_complex )
% 5.44/5.70 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.70 => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.44/5.70 != zero_zero_complex ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_neq_0_mono
% 5.44/5.70 thf(fact_8218_pochhammer__neq__0__mono,axiom,
% 5.44/5.70 ! [A: real,M: nat,N2: nat] :
% 5.44/5.70 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.44/5.70 != zero_zero_real )
% 5.44/5.70 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.70 => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.44/5.70 != zero_zero_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_neq_0_mono
% 5.44/5.70 thf(fact_8219_pochhammer__fact,axiom,
% 5.44/5.70 ( semiri4449623510593786356d_enat
% 5.44/5.70 = ( comm_s3181272606743183617d_enat @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_fact
% 5.44/5.70 thf(fact_8220_pochhammer__fact,axiom,
% 5.44/5.70 ( semiri5044797733671781792omplex
% 5.44/5.70 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_fact
% 5.44/5.70 thf(fact_8221_pochhammer__fact,axiom,
% 5.44/5.70 ( semiri1406184849735516958ct_int
% 5.44/5.70 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_fact
% 5.44/5.70 thf(fact_8222_pochhammer__fact,axiom,
% 5.44/5.70 ( semiri2265585572941072030t_real
% 5.44/5.70 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_fact
% 5.44/5.70 thf(fact_8223_pochhammer__fact,axiom,
% 5.44/5.70 ( semiri1408675320244567234ct_nat
% 5.44/5.70 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_fact
% 5.44/5.70 thf(fact_8224_le__floor__iff,axiom,
% 5.44/5.70 ! [Z: int,X: real] :
% 5.44/5.70 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % le_floor_iff
% 5.44/5.70 thf(fact_8225_floor__less__iff,axiom,
% 5.44/5.70 ! [X: real,Z: int] :
% 5.44/5.70 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 5.44/5.70 = ( ord_less_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_less_iff
% 5.44/5.70 thf(fact_8226_le__floor__add,axiom,
% 5.44/5.70 ! [X: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % le_floor_add
% 5.44/5.70 thf(fact_8227_floor__add__int,axiom,
% 5.44/5.70 ! [X: real,Z: int] :
% 5.44/5.70 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 5.44/5.70 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_add_int
% 5.44/5.70 thf(fact_8228_int__add__floor,axiom,
% 5.44/5.70 ! [Z: int,X: real] :
% 5.44/5.70 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % int_add_floor
% 5.44/5.70 thf(fact_8229_floor__divide__of__int__eq,axiom,
% 5.44/5.70 ! [K: int,L2: int] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L2 ) ) )
% 5.44/5.70 = ( divide_divide_int @ K @ L2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_divide_of_int_eq
% 5.44/5.70 thf(fact_8230_gbinomial__pochhammer,axiom,
% 5.44/5.70 ( gbinomial_complex
% 5.44/5.70 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A4 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_pochhammer
% 5.44/5.70 thf(fact_8231_gbinomial__pochhammer,axiom,
% 5.44/5.70 ( gbinomial_real
% 5.44/5.70 = ( ^ [A4: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A4 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_pochhammer
% 5.44/5.70 thf(fact_8232_gbinomial__pochhammer_H,axiom,
% 5.44/5.70 ( gbinomial_complex
% 5.44/5.70 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_pochhammer'
% 5.44/5.70 thf(fact_8233_gbinomial__pochhammer_H,axiom,
% 5.44/5.70 ( gbinomial_real
% 5.44/5.70 = ( ^ [A4: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_pochhammer'
% 5.44/5.70 thf(fact_8234_floor__power,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( X
% 5.44/5.70 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 5.44/5.70 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X @ N2 ) )
% 5.44/5.70 = ( power_power_int @ ( archim6058952711729229775r_real @ X ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_power
% 5.44/5.70 thf(fact_8235_gbinomial__Suc__Suc,axiom,
% 5.44/5.70 ! [A: complex,K: nat] :
% 5.44/5.70 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.44/5.70 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_Suc_Suc
% 5.44/5.70 thf(fact_8236_gbinomial__Suc__Suc,axiom,
% 5.44/5.70 ! [A: real,K: nat] :
% 5.44/5.70 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.44/5.70 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_Suc_Suc
% 5.44/5.70 thf(fact_8237_gbinomial__of__nat__symmetric,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 5.44/5.70 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_of_nat_symmetric
% 5.44/5.70 thf(fact_8238_gbinomial__of__nat__symmetric,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N2 ) @ K )
% 5.44/5.70 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_of_nat_symmetric
% 5.44/5.70 thf(fact_8239_pochhammer__nonneg,axiom,
% 5.44/5.70 ! [X: real,N2: nat] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_nonneg
% 5.44/5.70 thf(fact_8240_pochhammer__nonneg,axiom,
% 5.44/5.70 ! [X: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.44/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_nonneg
% 5.44/5.70 thf(fact_8241_pochhammer__nonneg,axiom,
% 5.44/5.70 ! [X: int,N2: nat] :
% 5.44/5.70 ( ( ord_less_int @ zero_zero_int @ X )
% 5.44/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_nonneg
% 5.44/5.70 thf(fact_8242_pochhammer__0__left,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ( N2 = zero_zero_nat )
% 5.44/5.70 => ( ( comm_s3181272606743183617d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 & ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( comm_s3181272606743183617d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.44/5.70 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0_left
% 5.44/5.70 thf(fact_8243_pochhammer__0__left,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ( N2 = zero_zero_nat )
% 5.44/5.70 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.44/5.70 = one_one_complex ) )
% 5.44/5.70 & ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.44/5.70 = zero_zero_complex ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0_left
% 5.44/5.70 thf(fact_8244_pochhammer__0__left,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ( N2 = zero_zero_nat )
% 5.44/5.70 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.44/5.70 = one_one_real ) )
% 5.44/5.70 & ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.44/5.70 = zero_zero_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0_left
% 5.44/5.70 thf(fact_8245_pochhammer__0__left,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ( N2 = zero_zero_nat )
% 5.44/5.70 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 = one_one_nat ) )
% 5.44/5.70 & ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.44/5.70 = zero_zero_nat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0_left
% 5.44/5.70 thf(fact_8246_pochhammer__0__left,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ( N2 = zero_zero_nat )
% 5.44/5.70 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.44/5.70 = one_one_int ) )
% 5.44/5.70 & ( ( N2 != zero_zero_nat )
% 5.44/5.70 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.44/5.70 = zero_zero_int ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_0_left
% 5.44/5.70 thf(fact_8247_one__add__floor,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.44/5.70 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % one_add_floor
% 5.44/5.70 thf(fact_8248_floor__divide__of__nat__eq,axiom,
% 5.44/5.70 ! [M: nat,N2: nat] :
% 5.44/5.70 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.44/5.70 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_divide_of_nat_eq
% 5.44/5.70 thf(fact_8249_gbinomial__addition__formula,axiom,
% 5.44/5.70 ! [A: complex,K: nat] :
% 5.44/5.70 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.44/5.70 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_addition_formula
% 5.44/5.70 thf(fact_8250_gbinomial__addition__formula,axiom,
% 5.44/5.70 ! [A: real,K: nat] :
% 5.44/5.70 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.44/5.70 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_addition_formula
% 5.44/5.70 thf(fact_8251_gbinomial__absorb__comp,axiom,
% 5.44/5.70 ! [A: real,K: nat] :
% 5.44/5.70 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.44/5.70 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_absorb_comp
% 5.44/5.70 thf(fact_8252_gbinomial__absorb__comp,axiom,
% 5.44/5.70 ! [A: complex,K: nat] :
% 5.44/5.70 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.44/5.70 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_absorb_comp
% 5.44/5.70 thf(fact_8253_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.44/5.70 ! [K: nat,A: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.44/5.70 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_ge_n_over_k_pow_k
% 5.44/5.70 thf(fact_8254_gbinomial__mult__1,axiom,
% 5.44/5.70 ! [A: real,K: nat] :
% 5.44/5.70 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.44/5.70 = ( 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 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_mult_1
% 5.44/5.70 thf(fact_8255_gbinomial__mult__1,axiom,
% 5.44/5.70 ! [A: complex,K: nat] :
% 5.44/5.70 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.44/5.70 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_mult_1
% 5.44/5.70 thf(fact_8256_gbinomial__mult__1_H,axiom,
% 5.44/5.70 ! [A: real,K: nat] :
% 5.44/5.70 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.44/5.70 = ( 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 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_mult_1'
% 5.44/5.70 thf(fact_8257_gbinomial__mult__1_H,axiom,
% 5.44/5.70 ! [A: complex,K: nat] :
% 5.44/5.70 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.44/5.70 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_mult_1'
% 5.44/5.70 thf(fact_8258_floor__eq,axiom,
% 5.44/5.70 ! [N2: int,X: real] :
% 5.44/5.70 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 5.44/5.70 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.44/5.70 => ( ( archim6058952711729229775r_real @ X )
% 5.44/5.70 = N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_eq
% 5.44/5.70 thf(fact_8259_real__of__int__floor__add__one__gt,axiom,
% 5.44/5.70 ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % real_of_int_floor_add_one_gt
% 5.44/5.70 thf(fact_8260_real__of__int__floor__add__one__ge,axiom,
% 5.44/5.70 ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % real_of_int_floor_add_one_ge
% 5.44/5.70 thf(fact_8261_real__of__int__floor__gt__diff__one,axiom,
% 5.44/5.70 ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % real_of_int_floor_gt_diff_one
% 5.44/5.70 thf(fact_8262_real__of__int__floor__ge__diff__one,axiom,
% 5.44/5.70 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % real_of_int_floor_ge_diff_one
% 5.44/5.70 thf(fact_8263_pochhammer__rec,axiom,
% 5.44/5.70 ! [A: extended_enat,N2: nat] :
% 5.44/5.70 ( ( comm_s3181272606743183617d_enat @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_7803423173614009249d_enat @ A @ ( comm_s3181272606743183617d_enat @ ( plus_p3455044024723400733d_enat @ A @ one_on7984719198319812577d_enat ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec
% 5.44/5.70 thf(fact_8264_pochhammer__rec,axiom,
% 5.44/5.70 ! [A: complex,N2: nat] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec
% 5.44/5.70 thf(fact_8265_pochhammer__rec,axiom,
% 5.44/5.70 ! [A: real,N2: nat] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec
% 5.44/5.70 thf(fact_8266_pochhammer__rec,axiom,
% 5.44/5.70 ! [A: nat,N2: nat] :
% 5.44/5.70 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec
% 5.44/5.70 thf(fact_8267_pochhammer__rec,axiom,
% 5.44/5.70 ! [A: int,N2: nat] :
% 5.44/5.70 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec
% 5.44/5.70 thf(fact_8268_pochhammer__Suc,axiom,
% 5.44/5.70 ! [A: real,N2: nat] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_Suc
% 5.44/5.70 thf(fact_8269_pochhammer__Suc,axiom,
% 5.44/5.70 ! [A: int,N2: nat] :
% 5.44/5.70 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_Suc
% 5.44/5.70 thf(fact_8270_pochhammer__Suc,axiom,
% 5.44/5.70 ! [A: nat,N2: nat] :
% 5.44/5.70 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_Suc
% 5.44/5.70 thf(fact_8271_pochhammer__Suc,axiom,
% 5.44/5.70 ! [A: complex,N2: nat] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N2 ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_Suc
% 5.44/5.70 thf(fact_8272_pochhammer__Suc,axiom,
% 5.44/5.70 ! [A: code_integer,N2: nat] :
% 5.44/5.70 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N2 ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_Suc
% 5.44/5.70 thf(fact_8273_pochhammer__rec_H,axiom,
% 5.44/5.70 ! [Z: real,N2: nat] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec'
% 5.44/5.70 thf(fact_8274_pochhammer__rec_H,axiom,
% 5.44/5.70 ! [Z: int,N2: nat] :
% 5.44/5.70 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec'
% 5.44/5.70 thf(fact_8275_pochhammer__rec_H,axiom,
% 5.44/5.70 ! [Z: nat,N2: nat] :
% 5.44/5.70 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec'
% 5.44/5.70 thf(fact_8276_pochhammer__rec_H,axiom,
% 5.44/5.70 ! [Z: complex,N2: nat] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec'
% 5.44/5.70 thf(fact_8277_pochhammer__rec_H,axiom,
% 5.44/5.70 ! [Z: code_integer,N2: nat] :
% 5.44/5.70 ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N2 ) )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ ( comm_s8582702949713902594nteger @ Z @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_rec'
% 5.44/5.70 thf(fact_8278_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.44/5.70 ! [N2: nat,K: nat] :
% 5.44/5.70 ( ( ord_less_nat @ N2 @ K )
% 5.44/5.70 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.44/5.70 = zero_zero_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_lemma
% 5.44/5.70 thf(fact_8279_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.44/5.70 ! [N2: nat,K: nat] :
% 5.44/5.70 ( ( ord_less_nat @ N2 @ K )
% 5.44/5.70 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.44/5.70 = zero_zero_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_lemma
% 5.44/5.70 thf(fact_8280_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.44/5.70 ! [N2: nat,K: nat] :
% 5.44/5.70 ( ( ord_less_nat @ N2 @ K )
% 5.44/5.70 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.44/5.70 = zero_zero_complex ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_lemma
% 5.44/5.70 thf(fact_8281_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.44/5.70 ! [N2: nat,K: nat] :
% 5.44/5.70 ( ( ord_less_nat @ N2 @ K )
% 5.44/5.70 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.44/5.70 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_lemma
% 5.44/5.70 thf(fact_8282_pochhammer__of__nat__eq__0__iff,axiom,
% 5.44/5.70 ! [N2: nat,K: nat] :
% 5.44/5.70 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.44/5.70 = zero_zero_real )
% 5.44/5.70 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_iff
% 5.44/5.70 thf(fact_8283_pochhammer__of__nat__eq__0__iff,axiom,
% 5.44/5.70 ! [N2: nat,K: nat] :
% 5.44/5.70 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.44/5.70 = zero_zero_int )
% 5.44/5.70 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_iff
% 5.44/5.70 thf(fact_8284_pochhammer__of__nat__eq__0__iff,axiom,
% 5.44/5.70 ! [N2: nat,K: nat] :
% 5.44/5.70 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.44/5.70 = zero_zero_complex )
% 5.44/5.70 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_iff
% 5.44/5.70 thf(fact_8285_pochhammer__of__nat__eq__0__iff,axiom,
% 5.44/5.70 ! [N2: nat,K: nat] :
% 5.44/5.70 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.44/5.70 = zero_z3403309356797280102nteger )
% 5.44/5.70 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_iff
% 5.44/5.70 thf(fact_8286_pochhammer__eq__0__iff,axiom,
% 5.44/5.70 ! [A: real,N2: nat] :
% 5.44/5.70 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.44/5.70 = zero_zero_real )
% 5.44/5.70 = ( ? [K3: nat] :
% 5.44/5.70 ( ( ord_less_nat @ K3 @ N2 )
% 5.44/5.70 & ( A
% 5.44/5.70 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_eq_0_iff
% 5.44/5.70 thf(fact_8287_pochhammer__eq__0__iff,axiom,
% 5.44/5.70 ! [A: complex,N2: nat] :
% 5.44/5.70 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.44/5.70 = zero_zero_complex )
% 5.44/5.70 = ( ? [K3: nat] :
% 5.44/5.70 ( ( ord_less_nat @ K3 @ N2 )
% 5.44/5.70 & ( A
% 5.44/5.70 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_eq_0_iff
% 5.44/5.70 thf(fact_8288_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.44/5.70 != zero_zero_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_lemma'
% 5.44/5.70 thf(fact_8289_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.44/5.70 != zero_zero_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_lemma'
% 5.44/5.70 thf(fact_8290_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.44/5.70 != zero_zero_complex ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_lemma'
% 5.44/5.70 thf(fact_8291_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.70 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.44/5.70 != zero_z3403309356797280102nteger ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_of_nat_eq_0_lemma'
% 5.44/5.70 thf(fact_8292_pochhammer__product_H,axiom,
% 5.44/5.70 ! [Z: real,N2: nat,M: nat] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.70 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product'
% 5.44/5.70 thf(fact_8293_pochhammer__product_H,axiom,
% 5.44/5.70 ! [Z: int,N2: nat,M: nat] :
% 5.44/5.70 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.70 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product'
% 5.44/5.70 thf(fact_8294_pochhammer__product_H,axiom,
% 5.44/5.70 ! [Z: nat,N2: nat,M: nat] :
% 5.44/5.70 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.70 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product'
% 5.44/5.70 thf(fact_8295_pochhammer__product_H,axiom,
% 5.44/5.70 ! [Z: complex,N2: nat,M: nat] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.70 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product'
% 5.44/5.70 thf(fact_8296_pochhammer__product_H,axiom,
% 5.44/5.70 ! [Z: code_integer,N2: nat,M: nat] :
% 5.44/5.70 ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product'
% 5.44/5.70 thf(fact_8297_floor__split,axiom,
% 5.44/5.70 ! [P: int > $o,T: real] :
% 5.44/5.70 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.44/5.70 = ( ! [I5: int] :
% 5.44/5.70 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I5 ) @ T )
% 5.44/5.70 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I5 ) @ one_one_real ) ) )
% 5.44/5.70 => ( P @ I5 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_split
% 5.44/5.70 thf(fact_8298_floor__eq__iff,axiom,
% 5.44/5.70 ! [X: real,A: int] :
% 5.44/5.70 ( ( ( archim6058952711729229775r_real @ X )
% 5.44/5.70 = A )
% 5.44/5.70 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 5.44/5.70 & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_eq_iff
% 5.44/5.70 thf(fact_8299_floor__unique,axiom,
% 5.44/5.70 ! [Z: int,X: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 5.44/5.70 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.44/5.70 => ( ( archim6058952711729229775r_real @ X )
% 5.44/5.70 = Z ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_unique
% 5.44/5.70 thf(fact_8300_le__mult__floor,axiom,
% 5.44/5.70 ! [A: real,B: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.70 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % le_mult_floor
% 5.44/5.70 thf(fact_8301_less__floor__iff,axiom,
% 5.44/5.70 ! [Z: int,X: real] :
% 5.44/5.70 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.70 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_floor_iff
% 5.44/5.70 thf(fact_8302_floor__le__iff,axiom,
% 5.44/5.70 ! [X: real,Z: int] :
% 5.44/5.70 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 5.44/5.70 = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_le_iff
% 5.44/5.70 thf(fact_8303_floor__correct,axiom,
% 5.44/5.70 ! [X: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 5.44/5.70 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_correct
% 5.44/5.70 thf(fact_8304_floor__eq2,axiom,
% 5.44/5.70 ! [N2: int,X: real] :
% 5.44/5.70 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 5.44/5.70 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.44/5.70 => ( ( archim6058952711729229775r_real @ X )
% 5.44/5.70 = N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_eq2
% 5.44/5.70 thf(fact_8305_Suc__times__gbinomial,axiom,
% 5.44/5.70 ! [K: nat,A: real] :
% 5.44/5.70 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.44/5.70 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Suc_times_gbinomial
% 5.44/5.70 thf(fact_8306_Suc__times__gbinomial,axiom,
% 5.44/5.70 ! [K: nat,A: complex] :
% 5.44/5.70 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.44/5.70 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Suc_times_gbinomial
% 5.44/5.70 thf(fact_8307_gbinomial__absorption,axiom,
% 5.44/5.70 ! [K: nat,A: real] :
% 5.44/5.70 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.44/5.70 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_absorption
% 5.44/5.70 thf(fact_8308_gbinomial__absorption,axiom,
% 5.44/5.70 ! [K: nat,A: complex] :
% 5.44/5.70 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.44/5.70 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_absorption
% 5.44/5.70 thf(fact_8309_floor__divide__real__eq__div,axiom,
% 5.44/5.70 ! [B: int,A: real] :
% 5.44/5.70 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.44/5.70 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.44/5.70 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_divide_real_eq_div
% 5.44/5.70 thf(fact_8310_gbinomial__trinomial__revision,axiom,
% 5.44/5.70 ! [K: nat,M: nat,A: real] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ M )
% 5.44/5.70 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.44/5.70 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_trinomial_revision
% 5.44/5.70 thf(fact_8311_gbinomial__trinomial__revision,axiom,
% 5.44/5.70 ! [K: nat,M: nat,A: complex] :
% 5.44/5.70 ( ( ord_less_eq_nat @ K @ M )
% 5.44/5.70 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.44/5.70 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_trinomial_revision
% 5.44/5.70 thf(fact_8312_pochhammer__product,axiom,
% 5.44/5.70 ! [M: nat,N2: nat,Z: real] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ( comm_s7457072308508201937r_real @ Z @ N2 )
% 5.44/5.70 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product
% 5.44/5.70 thf(fact_8313_pochhammer__product,axiom,
% 5.44/5.70 ! [M: nat,N2: nat,Z: int] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 5.44/5.70 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product
% 5.44/5.70 thf(fact_8314_pochhammer__product,axiom,
% 5.44/5.70 ! [M: nat,N2: nat,Z: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 5.44/5.70 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product
% 5.44/5.70 thf(fact_8315_pochhammer__product,axiom,
% 5.44/5.70 ! [M: nat,N2: nat,Z: complex] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ( comm_s2602460028002588243omplex @ Z @ N2 )
% 5.44/5.70 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product
% 5.44/5.70 thf(fact_8316_pochhammer__product,axiom,
% 5.44/5.70 ! [M: nat,N2: nat,Z: code_integer] :
% 5.44/5.70 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.70 => ( ( comm_s8582702949713902594nteger @ Z @ N2 )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_product
% 5.44/5.70 thf(fact_8317_floor__divide__lower,axiom,
% 5.44/5.70 ! [Q2: real,P5: real] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.44/5.70 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P5 @ Q2 ) ) ) @ Q2 ) @ P5 ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_divide_lower
% 5.44/5.70 thf(fact_8318_gbinomial__factors,axiom,
% 5.44/5.70 ! [A: real,K: nat] :
% 5.44/5.70 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.44/5.70 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_factors
% 5.44/5.70 thf(fact_8319_gbinomial__factors,axiom,
% 5.44/5.70 ! [A: complex,K: nat] :
% 5.44/5.70 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.44/5.70 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_factors
% 5.44/5.70 thf(fact_8320_gbinomial__rec,axiom,
% 5.44/5.70 ! [A: real,K: nat] :
% 5.44/5.70 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.44/5.70 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_rec
% 5.44/5.70 thf(fact_8321_gbinomial__rec,axiom,
% 5.44/5.70 ! [A: complex,K: nat] :
% 5.44/5.70 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.44/5.70 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_rec
% 5.44/5.70 thf(fact_8322_gbinomial__negated__upper,axiom,
% 5.44/5.70 ( gbinomial_real
% 5.44/5.70 = ( ^ [A4: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A4 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_negated_upper
% 5.44/5.70 thf(fact_8323_gbinomial__negated__upper,axiom,
% 5.44/5.70 ( gbinomial_complex
% 5.44/5.70 = ( ^ [A4: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A4 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_negated_upper
% 5.44/5.70 thf(fact_8324_gbinomial__index__swap,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ K ) )
% 5.44/5.70 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_index_swap
% 5.44/5.70 thf(fact_8325_gbinomial__index__swap,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ K ) )
% 5.44/5.70 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_index_swap
% 5.44/5.70 thf(fact_8326_pochhammer__absorb__comp,axiom,
% 5.44/5.70 ! [R: real,K: nat] :
% 5.44/5.70 ( ( times_times_real @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R ) @ K ) )
% 5.44/5.70 = ( times_times_real @ R @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R ) @ one_one_real ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_absorb_comp
% 5.44/5.70 thf(fact_8327_pochhammer__absorb__comp,axiom,
% 5.44/5.70 ! [R: int,K: nat] :
% 5.44/5.70 ( ( times_times_int @ ( minus_minus_int @ R @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R ) @ K ) )
% 5.44/5.70 = ( times_times_int @ R @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R ) @ one_one_int ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_absorb_comp
% 5.44/5.70 thf(fact_8328_pochhammer__absorb__comp,axiom,
% 5.44/5.70 ! [R: complex,K: nat] :
% 5.44/5.70 ( ( times_times_complex @ ( minus_minus_complex @ R @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R ) @ K ) )
% 5.44/5.70 = ( times_times_complex @ R @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R ) @ one_one_complex ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_absorb_comp
% 5.44/5.70 thf(fact_8329_pochhammer__absorb__comp,axiom,
% 5.44/5.70 ! [R: code_integer,K: nat] :
% 5.44/5.70 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R ) @ K ) )
% 5.44/5.70 = ( times_3573771949741848930nteger @ R @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_absorb_comp
% 5.44/5.70 thf(fact_8330_floor__divide__upper,axiom,
% 5.44/5.70 ! [Q2: real,P5: real] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.44/5.70 => ( ord_less_real @ P5 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P5 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_divide_upper
% 5.44/5.70 thf(fact_8331_pochhammer__same,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 5.44/5.70 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_same
% 5.44/5.70 thf(fact_8332_pochhammer__same,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ N2 )
% 5.44/5.70 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_same
% 5.44/5.70 thf(fact_8333_pochhammer__same,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_same
% 5.44/5.70 thf(fact_8334_pochhammer__same,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ N2 )
% 5.44/5.70 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_same
% 5.44/5.70 thf(fact_8335_round__def,axiom,
% 5.44/5.70 ( archim8280529875227126926d_real
% 5.44/5.70 = ( ^ [X2: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % round_def
% 5.44/5.70 thf(fact_8336_gbinomial__minus,axiom,
% 5.44/5.70 ! [A: real,K: nat] :
% 5.44/5.70 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.44/5.70 = ( 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 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_minus
% 5.44/5.70 thf(fact_8337_gbinomial__minus,axiom,
% 5.44/5.70 ! [A: complex,K: nat] :
% 5.44/5.70 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.44/5.70 = ( 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 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_minus
% 5.44/5.70 thf(fact_8338_gbinomial__reduce__nat,axiom,
% 5.44/5.70 ! [K: nat,A: complex] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.70 => ( ( gbinomial_complex @ A @ K )
% 5.44/5.70 = ( 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 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_reduce_nat
% 5.44/5.70 thf(fact_8339_gbinomial__reduce__nat,axiom,
% 5.44/5.70 ! [K: nat,A: real] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.70 => ( ( gbinomial_real @ A @ K )
% 5.44/5.70 = ( 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 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_reduce_nat
% 5.44/5.70 thf(fact_8340_pochhammer__minus_H,axiom,
% 5.44/5.70 ! [B: real,K: nat] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.44/5.70 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_minus'
% 5.44/5.70 thf(fact_8341_pochhammer__minus_H,axiom,
% 5.44/5.70 ! [B: int,K: nat] :
% 5.44/5.70 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.44/5.70 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_minus'
% 5.44/5.70 thf(fact_8342_pochhammer__minus_H,axiom,
% 5.44/5.70 ! [B: complex,K: nat] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.44/5.70 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_minus'
% 5.44/5.70 thf(fact_8343_pochhammer__minus_H,axiom,
% 5.44/5.70 ! [B: code_integer,K: nat] :
% 5.44/5.70 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_minus'
% 5.44/5.70 thf(fact_8344_pochhammer__minus,axiom,
% 5.44/5.70 ! [B: real,K: nat] :
% 5.44/5.70 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.44/5.70 = ( 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 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_minus
% 5.44/5.70 thf(fact_8345_pochhammer__minus,axiom,
% 5.44/5.70 ! [B: int,K: nat] :
% 5.44/5.70 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.44/5.70 = ( 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 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_minus
% 5.44/5.70 thf(fact_8346_pochhammer__minus,axiom,
% 5.44/5.70 ! [B: complex,K: nat] :
% 5.44/5.70 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.44/5.70 = ( 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 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_minus
% 5.44/5.70 thf(fact_8347_pochhammer__minus,axiom,
% 5.44/5.70 ! [B: code_integer,K: nat] :
% 5.44/5.70 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.44/5.70 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_minus
% 5.44/5.70 thf(fact_8348_gbinomial__sum__up__index,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.70 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_sum_up_index
% 5.44/5.70 thf(fact_8349_gbinomial__sum__up__index,axiom,
% 5.44/5.70 ! [K: nat,N2: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.70 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_sum_up_index
% 5.44/5.70 thf(fact_8350_floor__log__eq__powr__iff,axiom,
% 5.44/5.70 ! [X: real,B: real,K: int] :
% 5.44/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.70 => ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.70 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 5.44/5.70 = K )
% 5.44/5.70 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 5.44/5.70 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_log_eq_powr_iff
% 5.44/5.70 thf(fact_8351_gbinomial__absorption_H,axiom,
% 5.44/5.70 ! [K: nat,A: real] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.70 => ( ( gbinomial_real @ A @ K )
% 5.44/5.70 = ( 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 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_absorption'
% 5.44/5.70 thf(fact_8352_gbinomial__absorption_H,axiom,
% 5.44/5.70 ! [K: nat,A: complex] :
% 5.44/5.70 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.70 => ( ( gbinomial_complex @ A @ K )
% 5.44/5.70 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_absorption'
% 5.44/5.70 thf(fact_8353_floor__log2__div2,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.70 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_log2_div2
% 5.44/5.70 thf(fact_8354_fact__double,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_double
% 5.44/5.70 thf(fact_8355_fact__double,axiom,
% 5.44/5.70 ! [N2: nat] :
% 5.44/5.70 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % fact_double
% 5.44/5.70 thf(fact_8356_floor__log__nat__eq__if,axiom,
% 5.44/5.70 ! [B: nat,N2: nat,K: nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.44/5.70 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.44/5.70 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.44/5.70 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.44/5.70 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % floor_log_nat_eq_if
% 5.44/5.70 thf(fact_8357_gbinomial__code,axiom,
% 5.44/5.70 ( gbinomial_complex
% 5.44/5.70 = ( ^ [A4: complex,K3: nat] :
% 5.44/5.70 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.44/5.70 @ ( divide1717551699836669952omplex
% 5.44/5.70 @ ( set_fo1517530859248394432omplex
% 5.44/5.70 @ ^ [L: nat] : ( times_times_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ L ) ) )
% 5.44/5.70 @ zero_zero_nat
% 5.44/5.70 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.44/5.70 @ one_one_complex )
% 5.44/5.70 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_code
% 5.44/5.70 thf(fact_8358_gbinomial__code,axiom,
% 5.44/5.70 ( gbinomial_real
% 5.44/5.70 = ( ^ [A4: real,K3: nat] :
% 5.44/5.70 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.44/5.70 @ ( divide_divide_real
% 5.44/5.70 @ ( set_fo3111899725591712190t_real
% 5.44/5.70 @ ^ [L: nat] : ( times_times_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ L ) ) )
% 5.44/5.70 @ zero_zero_nat
% 5.44/5.70 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.44/5.70 @ one_one_real )
% 5.44/5.70 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_code
% 5.44/5.70 thf(fact_8359_pochhammer__times__pochhammer__half,axiom,
% 5.44/5.70 ! [Z: real,N2: nat] :
% 5.44/5.70 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( groups129246275422532515t_real
% 5.44/5.70 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_times_pochhammer_half
% 5.44/5.70 thf(fact_8360_pochhammer__times__pochhammer__half,axiom,
% 5.44/5.70 ! [Z: complex,N2: nat] :
% 5.44/5.70 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_times_pochhammer_half
% 5.44/5.70 thf(fact_8361_pochhammer__code,axiom,
% 5.44/5.70 ( comm_s3181272606743183617d_enat
% 5.44/5.70 = ( ^ [A4: extended_enat,N: nat] :
% 5.44/5.70 ( if_Extended_enat @ ( N = zero_zero_nat ) @ one_on7984719198319812577d_enat
% 5.44/5.70 @ ( set_fo2538466533108834004d_enat
% 5.44/5.70 @ ^ [O: nat] : ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A4 @ ( semiri4216267220026989637d_enat @ O ) ) )
% 5.44/5.70 @ zero_zero_nat
% 5.44/5.70 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.44/5.70 @ one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_code
% 5.44/5.70 thf(fact_8362_pochhammer__code,axiom,
% 5.44/5.70 ( comm_s7457072308508201937r_real
% 5.44/5.70 = ( ^ [A4: real,N: nat] :
% 5.44/5.70 ( if_real @ ( N = zero_zero_nat ) @ one_one_real
% 5.44/5.70 @ ( set_fo3111899725591712190t_real
% 5.44/5.70 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.44/5.70 @ zero_zero_nat
% 5.44/5.70 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.44/5.70 @ one_one_real ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_code
% 5.44/5.70 thf(fact_8363_pochhammer__code,axiom,
% 5.44/5.70 ( comm_s4660882817536571857er_int
% 5.44/5.70 = ( ^ [A4: int,N: nat] :
% 5.44/5.70 ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 5.44/5.70 @ ( set_fo2581907887559384638at_int
% 5.44/5.70 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.44/5.70 @ zero_zero_nat
% 5.44/5.70 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.44/5.70 @ one_one_int ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_code
% 5.44/5.70 thf(fact_8364_pochhammer__code,axiom,
% 5.44/5.70 ( comm_s2602460028002588243omplex
% 5.44/5.70 = ( ^ [A4: complex,N: nat] :
% 5.44/5.70 ( if_complex @ ( N = zero_zero_nat ) @ one_one_complex
% 5.44/5.70 @ ( set_fo1517530859248394432omplex
% 5.44/5.70 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.44/5.70 @ zero_zero_nat
% 5.44/5.70 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.44/5.70 @ one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_code
% 5.44/5.70 thf(fact_8365_pochhammer__code,axiom,
% 5.44/5.70 ( comm_s8582702949713902594nteger
% 5.44/5.70 = ( ^ [A4: code_integer,N: nat] :
% 5.44/5.70 ( if_Code_integer @ ( N = zero_zero_nat ) @ one_one_Code_integer
% 5.44/5.70 @ ( set_fo1084959871951514735nteger
% 5.44/5.70 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A4 @ ( semiri4939895301339042750nteger @ O ) ) )
% 5.44/5.70 @ zero_zero_nat
% 5.44/5.70 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.44/5.70 @ one_one_Code_integer ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_code
% 5.44/5.70 thf(fact_8366_pochhammer__code,axiom,
% 5.44/5.70 ( comm_s4663373288045622133er_nat
% 5.44/5.70 = ( ^ [A4: nat,N: nat] :
% 5.44/5.70 ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 5.44/5.70 @ ( set_fo2584398358068434914at_nat
% 5.44/5.70 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.44/5.70 @ zero_zero_nat
% 5.44/5.70 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.44/5.70 @ one_one_nat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % pochhammer_code
% 5.44/5.70 thf(fact_8367_gbinomial__partial__row__sum,axiom,
% 5.44/5.70 ! [A: complex,M: nat] :
% 5.44/5.70 ( ( groups2073611262835488442omplex
% 5.44/5.70 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.70 = ( 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 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_partial_row_sum
% 5.44/5.70 thf(fact_8368_gbinomial__partial__row__sum,axiom,
% 5.44/5.70 ! [A: real,M: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real
% 5.44/5.70 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.70 = ( 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 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % gbinomial_partial_row_sum
% 5.44/5.70 thf(fact_8369_atMost__iff,axiom,
% 5.44/5.70 ! [I2: real,K: real] :
% 5.44/5.70 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K ) )
% 5.44/5.70 = ( ord_less_eq_real @ I2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_iff
% 5.44/5.70 thf(fact_8370_atMost__iff,axiom,
% 5.44/5.70 ! [I2: set_real,K: set_real] :
% 5.44/5.70 ( ( member_set_real @ I2 @ ( set_or5092868708245317595t_real @ K ) )
% 5.44/5.70 = ( ord_less_eq_set_real @ I2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_iff
% 5.44/5.70 thf(fact_8371_atMost__iff,axiom,
% 5.44/5.70 ! [I2: set_nat,K: set_nat] :
% 5.44/5.70 ( ( member_set_nat @ I2 @ ( set_or4236626031148496127et_nat @ K ) )
% 5.44/5.70 = ( ord_less_eq_set_nat @ I2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_iff
% 5.44/5.70 thf(fact_8372_atMost__iff,axiom,
% 5.44/5.70 ! [I2: num,K: num] :
% 5.44/5.70 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 5.44/5.70 = ( ord_less_eq_num @ I2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_iff
% 5.44/5.70 thf(fact_8373_atMost__iff,axiom,
% 5.44/5.70 ! [I2: int,K: int] :
% 5.44/5.70 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 5.44/5.70 = ( ord_less_eq_int @ I2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_iff
% 5.44/5.70 thf(fact_8374_atMost__iff,axiom,
% 5.44/5.70 ! [I2: nat,K: nat] :
% 5.44/5.70 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 5.44/5.70 = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_iff
% 5.44/5.70 thf(fact_8375_prod_Oneutral__const,axiom,
% 5.44/5.70 ! [A2: set_nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [Uu3: nat] : one_one_nat
% 5.44/5.70 @ A2 )
% 5.44/5.70 = one_one_nat ) ).
% 5.44/5.70
% 5.44/5.70 % prod.neutral_const
% 5.44/5.70 thf(fact_8376_prod_Oneutral__const,axiom,
% 5.44/5.70 ! [A2: set_nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [Uu3: nat] : one_one_int
% 5.44/5.70 @ A2 )
% 5.44/5.70 = one_one_int ) ).
% 5.44/5.70
% 5.44/5.70 % prod.neutral_const
% 5.44/5.70 thf(fact_8377_prod_Oneutral__const,axiom,
% 5.44/5.70 ! [A2: set_int] :
% 5.44/5.70 ( ( groups1705073143266064639nt_int
% 5.44/5.70 @ ^ [Uu3: int] : one_one_int
% 5.44/5.70 @ A2 )
% 5.44/5.70 = one_one_int ) ).
% 5.44/5.70
% 5.44/5.70 % prod.neutral_const
% 5.44/5.70 thf(fact_8378_prod_Oempty,axiom,
% 5.44/5.70 ! [G: nat > extended_enat] :
% 5.44/5.70 ( ( groups7961826882256487087d_enat @ G @ bot_bot_set_nat )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8379_prod_Oempty,axiom,
% 5.44/5.70 ! [G: nat > complex] :
% 5.44/5.70 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.44/5.70 = one_one_complex ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8380_prod_Oempty,axiom,
% 5.44/5.70 ! [G: nat > real] :
% 5.44/5.70 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8381_prod_Oempty,axiom,
% 5.44/5.70 ! [G: int > extended_enat] :
% 5.44/5.70 ( ( groups5078248829458667347d_enat @ G @ bot_bot_set_int )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8382_prod_Oempty,axiom,
% 5.44/5.70 ! [G: int > complex] :
% 5.44/5.70 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.44/5.70 = one_one_complex ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8383_prod_Oempty,axiom,
% 5.44/5.70 ! [G: int > real] :
% 5.44/5.70 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8384_prod_Oempty,axiom,
% 5.44/5.70 ! [G: int > nat] :
% 5.44/5.70 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.44/5.70 = one_one_nat ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8385_prod_Oempty,axiom,
% 5.44/5.70 ! [G: real > extended_enat] :
% 5.44/5.70 ( ( groups7973222482632965587d_enat @ G @ bot_bot_set_real )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8386_prod_Oempty,axiom,
% 5.44/5.70 ! [G: real > complex] :
% 5.44/5.70 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 5.44/5.70 = one_one_complex ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8387_prod_Oempty,axiom,
% 5.44/5.70 ! [G: real > real] :
% 5.44/5.70 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 5.44/5.70 = one_one_real ) ).
% 5.44/5.70
% 5.44/5.70 % prod.empty
% 5.44/5.70 thf(fact_8388_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > extended_enat] :
% 5.44/5.70 ( ~ ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat @ G @ A2 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8389_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > extended_enat] :
% 5.44/5.70 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat @ G @ A2 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8390_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > complex] :
% 5.44/5.70 ( ~ ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.44/5.70 = one_one_complex ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8391_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > complex] :
% 5.44/5.70 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.44/5.70 = one_one_complex ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8392_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > real] :
% 5.44/5.70 ( ~ ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.44/5.70 = one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8393_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > real] :
% 5.44/5.70 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.44/5.70 = one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8394_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > nat] :
% 5.44/5.70 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.44/5.70 = one_one_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8395_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > int] :
% 5.44/5.70 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.44/5.70 = one_one_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8396_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > nat] :
% 5.44/5.70 ( ~ ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.44/5.70 = one_one_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8397_prod_Oinfinite,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > int] :
% 5.44/5.70 ( ~ ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.44/5.70 = one_one_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.infinite
% 5.44/5.70 thf(fact_8398_atMost__subset__iff,axiom,
% 5.44/5.70 ! [X: set_real,Y: set_real] :
% 5.44/5.70 ( ( ord_le3558479182127378552t_real @ ( set_or5092868708245317595t_real @ X ) @ ( set_or5092868708245317595t_real @ Y ) )
% 5.44/5.70 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_subset_iff
% 5.44/5.70 thf(fact_8399_atMost__subset__iff,axiom,
% 5.44/5.70 ! [X: set_nat,Y: set_nat] :
% 5.44/5.70 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X ) @ ( set_or4236626031148496127et_nat @ Y ) )
% 5.44/5.70 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_subset_iff
% 5.44/5.70 thf(fact_8400_atMost__subset__iff,axiom,
% 5.44/5.70 ! [X: num,Y: num] :
% 5.44/5.70 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 5.44/5.70 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_subset_iff
% 5.44/5.70 thf(fact_8401_atMost__subset__iff,axiom,
% 5.44/5.70 ! [X: int,Y: int] :
% 5.44/5.70 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 5.44/5.70 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_subset_iff
% 5.44/5.70 thf(fact_8402_atMost__subset__iff,axiom,
% 5.44/5.70 ! [X: real,Y: real] :
% 5.44/5.70 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ X ) @ ( set_ord_atMost_real @ Y ) )
% 5.44/5.70 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_subset_iff
% 5.44/5.70 thf(fact_8403_atMost__subset__iff,axiom,
% 5.44/5.70 ! [X: nat,Y: nat] :
% 5.44/5.70 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 5.44/5.70 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_subset_iff
% 5.44/5.70 thf(fact_8404_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_real,A: real,B: real > extended_enat] :
% 5.44/5.70 ( ( finite_finite_real @ S )
% 5.44/5.70 => ( ( ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat
% 5.44/5.70 @ ^ [K3: real] : ( if_Extended_enat @ ( A = K3 ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat
% 5.44/5.70 @ ^ [K3: real] : ( if_Extended_enat @ ( A = K3 ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8405_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_int,A: int,B: int > extended_enat] :
% 5.44/5.70 ( ( finite_finite_int @ S )
% 5.44/5.70 => ( ( ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups5078248829458667347d_enat
% 5.44/5.70 @ ^ [K3: int] : ( if_Extended_enat @ ( A = K3 ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups5078248829458667347d_enat
% 5.44/5.70 @ ^ [K3: int] : ( if_Extended_enat @ ( A = K3 ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8406_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_nat,A: nat,B: nat > extended_enat] :
% 5.44/5.70 ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ( ( member_nat @ A @ S )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat
% 5.44/5.70 @ ^ [K3: nat] : ( if_Extended_enat @ ( A = K3 ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_nat @ A @ S )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat
% 5.44/5.70 @ ^ [K3: nat] : ( if_Extended_enat @ ( A = K3 ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8407_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_complex,A: complex,B: complex > extended_enat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ( ( member_complex @ A @ S )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat
% 5.44/5.70 @ ^ [K3: complex] : ( if_Extended_enat @ ( A = K3 ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_complex @ A @ S )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat
% 5.44/5.70 @ ^ [K3: complex] : ( if_Extended_enat @ ( A = K3 ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8408_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_real,A: real,B: real > complex] :
% 5.44/5.70 ( ( finite_finite_real @ S )
% 5.44/5.70 => ( ( ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups713298508707869441omplex
% 5.44/5.70 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups713298508707869441omplex
% 5.44/5.70 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8409_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_int,A: int,B: int > complex] :
% 5.44/5.70 ( ( finite_finite_int @ S )
% 5.44/5.70 => ( ( ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups7440179247065528705omplex
% 5.44/5.70 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups7440179247065528705omplex
% 5.44/5.70 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8410_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_nat,A: nat,B: nat > complex] :
% 5.44/5.70 ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ( ( member_nat @ A @ S )
% 5.44/5.70 => ( ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_nat @ A @ S )
% 5.44/5.70 => ( ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8411_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_complex,A: complex,B: complex > complex] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ( ( member_complex @ A @ S )
% 5.44/5.70 => ( ( groups3708469109370488835omplex
% 5.44/5.70 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_complex @ A @ S )
% 5.44/5.70 => ( ( groups3708469109370488835omplex
% 5.44/5.70 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8412_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_real,A: real,B: real > real] :
% 5.44/5.70 ( ( finite_finite_real @ S )
% 5.44/5.70 => ( ( ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups1681761925125756287l_real
% 5.44/5.70 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups1681761925125756287l_real
% 5.44/5.70 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_real ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8413_prod_Odelta_H,axiom,
% 5.44/5.70 ! [S: set_int,A: int,B: int > real] :
% 5.44/5.70 ( ( finite_finite_int @ S )
% 5.44/5.70 => ( ( ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups2316167850115554303t_real
% 5.44/5.70 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups2316167850115554303t_real
% 5.44/5.70 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_real ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta'
% 5.44/5.70 thf(fact_8414_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_real,A: real,B: real > extended_enat] :
% 5.44/5.70 ( ( finite_finite_real @ S )
% 5.44/5.70 => ( ( ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat
% 5.44/5.70 @ ^ [K3: real] : ( if_Extended_enat @ ( K3 = A ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat
% 5.44/5.70 @ ^ [K3: real] : ( if_Extended_enat @ ( K3 = A ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8415_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_int,A: int,B: int > extended_enat] :
% 5.44/5.70 ( ( finite_finite_int @ S )
% 5.44/5.70 => ( ( ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups5078248829458667347d_enat
% 5.44/5.70 @ ^ [K3: int] : ( if_Extended_enat @ ( K3 = A ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups5078248829458667347d_enat
% 5.44/5.70 @ ^ [K3: int] : ( if_Extended_enat @ ( K3 = A ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8416_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_nat,A: nat,B: nat > extended_enat] :
% 5.44/5.70 ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ( ( member_nat @ A @ S )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat
% 5.44/5.70 @ ^ [K3: nat] : ( if_Extended_enat @ ( K3 = A ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_nat @ A @ S )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat
% 5.44/5.70 @ ^ [K3: nat] : ( if_Extended_enat @ ( K3 = A ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8417_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_complex,A: complex,B: complex > extended_enat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ( ( member_complex @ A @ S )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat
% 5.44/5.70 @ ^ [K3: complex] : ( if_Extended_enat @ ( K3 = A ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_complex @ A @ S )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat
% 5.44/5.70 @ ^ [K3: complex] : ( if_Extended_enat @ ( K3 = A ) @ ( B @ K3 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8418_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_real,A: real,B: real > complex] :
% 5.44/5.70 ( ( finite_finite_real @ S )
% 5.44/5.70 => ( ( ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups713298508707869441omplex
% 5.44/5.70 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups713298508707869441omplex
% 5.44/5.70 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8419_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_int,A: int,B: int > complex] :
% 5.44/5.70 ( ( finite_finite_int @ S )
% 5.44/5.70 => ( ( ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups7440179247065528705omplex
% 5.44/5.70 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups7440179247065528705omplex
% 5.44/5.70 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8420_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_nat,A: nat,B: nat > complex] :
% 5.44/5.70 ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ( ( member_nat @ A @ S )
% 5.44/5.70 => ( ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_nat @ A @ S )
% 5.44/5.70 => ( ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8421_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_complex,A: complex,B: complex > complex] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ( ( member_complex @ A @ S )
% 5.44/5.70 => ( ( groups3708469109370488835omplex
% 5.44/5.70 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_complex @ A @ S )
% 5.44/5.70 => ( ( groups3708469109370488835omplex
% 5.44/5.70 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_complex ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8422_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_real,A: real,B: real > real] :
% 5.44/5.70 ( ( finite_finite_real @ S )
% 5.44/5.70 => ( ( ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups1681761925125756287l_real
% 5.44/5.70 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_real @ A @ S )
% 5.44/5.70 => ( ( groups1681761925125756287l_real
% 5.44/5.70 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_real ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8423_prod_Odelta,axiom,
% 5.44/5.70 ! [S: set_int,A: int,B: int > real] :
% 5.44/5.70 ( ( finite_finite_int @ S )
% 5.44/5.70 => ( ( ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups2316167850115554303t_real
% 5.44/5.70 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.44/5.70 @ S )
% 5.44/5.70 = ( B @ A ) ) )
% 5.44/5.70 & ( ~ ( member_int @ A @ S )
% 5.44/5.70 => ( ( groups2316167850115554303t_real
% 5.44/5.70 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 5.44/5.70 @ S )
% 5.44/5.70 = one_one_real ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.delta
% 5.44/5.70 thf(fact_8424_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_real,X: real,G: real > complex] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ~ ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8425_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_int,X: int,G: int > complex] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ~ ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8426_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_nat,X: nat,G: nat > complex] :
% 5.44/5.70 ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ~ ( member_nat @ X @ A2 )
% 5.44/5.70 => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8427_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_complex,X: complex,G: complex > complex] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ~ ( member_complex @ X @ A2 )
% 5.44/5.70 => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8428_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_real,X: real,G: real > real] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ~ ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8429_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_int,X: int,G: int > real] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ~ ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8430_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_nat,X: nat,G: nat > real] :
% 5.44/5.70 ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ~ ( member_nat @ X @ A2 )
% 5.44/5.70 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8431_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ~ ( member_complex @ X @ A2 )
% 5.44/5.70 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8432_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_real,X: real,G: real > nat] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ~ ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( times_times_nat @ ( G @ X ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8433_prod_Oinsert,axiom,
% 5.44/5.70 ! [A2: set_int,X: int,G: int > nat] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ~ ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups1707563613775114915nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( times_times_nat @ ( G @ X ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert
% 5.44/5.70 thf(fact_8434_Icc__subset__Iic__iff,axiom,
% 5.44/5.70 ! [L2: set_real,H2: set_real,H3: set_real] :
% 5.44/5.70 ( ( ord_le3558479182127378552t_real @ ( set_or7743017856606604397t_real @ L2 @ H2 ) @ ( set_or5092868708245317595t_real @ H3 ) )
% 5.44/5.70 = ( ~ ( ord_less_eq_set_real @ L2 @ H2 )
% 5.44/5.70 | ( ord_less_eq_set_real @ H2 @ H3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Icc_subset_Iic_iff
% 5.44/5.70 thf(fact_8435_Icc__subset__Iic__iff,axiom,
% 5.44/5.70 ! [L2: set_nat,H2: set_nat,H3: set_nat] :
% 5.44/5.70 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L2 @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 5.44/5.70 = ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 5.44/5.70 | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Icc_subset_Iic_iff
% 5.44/5.70 thf(fact_8436_Icc__subset__Iic__iff,axiom,
% 5.44/5.70 ! [L2: num,H2: num,H3: num] :
% 5.44/5.70 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L2 @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.44/5.70 = ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.44/5.70 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Icc_subset_Iic_iff
% 5.44/5.70 thf(fact_8437_Icc__subset__Iic__iff,axiom,
% 5.44/5.70 ! [L2: nat,H2: nat,H3: nat] :
% 5.44/5.70 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L2 @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.44/5.70 = ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.44/5.70 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Icc_subset_Iic_iff
% 5.44/5.70 thf(fact_8438_Icc__subset__Iic__iff,axiom,
% 5.44/5.70 ! [L2: int,H2: int,H3: int] :
% 5.44/5.70 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L2 @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.44/5.70 = ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.44/5.70 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Icc_subset_Iic_iff
% 5.44/5.70 thf(fact_8439_Icc__subset__Iic__iff,axiom,
% 5.44/5.70 ! [L2: real,H2: real,H3: real] :
% 5.44/5.70 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L2 @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.44/5.70 = ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.44/5.70 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % Icc_subset_Iic_iff
% 5.44/5.70 thf(fact_8440_sum_OatMost__Suc,axiom,
% 5.44/5.70 ! [G: nat > complex,N2: nat] :
% 5.44/5.70 ( ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.atMost_Suc
% 5.44/5.70 thf(fact_8441_sum_OatMost__Suc,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat] :
% 5.44/5.70 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.atMost_Suc
% 5.44/5.70 thf(fact_8442_sum_OatMost__Suc,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.atMost_Suc
% 5.44/5.70 thf(fact_8443_sum_OatMost__Suc,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % sum.atMost_Suc
% 5.44/5.70 thf(fact_8444_prod_OlessThan__Suc,axiom,
% 5.44/5.70 ! [G: nat > complex,N2: nat] :
% 5.44/5.70 ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.lessThan_Suc
% 5.44/5.70 thf(fact_8445_prod_OlessThan__Suc,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.lessThan_Suc
% 5.44/5.70 thf(fact_8446_prod_OlessThan__Suc,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.lessThan_Suc
% 5.44/5.70 thf(fact_8447_prod_OlessThan__Suc,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.lessThan_Suc
% 5.44/5.70 thf(fact_8448_prod_OatMost__Suc,axiom,
% 5.44/5.70 ! [G: nat > complex,N2: nat] :
% 5.44/5.70 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_Suc
% 5.44/5.70 thf(fact_8449_prod_OatMost__Suc,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_Suc
% 5.44/5.70 thf(fact_8450_prod_OatMost__Suc,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_Suc
% 5.44/5.70 thf(fact_8451_prod_OatMost__Suc,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_Suc
% 5.44/5.70 thf(fact_8452_prod_Ocl__ivl__Suc,axiom,
% 5.44/5.70 ! [N2: nat,M: nat,G: nat > extended_enat] :
% 5.44/5.70 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_7803423173614009249d_enat @ ( groups7961826882256487087d_enat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.cl_ivl_Suc
% 5.44/5.70 thf(fact_8453_prod_Ocl__ivl__Suc,axiom,
% 5.44/5.70 ! [N2: nat,M: nat,G: nat > complex] :
% 5.44/5.70 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = one_one_complex ) )
% 5.44/5.70 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.cl_ivl_Suc
% 5.44/5.70 thf(fact_8454_prod_Ocl__ivl__Suc,axiom,
% 5.44/5.70 ! [N2: nat,M: nat,G: nat > real] :
% 5.44/5.70 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = one_one_real ) )
% 5.44/5.70 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.cl_ivl_Suc
% 5.44/5.70 thf(fact_8455_prod_Ocl__ivl__Suc,axiom,
% 5.44/5.70 ! [N2: nat,M: nat,G: nat > nat] :
% 5.44/5.70 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = one_one_nat ) )
% 5.44/5.70 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.cl_ivl_Suc
% 5.44/5.70 thf(fact_8456_prod_Ocl__ivl__Suc,axiom,
% 5.44/5.70 ! [N2: nat,M: nat,G: nat > int] :
% 5.44/5.70 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = one_one_int ) )
% 5.44/5.70 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.44/5.70 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.cl_ivl_Suc
% 5.44/5.70 thf(fact_8457_prod_Oneutral,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > nat] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ( G @ X5 )
% 5.44/5.70 = one_one_nat ) )
% 5.44/5.70 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.44/5.70 = one_one_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.neutral
% 5.44/5.70 thf(fact_8458_prod_Oneutral,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > int] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ( G @ X5 )
% 5.44/5.70 = one_one_int ) )
% 5.44/5.70 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.44/5.70 = one_one_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.neutral
% 5.44/5.70 thf(fact_8459_prod_Oneutral,axiom,
% 5.44/5.70 ! [A2: set_int,G: int > int] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ( G @ X5 )
% 5.44/5.70 = one_one_int ) )
% 5.44/5.70 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.44/5.70 = one_one_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.neutral
% 5.44/5.70 thf(fact_8460_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: nat > extended_enat,A2: set_nat] :
% 5.44/5.70 ( ( ( groups7961826882256487087d_enat @ G @ A2 )
% 5.44/5.70 != one_on7984719198319812577d_enat )
% 5.44/5.70 => ~ ! [A3: nat] :
% 5.44/5.70 ( ( member_nat @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8461_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: real > extended_enat,A2: set_real] :
% 5.44/5.70 ( ( ( groups7973222482632965587d_enat @ G @ A2 )
% 5.44/5.70 != one_on7984719198319812577d_enat )
% 5.44/5.70 => ~ ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8462_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: int > extended_enat,A2: set_int] :
% 5.44/5.70 ( ( ( groups5078248829458667347d_enat @ G @ A2 )
% 5.44/5.70 != one_on7984719198319812577d_enat )
% 5.44/5.70 => ~ ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8463_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: complex > extended_enat,A2: set_complex] :
% 5.44/5.70 ( ( ( groups8780218893797010257d_enat @ G @ A2 )
% 5.44/5.70 != one_on7984719198319812577d_enat )
% 5.44/5.70 => ~ ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8464_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: nat > complex,A2: set_nat] :
% 5.44/5.70 ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.44/5.70 != one_one_complex )
% 5.44/5.70 => ~ ! [A3: nat] :
% 5.44/5.70 ( ( member_nat @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_complex ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8465_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: real > complex,A2: set_real] :
% 5.44/5.70 ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.44/5.70 != one_one_complex )
% 5.44/5.70 => ~ ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_complex ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8466_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: int > complex,A2: set_int] :
% 5.44/5.70 ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.44/5.70 != one_one_complex )
% 5.44/5.70 => ~ ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_complex ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8467_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: complex > complex,A2: set_complex] :
% 5.44/5.70 ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.44/5.70 != one_one_complex )
% 5.44/5.70 => ~ ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_complex ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8468_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: nat > real,A2: set_nat] :
% 5.44/5.70 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 5.44/5.70 != one_one_real )
% 5.44/5.70 => ~ ! [A3: nat] :
% 5.44/5.70 ( ( member_nat @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8469_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.44/5.70 ! [G: real > real,A2: set_real] :
% 5.44/5.70 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.44/5.70 != one_one_real )
% 5.44/5.70 => ~ ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ A2 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_real ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.not_neutral_contains_not_neutral
% 5.44/5.70 thf(fact_8470_prod_Odistrib,axiom,
% 5.44/5.70 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.44/5.70 @ A2 )
% 5.44/5.70 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.distrib
% 5.44/5.70 thf(fact_8471_prod_Odistrib,axiom,
% 5.44/5.70 ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [X2: nat] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.44/5.70 @ A2 )
% 5.44/5.70 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.distrib
% 5.44/5.70 thf(fact_8472_prod_Odistrib,axiom,
% 5.44/5.70 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.44/5.70 ( ( groups1705073143266064639nt_int
% 5.44/5.70 @ ^ [X2: int] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.44/5.70 @ A2 )
% 5.44/5.70 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.distrib
% 5.44/5.70 thf(fact_8473_prod__power__distrib,axiom,
% 5.44/5.70 ! [F: nat > nat,A2: set_nat,N2: nat] :
% 5.44/5.70 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N2 )
% 5.44/5.70 = ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N2 )
% 5.44/5.70 @ A2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_power_distrib
% 5.44/5.70 thf(fact_8474_prod__power__distrib,axiom,
% 5.44/5.70 ! [F: nat > int,A2: set_nat,N2: nat] :
% 5.44/5.70 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N2 )
% 5.44/5.70 = ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [X2: nat] : ( power_power_int @ ( F @ X2 ) @ N2 )
% 5.44/5.70 @ A2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_power_distrib
% 5.44/5.70 thf(fact_8475_prod__power__distrib,axiom,
% 5.44/5.70 ! [F: int > int,A2: set_int,N2: nat] :
% 5.44/5.70 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N2 )
% 5.44/5.70 = ( groups1705073143266064639nt_int
% 5.44/5.70 @ ^ [X2: int] : ( power_power_int @ ( F @ X2 ) @ N2 )
% 5.44/5.70 @ A2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_power_distrib
% 5.44/5.70 thf(fact_8476_mod__prod__eq,axiom,
% 5.44/5.70 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.44/5.70 ( ( modulo_modulo_nat
% 5.44/5.70 @ ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( modulo_modulo_nat @ ( F @ I5 ) @ A )
% 5.44/5.70 @ A2 )
% 5.44/5.70 @ A )
% 5.44/5.70 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 5.44/5.70
% 5.44/5.70 % mod_prod_eq
% 5.44/5.70 thf(fact_8477_mod__prod__eq,axiom,
% 5.44/5.70 ! [F: nat > int,A: int,A2: set_nat] :
% 5.44/5.70 ( ( modulo_modulo_int
% 5.44/5.70 @ ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 5.44/5.70 @ A2 )
% 5.44/5.70 @ A )
% 5.44/5.70 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 5.44/5.70
% 5.44/5.70 % mod_prod_eq
% 5.44/5.70 thf(fact_8478_mod__prod__eq,axiom,
% 5.44/5.70 ! [F: int > int,A: int,A2: set_int] :
% 5.44/5.70 ( ( modulo_modulo_int
% 5.44/5.70 @ ( groups1705073143266064639nt_int
% 5.44/5.70 @ ^ [I5: int] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 5.44/5.70 @ A2 )
% 5.44/5.70 @ A )
% 5.44/5.70 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 5.44/5.70
% 5.44/5.70 % mod_prod_eq
% 5.44/5.70 thf(fact_8479_prod_OatMost__Suc__shift,axiom,
% 5.44/5.70 ! [G: nat > complex,N2: nat] :
% 5.44/5.70 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_Suc_shift
% 5.44/5.70 thf(fact_8480_prod_OatMost__Suc__shift,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups129246275422532515t_real
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_Suc_shift
% 5.44/5.70 thf(fact_8481_prod_OatMost__Suc__shift,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_Suc_shift
% 5.44/5.70 thf(fact_8482_prod_OatMost__Suc__shift,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_Suc_shift
% 5.44/5.70 thf(fact_8483_prod_Onested__swap_H,axiom,
% 5.44/5.70 ! [A: nat > nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( groups708209901874060359at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.70 = ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [J3: nat] :
% 5.44/5.70 ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.nested_swap'
% 5.44/5.70 thf(fact_8484_prod_Onested__swap_H,axiom,
% 5.44/5.70 ! [A: nat > nat > int,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( groups705719431365010083at_int @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.70 = ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [J3: nat] :
% 5.44/5.70 ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.nested_swap'
% 5.44/5.70 thf(fact_8485_atMost__def,axiom,
% 5.44/5.70 ( set_ord_atMost_real
% 5.44/5.70 = ( ^ [U2: real] :
% 5.44/5.70 ( collect_real
% 5.44/5.70 @ ^ [X2: real] : ( ord_less_eq_real @ X2 @ U2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_def
% 5.44/5.70 thf(fact_8486_atMost__def,axiom,
% 5.44/5.70 ( set_or5092868708245317595t_real
% 5.44/5.70 = ( ^ [U2: set_real] :
% 5.44/5.70 ( collect_set_real
% 5.44/5.70 @ ^ [X2: set_real] : ( ord_less_eq_set_real @ X2 @ U2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_def
% 5.44/5.70 thf(fact_8487_atMost__def,axiom,
% 5.44/5.70 ( set_or4236626031148496127et_nat
% 5.44/5.70 = ( ^ [U2: set_nat] :
% 5.44/5.70 ( collect_set_nat
% 5.44/5.70 @ ^ [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ U2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_def
% 5.44/5.70 thf(fact_8488_atMost__def,axiom,
% 5.44/5.70 ( set_ord_atMost_num
% 5.44/5.70 = ( ^ [U2: num] :
% 5.44/5.70 ( collect_num
% 5.44/5.70 @ ^ [X2: num] : ( ord_less_eq_num @ X2 @ U2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_def
% 5.44/5.70 thf(fact_8489_atMost__def,axiom,
% 5.44/5.70 ( set_ord_atMost_int
% 5.44/5.70 = ( ^ [U2: int] :
% 5.44/5.70 ( collect_int
% 5.44/5.70 @ ^ [X2: int] : ( ord_less_eq_int @ X2 @ U2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_def
% 5.44/5.70 thf(fact_8490_atMost__def,axiom,
% 5.44/5.70 ( set_ord_atMost_nat
% 5.44/5.70 = ( ^ [U2: nat] :
% 5.44/5.70 ( collect_nat
% 5.44/5.70 @ ^ [X2: nat] : ( ord_less_eq_nat @ X2 @ U2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_def
% 5.44/5.70 thf(fact_8491_prod__nonneg,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > nat] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_nonneg
% 5.44/5.70 thf(fact_8492_prod__nonneg,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > int] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_nonneg
% 5.44/5.70 thf(fact_8493_prod__nonneg,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > int] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_nonneg
% 5.44/5.70 thf(fact_8494_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.44/5.70 ( ! [I4: nat] :
% 5.44/5.70 ( ( member_nat @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8495_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > real,G: real > real] :
% 5.44/5.70 ( ! [I4: real] :
% 5.44/5.70 ( ( member_real @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8496_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > real,G: int > real] :
% 5.44/5.70 ( ! [I4: int] :
% 5.44/5.70 ( ( member_int @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8497_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.44/5.70 ( ! [I4: complex] :
% 5.44/5.70 ( ( member_complex @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8498_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.44/5.70 ( ! [I4: real] :
% 5.44/5.70 ( ( member_real @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8499_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.44/5.70 ( ! [I4: int] :
% 5.44/5.70 ( ( member_int @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8500_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.44/5.70 ( ! [I4: complex] :
% 5.44/5.70 ( ( member_complex @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8501_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > int,G: real > int] :
% 5.44/5.70 ( ! [I4: real] :
% 5.44/5.70 ( ( member_real @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8502_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.44/5.70 ( ! [I4: complex] :
% 5.44/5.70 ( ( member_complex @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8503_prod__mono,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.44/5.70 ( ! [I4: nat] :
% 5.44/5.70 ( ( member_nat @ I4 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.44/5.70 & ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_mono
% 5.44/5.70 thf(fact_8504_prod__pos,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > nat] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_pos
% 5.44/5.70 thf(fact_8505_prod__pos,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > int] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_pos
% 5.44/5.70 thf(fact_8506_prod__pos,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > int] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_pos
% 5.44/5.70 thf(fact_8507_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > extended_enat] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( groups7961826882256487087d_enat @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8508_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > extended_enat] :
% 5.44/5.70 ( ! [X5: real] :
% 5.44/5.70 ( ( member_real @ X5 @ A2 )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( groups7973222482632965587d_enat @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8509_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > extended_enat] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( groups5078248829458667347d_enat @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8510_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > extended_enat] :
% 5.44/5.70 ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ A2 )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( groups8780218893797010257d_enat @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8511_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > real] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8512_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > real] :
% 5.44/5.70 ( ! [X5: real] :
% 5.44/5.70 ( ( member_real @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8513_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > real] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8514_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > real] :
% 5.44/5.70 ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8515_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > nat] :
% 5.44/5.70 ( ! [X5: real] :
% 5.44/5.70 ( ( member_real @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8516_prod__ge__1,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > nat] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_ge_1
% 5.44/5.70 thf(fact_8517_prod__atLeastAtMost__code,axiom,
% 5.44/5.70 ! [F: nat > extended_enat,A: nat,B: nat] :
% 5.44/5.70 ( ( groups7961826882256487087d_enat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.70 = ( set_fo2538466533108834004d_enat
% 5.44/5.70 @ ^ [A4: nat] : ( times_7803423173614009249d_enat @ ( F @ A4 ) )
% 5.44/5.70 @ A
% 5.44/5.70 @ B
% 5.44/5.70 @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_atLeastAtMost_code
% 5.44/5.70 thf(fact_8518_prod__atLeastAtMost__code,axiom,
% 5.44/5.70 ! [F: nat > complex,A: nat,B: nat] :
% 5.44/5.70 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.70 = ( set_fo1517530859248394432omplex
% 5.44/5.70 @ ^ [A4: nat] : ( times_times_complex @ ( F @ A4 ) )
% 5.44/5.70 @ A
% 5.44/5.70 @ B
% 5.44/5.70 @ one_one_complex ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_atLeastAtMost_code
% 5.44/5.70 thf(fact_8519_prod__atLeastAtMost__code,axiom,
% 5.44/5.70 ! [F: nat > real,A: nat,B: nat] :
% 5.44/5.70 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.70 = ( set_fo3111899725591712190t_real
% 5.44/5.70 @ ^ [A4: nat] : ( times_times_real @ ( F @ A4 ) )
% 5.44/5.70 @ A
% 5.44/5.70 @ B
% 5.44/5.70 @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_atLeastAtMost_code
% 5.44/5.70 thf(fact_8520_prod__atLeastAtMost__code,axiom,
% 5.44/5.70 ! [F: nat > nat,A: nat,B: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.70 = ( set_fo2584398358068434914at_nat
% 5.44/5.70 @ ^ [A4: nat] : ( times_times_nat @ ( F @ A4 ) )
% 5.44/5.70 @ A
% 5.44/5.70 @ B
% 5.44/5.70 @ one_one_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_atLeastAtMost_code
% 5.44/5.70 thf(fact_8521_prod__atLeastAtMost__code,axiom,
% 5.44/5.70 ! [F: nat > int,A: nat,B: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.70 = ( set_fo2581907887559384638at_int
% 5.44/5.70 @ ^ [A4: nat] : ( times_times_int @ ( F @ A4 ) )
% 5.44/5.70 @ A
% 5.44/5.70 @ B
% 5.44/5.70 @ one_one_int ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_atLeastAtMost_code
% 5.44/5.70 thf(fact_8522_prod_OatMost__shift,axiom,
% 5.44/5.70 ! [G: nat > complex,N2: nat] :
% 5.44/5.70 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_shift
% 5.44/5.70 thf(fact_8523_prod_OatMost__shift,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups129246275422532515t_real
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_shift
% 5.44/5.70 thf(fact_8524_prod_OatMost__shift,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.70 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_shift
% 5.44/5.70 thf(fact_8525_prod_OatMost__shift,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.70 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.44/5.70 @ ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atMost_shift
% 5.44/5.70 thf(fact_8526_lessThan__Suc__atMost,axiom,
% 5.44/5.70 ! [K: nat] :
% 5.44/5.70 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.44/5.70 = ( set_ord_atMost_nat @ K ) ) ).
% 5.44/5.70
% 5.44/5.70 % lessThan_Suc_atMost
% 5.44/5.70 thf(fact_8527_atMost__Suc,axiom,
% 5.44/5.70 ! [K: nat] :
% 5.44/5.70 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.44/5.70 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_Suc
% 5.44/5.70 thf(fact_8528_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_int,G: int > extended_enat,P: int > $o] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ( groups5078248829458667347d_enat @ G
% 5.44/5.70 @ ( collect_int
% 5.44/5.70 @ ^ [X2: int] :
% 5.44/5.70 ( ( member_int @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups5078248829458667347d_enat
% 5.44/5.70 @ ^ [X2: int] : ( if_Extended_enat @ ( P @ X2 ) @ ( G @ X2 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8529_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > extended_enat,P: real > $o] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat @ G
% 5.44/5.70 @ ( collect_real
% 5.44/5.70 @ ^ [X2: real] :
% 5.44/5.70 ( ( member_real @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups7973222482632965587d_enat
% 5.44/5.70 @ ^ [X2: real] : ( if_Extended_enat @ ( P @ X2 ) @ ( G @ X2 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8530_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > extended_enat,P: nat > $o] :
% 5.44/5.70 ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat @ G
% 5.44/5.70 @ ( collect_nat
% 5.44/5.70 @ ^ [X2: nat] :
% 5.44/5.70 ( ( member_nat @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups7961826882256487087d_enat
% 5.44/5.70 @ ^ [X2: nat] : ( if_Extended_enat @ ( P @ X2 ) @ ( G @ X2 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8531_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > extended_enat,P: complex > $o] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat @ G
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [X2: complex] :
% 5.44/5.70 ( ( member_complex @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups8780218893797010257d_enat
% 5.44/5.70 @ ^ [X2: complex] : ( if_Extended_enat @ ( P @ X2 ) @ ( G @ X2 ) @ one_on7984719198319812577d_enat )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8532_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_int,G: int > complex,P: int > $o] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ( groups7440179247065528705omplex @ G
% 5.44/5.70 @ ( collect_int
% 5.44/5.70 @ ^ [X2: int] :
% 5.44/5.70 ( ( member_int @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups7440179247065528705omplex
% 5.44/5.70 @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8533_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > complex,P: real > $o] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups713298508707869441omplex @ G
% 5.44/5.70 @ ( collect_real
% 5.44/5.70 @ ^ [X2: real] :
% 5.44/5.70 ( ( member_real @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups713298508707869441omplex
% 5.44/5.70 @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8534_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 5.44/5.70 ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups6464643781859351333omplex @ G
% 5.44/5.70 @ ( collect_nat
% 5.44/5.70 @ ^ [X2: nat] :
% 5.44/5.70 ( ( member_nat @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8535_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups3708469109370488835omplex @ G
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [X2: complex] :
% 5.44/5.70 ( ( member_complex @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups3708469109370488835omplex
% 5.44/5.70 @ ^ [X2: complex] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8536_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_int,G: int > real,P: int > $o] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ( groups2316167850115554303t_real @ G
% 5.44/5.70 @ ( collect_int
% 5.44/5.70 @ ^ [X2: int] :
% 5.44/5.70 ( ( member_int @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups2316167850115554303t_real
% 5.44/5.70 @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8537_prod_Ointer__filter,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > real,P: real > $o] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups1681761925125756287l_real @ G
% 5.44/5.70 @ ( collect_real
% 5.44/5.70 @ ^ [X2: real] :
% 5.44/5.70 ( ( member_real @ X2 @ A2 )
% 5.44/5.70 & ( P @ X2 ) ) ) )
% 5.44/5.70 = ( groups1681761925125756287l_real
% 5.44/5.70 @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.44/5.70 @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.inter_filter
% 5.44/5.70 thf(fact_8538_not__Iic__le__Icc,axiom,
% 5.44/5.70 ! [H2: int,L3: int,H3: int] :
% 5.44/5.70 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 5.44/5.70
% 5.44/5.70 % not_Iic_le_Icc
% 5.44/5.70 thf(fact_8539_not__Iic__le__Icc,axiom,
% 5.44/5.70 ! [H2: real,L3: real,H3: real] :
% 5.44/5.70 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 5.44/5.70
% 5.44/5.70 % not_Iic_le_Icc
% 5.44/5.70 thf(fact_8540_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.44/5.70 ! [G: nat > nat,M: nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.shift_bounds_cl_Suc_ivl
% 5.44/5.70 thf(fact_8541_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.44/5.70 ! [G: nat > int,M: nat,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.44/5.70 = ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.shift_bounds_cl_Suc_ivl
% 5.44/5.70 thf(fact_8542_power__sum,axiom,
% 5.44/5.70 ! [C: real,F: nat > nat,A2: set_nat] :
% 5.44/5.70 ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.44/5.70 = ( groups129246275422532515t_real
% 5.44/5.70 @ ^ [A4: nat] : ( power_power_real @ C @ ( F @ A4 ) )
% 5.44/5.70 @ A2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_sum
% 5.44/5.70 thf(fact_8543_power__sum,axiom,
% 5.44/5.70 ! [C: complex,F: nat > nat,A2: set_nat] :
% 5.44/5.70 ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.44/5.70 = ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [A4: nat] : ( power_power_complex @ C @ ( F @ A4 ) )
% 5.44/5.70 @ A2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_sum
% 5.44/5.70 thf(fact_8544_power__sum,axiom,
% 5.44/5.70 ! [C: nat,F: nat > nat,A2: set_nat] :
% 5.44/5.70 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.44/5.70 = ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [A4: nat] : ( power_power_nat @ C @ ( F @ A4 ) )
% 5.44/5.70 @ A2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_sum
% 5.44/5.70 thf(fact_8545_power__sum,axiom,
% 5.44/5.70 ! [C: int,F: nat > nat,A2: set_nat] :
% 5.44/5.70 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.44/5.70 = ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [A4: nat] : ( power_power_int @ C @ ( F @ A4 ) )
% 5.44/5.70 @ A2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_sum
% 5.44/5.70 thf(fact_8546_power__sum,axiom,
% 5.44/5.70 ! [C: int,F: int > nat,A2: set_int] :
% 5.44/5.70 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.44/5.70 = ( groups1705073143266064639nt_int
% 5.44/5.70 @ ^ [A4: int] : ( power_power_int @ C @ ( F @ A4 ) )
% 5.44/5.70 @ A2 ) ) ).
% 5.44/5.70
% 5.44/5.70 % power_sum
% 5.44/5.70 thf(fact_8547_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.44/5.70 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.44/5.70 = ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.shift_bounds_cl_nat_ivl
% 5.44/5.70 thf(fact_8548_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.44/5.70 ! [G: nat > int,M: nat,K: nat,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.44/5.70 = ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.shift_bounds_cl_nat_ivl
% 5.44/5.70 thf(fact_8549_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > extended_enat] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ one_on7984719198319812577d_enat ) ) )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ ( groups7961826882256487087d_enat @ F @ A2 ) @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8550_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > extended_enat] :
% 5.44/5.70 ( ! [X5: real] :
% 5.44/5.70 ( ( member_real @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ one_on7984719198319812577d_enat ) ) )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ ( groups7973222482632965587d_enat @ F @ A2 ) @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8551_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > extended_enat] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ one_on7984719198319812577d_enat ) ) )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ ( groups5078248829458667347d_enat @ F @ A2 ) @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8552_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > extended_enat] :
% 5.44/5.70 ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_le2932123472753598470d_enat @ ( F @ X5 ) @ one_on7984719198319812577d_enat ) ) )
% 5.44/5.70 => ( ord_le2932123472753598470d_enat @ ( groups8780218893797010257d_enat @ F @ A2 ) @ one_on7984719198319812577d_enat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8553_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_nat,F: nat > real] :
% 5.44/5.70 ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8554_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > real] :
% 5.44/5.70 ( ! [X5: real] :
% 5.44/5.70 ( ( member_real @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8555_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > real] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8556_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_complex,F: complex > real] :
% 5.44/5.70 ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.44/5.70 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8557_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_real,F: real > nat] :
% 5.44/5.70 ( ! [X5: real] :
% 5.44/5.70 ( ( member_real @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_less_eq_nat @ ( F @ X5 ) @ one_one_nat ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8558_prod__le__1,axiom,
% 5.44/5.70 ! [A2: set_int,F: int > nat] :
% 5.44/5.70 ( ! [X5: int] :
% 5.44/5.70 ( ( member_int @ X5 @ A2 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) )
% 5.44/5.70 & ( ord_less_eq_nat @ ( F @ X5 ) @ one_one_nat ) ) )
% 5.44/5.70 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_le_1
% 5.44/5.70 thf(fact_8559_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: extended_enat > extended_enat > $o,S: set_nat,H2: nat > extended_enat,G: nat > extended_enat] :
% 5.44/5.70 ( ( R2 @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 5.44/5.70 => ( ! [X15: extended_enat,Y15: extended_enat,X23: extended_enat,Y23: extended_enat] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_7803423173614009249d_enat @ X15 @ Y15 ) @ ( times_7803423173614009249d_enat @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups7961826882256487087d_enat @ H2 @ S ) @ ( groups7961826882256487087d_enat @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8560_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: extended_enat > extended_enat > $o,S: set_complex,H2: complex > extended_enat,G: complex > extended_enat] :
% 5.44/5.70 ( ( R2 @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 5.44/5.70 => ( ! [X15: extended_enat,Y15: extended_enat,X23: extended_enat,Y23: extended_enat] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_7803423173614009249d_enat @ X15 @ Y15 ) @ ( times_7803423173614009249d_enat @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups8780218893797010257d_enat @ H2 @ S ) @ ( groups8780218893797010257d_enat @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8561_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: complex > complex > $o,S: set_nat,H2: nat > complex,G: nat > complex] :
% 5.44/5.70 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.44/5.70 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups6464643781859351333omplex @ H2 @ S ) @ ( groups6464643781859351333omplex @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8562_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: complex > complex > $o,S: set_complex,H2: complex > complex,G: complex > complex] :
% 5.44/5.70 ( ( R2 @ one_one_complex @ one_one_complex )
% 5.44/5.70 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups3708469109370488835omplex @ H2 @ S ) @ ( groups3708469109370488835omplex @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8563_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: real > real > $o,S: set_nat,H2: nat > real,G: nat > real] :
% 5.44/5.70 ( ( R2 @ one_one_real @ one_one_real )
% 5.44/5.70 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups129246275422532515t_real @ H2 @ S ) @ ( groups129246275422532515t_real @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8564_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: real > real > $o,S: set_complex,H2: complex > real,G: complex > real] :
% 5.44/5.70 ( ( R2 @ one_one_real @ one_one_real )
% 5.44/5.70 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups766887009212190081x_real @ H2 @ S ) @ ( groups766887009212190081x_real @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8565_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: nat > nat > $o,S: set_complex,H2: complex > nat,G: complex > nat] :
% 5.44/5.70 ( ( R2 @ one_one_nat @ one_one_nat )
% 5.44/5.70 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups861055069439313189ex_nat @ H2 @ S ) @ ( groups861055069439313189ex_nat @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8566_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: int > int > $o,S: set_complex,H2: complex > int,G: complex > int] :
% 5.44/5.70 ( ( R2 @ one_one_int @ one_one_int )
% 5.44/5.70 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_times_int @ X15 @ Y15 ) @ ( times_times_int @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ S )
% 5.44/5.70 => ( ! [X5: complex] :
% 5.44/5.70 ( ( member_complex @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups858564598930262913ex_int @ H2 @ S ) @ ( groups858564598930262913ex_int @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8567_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: nat > nat > $o,S: set_nat,H2: nat > nat,G: nat > nat] :
% 5.44/5.70 ( ( R2 @ one_one_nat @ one_one_nat )
% 5.44/5.70 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_times_nat @ X15 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups708209901874060359at_nat @ H2 @ S ) @ ( groups708209901874060359at_nat @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8568_prod_Orelated,axiom,
% 5.44/5.70 ! [R2: int > int > $o,S: set_nat,H2: nat > int,G: nat > int] :
% 5.44/5.70 ( ( R2 @ one_one_int @ one_one_int )
% 5.44/5.70 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.44/5.70 ( ( ( R2 @ X15 @ X23 )
% 5.44/5.70 & ( R2 @ Y15 @ Y23 ) )
% 5.44/5.70 => ( R2 @ ( times_times_int @ X15 @ Y15 ) @ ( times_times_int @ X23 @ Y23 ) ) )
% 5.44/5.70 => ( ( finite_finite_nat @ S )
% 5.44/5.70 => ( ! [X5: nat] :
% 5.44/5.70 ( ( member_nat @ X5 @ S )
% 5.44/5.70 => ( R2 @ ( H2 @ X5 ) @ ( G @ X5 ) ) )
% 5.44/5.70 => ( R2 @ ( groups705719431365010083at_int @ H2 @ S ) @ ( groups705719431365010083at_int @ G @ S ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.related
% 5.44/5.70 thf(fact_8569_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_real,X: real,G: real > complex] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( groups713298508707869441omplex @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8570_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_int,X: int,G: int > complex] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ( ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( groups7440179247065528705omplex @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8571_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_nat,X: nat,G: nat > complex] :
% 5.44/5.70 ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( ( member_nat @ X @ A2 )
% 5.44/5.70 => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.70 = ( groups6464643781859351333omplex @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_nat @ X @ A2 )
% 5.44/5.70 => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8572_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_complex,X: complex,G: complex > complex] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( ( member_complex @ X @ A2 )
% 5.44/5.70 => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.70 = ( groups3708469109370488835omplex @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_complex @ X @ A2 )
% 5.44/5.70 => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.70 = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8573_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_real,X: real,G: real > real] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( groups1681761925125756287l_real @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8574_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_int,X: int,G: int > real] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ( ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( groups2316167850115554303t_real @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8575_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_nat,X: nat,G: nat > real] :
% 5.44/5.70 ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( ( member_nat @ X @ A2 )
% 5.44/5.70 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.70 = ( groups129246275422532515t_real @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_nat @ X @ A2 )
% 5.44/5.70 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8576_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( ( member_complex @ X @ A2 )
% 5.44/5.70 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.70 = ( groups766887009212190081x_real @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_complex @ X @ A2 )
% 5.44/5.70 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.70 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8577_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_real,X: real,G: real > nat] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( groups4696554848551431203al_nat @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_real @ X @ A2 )
% 5.44/5.70 => ( ( groups4696554848551431203al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.70 = ( times_times_nat @ ( G @ X ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8578_prod_Oinsert__if,axiom,
% 5.44/5.70 ! [A2: set_int,X: int,G: int > nat] :
% 5.44/5.70 ( ( finite_finite_int @ A2 )
% 5.44/5.70 => ( ( ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups1707563613775114915nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( groups1707563613775114915nt_nat @ G @ A2 ) ) )
% 5.44/5.70 & ( ~ ( member_int @ X @ A2 )
% 5.44/5.70 => ( ( groups1707563613775114915nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.70 = ( times_times_nat @ ( G @ X ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.insert_if
% 5.44/5.70 thf(fact_8579_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,F: complex > nat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8580_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8581_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,F: complex > code_integer] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( groups8682486955453173170nteger @ F @ A2 ) @ ( groups8682486955453173170nteger @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8582_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,F: real > nat] :
% 5.44/5.70 ( ( finite_finite_real @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8583_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,F: real > int] :
% 5.44/5.70 ( ( finite_finite_real @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8584_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,F: real > code_integer] :
% 5.44/5.70 ( ( finite_finite_real @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( groups6225526099057966256nteger @ F @ A2 ) @ ( groups6225526099057966256nteger @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8585_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_nat,A2: set_nat,F: nat > code_integer] :
% 5.44/5.70 ( ( finite_finite_nat @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( groups3455450783089532116nteger @ F @ A2 ) @ ( groups3455450783089532116nteger @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8586_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_nat,A2: set_nat,F: nat > nat] :
% 5.44/5.70 ( ( finite_finite_nat @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8587_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_nat,A2: set_nat,F: nat > int] :
% 5.44/5.70 ( ( finite_finite_nat @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8588_prod__dvd__prod__subset,axiom,
% 5.44/5.70 ! [B2: set_int,A2: set_int,F: int > int] :
% 5.44/5.70 ( ( finite_finite_int @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.70 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ F @ B2 ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset
% 5.44/5.70 thf(fact_8589_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_int,A2: set_int,F: int > nat,G: int > nat] :
% 5.44/5.70 ( ( finite_finite_int @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8590_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8591_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,F: complex > int,G: complex > int] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8592_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_int,A2: set_int,F: int > code_integer,G: int > code_integer] :
% 5.44/5.70 ( ( finite_finite_int @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( groups3827104343326376752nteger @ F @ A2 ) @ ( groups3827104343326376752nteger @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8593_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,F: complex > code_integer,G: complex > code_integer] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( groups8682486955453173170nteger @ F @ A2 ) @ ( groups8682486955453173170nteger @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8594_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,F: real > nat,G: real > nat] :
% 5.44/5.70 ( ( finite_finite_real @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8595_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,F: real > int,G: real > int] :
% 5.44/5.70 ( ( finite_finite_real @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8596_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,F: real > code_integer,G: real > code_integer] :
% 5.44/5.70 ( ( finite_finite_real @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( groups6225526099057966256nteger @ F @ A2 ) @ ( groups6225526099057966256nteger @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8597_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_nat,A2: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 5.44/5.70 ( ( finite_finite_nat @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: nat] :
% 5.44/5.70 ( ( member_nat @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_Code_integer @ ( groups3455450783089532116nteger @ F @ A2 ) @ ( groups3455450783089532116nteger @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8598_prod__dvd__prod__subset2,axiom,
% 5.44/5.70 ! [B2: set_nat,A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.44/5.70 ( ( finite_finite_nat @ B2 )
% 5.44/5.70 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.70 => ( ! [A3: nat] :
% 5.44/5.70 ( ( member_nat @ A3 @ A2 )
% 5.44/5.70 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 5.44/5.70 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod_dvd_prod_subset2
% 5.44/5.70 thf(fact_8599_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_real,T5: set_real,S: set_real,I2: real > real,J: real > real,T3: set_real,G: real > extended_enat,H2: real > extended_enat] :
% 5.44/5.70 ( ( finite_finite_real @ S5 )
% 5.44/5.70 => ( ( finite_finite_real @ T5 )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S5 ) )
% 5.44/5.70 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.70 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat @ G @ S )
% 5.44/5.70 = ( groups7973222482632965587d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8600_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_real,T5: set_int,S: set_real,I2: int > real,J: real > int,T3: set_int,G: real > extended_enat,H2: int > extended_enat] :
% 5.44/5.70 ( ( finite_finite_real @ S5 )
% 5.44/5.70 => ( ( finite_finite_int @ T5 )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S5 ) )
% 5.44/5.70 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.70 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat @ G @ S )
% 5.44/5.70 = ( groups5078248829458667347d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8601_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_int,T5: set_real,S: set_int,I2: real > int,J: int > real,T3: set_real,G: int > extended_enat,H2: real > extended_enat] :
% 5.44/5.70 ( ( finite_finite_int @ S5 )
% 5.44/5.70 => ( ( finite_finite_real @ T5 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S5 ) )
% 5.44/5.70 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.70 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups5078248829458667347d_enat @ G @ S )
% 5.44/5.70 = ( groups7973222482632965587d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8602_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_int,T5: set_int,S: set_int,I2: int > int,J: int > int,T3: set_int,G: int > extended_enat,H2: int > extended_enat] :
% 5.44/5.70 ( ( finite_finite_int @ S5 )
% 5.44/5.70 => ( ( finite_finite_int @ T5 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S5 ) )
% 5.44/5.70 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.70 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups5078248829458667347d_enat @ G @ S )
% 5.44/5.70 = ( groups5078248829458667347d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8603_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_real,T5: set_complex,S: set_real,I2: complex > real,J: real > complex,T3: set_complex,G: real > extended_enat,H2: complex > extended_enat] :
% 5.44/5.70 ( ( finite_finite_real @ S5 )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ T5 )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S5 ) )
% 5.44/5.70 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.70 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat @ G @ S )
% 5.44/5.70 = ( groups8780218893797010257d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8604_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_int,T5: set_complex,S: set_int,I2: complex > int,J: int > complex,T3: set_complex,G: int > extended_enat,H2: complex > extended_enat] :
% 5.44/5.70 ( ( finite_finite_int @ S5 )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ T5 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ S @ S5 ) )
% 5.44/5.70 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.70 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups5078248829458667347d_enat @ G @ S )
% 5.44/5.70 = ( groups8780218893797010257d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8605_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_complex,T5: set_real,S: set_complex,I2: real > complex,J: complex > real,T3: set_real,G: complex > extended_enat,H2: real > extended_enat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ S5 )
% 5.44/5.70 => ( ( finite_finite_real @ T5 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S @ S5 ) )
% 5.44/5.70 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.70 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat @ G @ S )
% 5.44/5.70 = ( groups7973222482632965587d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8606_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_complex,T5: set_int,S: set_complex,I2: int > complex,J: complex > int,T3: set_int,G: complex > extended_enat,H2: int > extended_enat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ S5 )
% 5.44/5.70 => ( ( finite_finite_int @ T5 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S @ S5 ) )
% 5.44/5.70 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.70 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat @ G @ S )
% 5.44/5.70 = ( groups5078248829458667347d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8607_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_complex,T5: set_complex,S: set_complex,I2: complex > complex,J: complex > complex,T3: set_complex,G: complex > extended_enat,H2: complex > extended_enat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ S5 )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ T5 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S @ S5 ) )
% 5.44/5.70 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.70 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat @ G @ S )
% 5.44/5.70 = ( groups8780218893797010257d_enat @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8608_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.44/5.70 ! [S5: set_real,T5: set_real,S: set_real,I2: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 5.44/5.70 ( ( finite_finite_real @ S5 )
% 5.44/5.70 => ( ( finite_finite_real @ T5 )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S5 ) )
% 5.44/5.70 => ( ( I2 @ ( J @ A3 ) )
% 5.44/5.70 = A3 ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ ( minus_minus_set_real @ S @ S5 ) )
% 5.44/5.70 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.70 => ( ( J @ ( I2 @ B3 ) )
% 5.44/5.70 = B3 ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.70 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S @ S5 ) ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ S5 )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_complex ) )
% 5.44/5.70 => ( ! [B3: real] :
% 5.44/5.70 ( ( member_real @ B3 @ T5 )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_one_complex ) )
% 5.44/5.70 => ( ! [A3: real] :
% 5.44/5.70 ( ( member_real @ A3 @ S )
% 5.44/5.70 => ( ( H2 @ ( J @ A3 ) )
% 5.44/5.70 = ( G @ A3 ) ) )
% 5.44/5.70 => ( ( groups713298508707869441omplex @ G @ S )
% 5.44/5.70 = ( groups713298508707869441omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.reindex_bij_witness_not_neutral
% 5.44/5.70 thf(fact_8609_prod_Oin__pairs__0,axiom,
% 5.44/5.70 ! [G: nat > complex,N2: nat] :
% 5.44/5.70 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.70 = ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [I5: nat] : ( times_times_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.in_pairs_0
% 5.44/5.70 thf(fact_8610_prod_Oin__pairs__0,axiom,
% 5.44/5.70 ! [G: nat > real,N2: nat] :
% 5.44/5.70 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.70 = ( groups129246275422532515t_real
% 5.44/5.70 @ ^ [I5: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.in_pairs_0
% 5.44/5.70 thf(fact_8611_prod_Oin__pairs__0,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.70 = ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.in_pairs_0
% 5.44/5.70 thf(fact_8612_prod_Oin__pairs__0,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.70 = ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.in_pairs_0
% 5.44/5.70 thf(fact_8613_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > extended_enat] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups7973222482632965587d_enat @ G
% 5.44/5.70 @ ( minus_minus_set_real @ A2
% 5.44/5.70 @ ( collect_real
% 5.44/5.70 @ ^ [X2: real] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.70 = ( groups7973222482632965587d_enat @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8614_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > extended_enat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups8780218893797010257d_enat @ G
% 5.44/5.70 @ ( minus_811609699411566653omplex @ A2
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [X2: complex] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) ) ) )
% 5.44/5.70 = ( groups8780218893797010257d_enat @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8615_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > complex] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups713298508707869441omplex @ G
% 5.44/5.70 @ ( minus_minus_set_real @ A2
% 5.44/5.70 @ ( collect_real
% 5.44/5.70 @ ^ [X2: real] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_one_complex ) ) ) )
% 5.44/5.70 = ( groups713298508707869441omplex @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8616_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > complex] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups3708469109370488835omplex @ G
% 5.44/5.70 @ ( minus_811609699411566653omplex @ A2
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [X2: complex] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_one_complex ) ) ) )
% 5.44/5.70 = ( groups3708469109370488835omplex @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8617_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > real] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups1681761925125756287l_real @ G
% 5.44/5.70 @ ( minus_minus_set_real @ A2
% 5.44/5.70 @ ( collect_real
% 5.44/5.70 @ ^ [X2: real] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_one_real ) ) ) )
% 5.44/5.70 = ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8618_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > real] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups766887009212190081x_real @ G
% 5.44/5.70 @ ( minus_811609699411566653omplex @ A2
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [X2: complex] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_one_real ) ) ) )
% 5.44/5.70 = ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8619_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > nat] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups4696554848551431203al_nat @ G
% 5.44/5.70 @ ( minus_minus_set_real @ A2
% 5.44/5.70 @ ( collect_real
% 5.44/5.70 @ ^ [X2: real] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_one_nat ) ) ) )
% 5.44/5.70 = ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8620_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > nat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups861055069439313189ex_nat @ G
% 5.44/5.70 @ ( minus_811609699411566653omplex @ A2
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [X2: complex] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_one_nat ) ) ) )
% 5.44/5.70 = ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8621_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_real,G: real > int] :
% 5.44/5.70 ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups4694064378042380927al_int @ G
% 5.44/5.70 @ ( minus_minus_set_real @ A2
% 5.44/5.70 @ ( collect_real
% 5.44/5.70 @ ^ [X2: real] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_one_int ) ) ) )
% 5.44/5.70 = ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8622_prod_Osetdiff__irrelevant,axiom,
% 5.44/5.70 ! [A2: set_complex,G: complex > int] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups858564598930262913ex_int @ G
% 5.44/5.70 @ ( minus_811609699411566653omplex @ A2
% 5.44/5.70 @ ( collect_complex
% 5.44/5.70 @ ^ [X2: complex] :
% 5.44/5.70 ( ( G @ X2 )
% 5.44/5.70 = one_one_int ) ) ) )
% 5.44/5.70 = ( groups858564598930262913ex_int @ G @ A2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.setdiff_irrelevant
% 5.44/5.70 thf(fact_8623_atMost__nat__numeral,axiom,
% 5.44/5.70 ! [K: num] :
% 5.44/5.70 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.44/5.70 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % atMost_nat_numeral
% 5.44/5.70 thf(fact_8624_prod_Onat__diff__reindex,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.nat_diff_reindex
% 5.44/5.70 thf(fact_8625_prod_Onat__diff__reindex,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.44/5.70 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.70 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.nat_diff_reindex
% 5.44/5.70 thf(fact_8626_prod_OatLeastAtMost__rev,axiom,
% 5.44/5.70 ! [G: nat > nat,N2: nat,M: nat] :
% 5.44/5.70 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.44/5.70 = ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atLeastAtMost_rev
% 5.44/5.70 thf(fact_8627_prod_OatLeastAtMost__rev,axiom,
% 5.44/5.70 ! [G: nat > int,N2: nat,M: nat] :
% 5.44/5.70 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.44/5.70 = ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.44/5.70 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.atLeastAtMost_rev
% 5.44/5.70 thf(fact_8628_Iic__subset__Iio__iff,axiom,
% 5.44/5.70 ! [A: extended_enat,B: extended_enat] :
% 5.44/5.70 ( ( ord_le7203529160286727270d_enat @ ( set_or8332593352340944941d_enat @ A ) @ ( set_or8419480210114673929d_enat @ B ) )
% 5.44/5.70 = ( ord_le72135733267957522d_enat @ A @ B ) ) ).
% 5.44/5.70
% 5.44/5.70 % Iic_subset_Iio_iff
% 5.44/5.70 thf(fact_8629_Iic__subset__Iio__iff,axiom,
% 5.44/5.70 ! [A: num,B: num] :
% 5.44/5.70 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.44/5.70 = ( ord_less_num @ A @ B ) ) ).
% 5.44/5.70
% 5.44/5.70 % Iic_subset_Iio_iff
% 5.44/5.70 thf(fact_8630_Iic__subset__Iio__iff,axiom,
% 5.44/5.70 ! [A: int,B: int] :
% 5.44/5.70 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.44/5.70 = ( ord_less_int @ A @ B ) ) ).
% 5.44/5.70
% 5.44/5.70 % Iic_subset_Iio_iff
% 5.44/5.70 thf(fact_8631_Iic__subset__Iio__iff,axiom,
% 5.44/5.70 ! [A: nat,B: nat] :
% 5.44/5.70 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.44/5.70 = ( ord_less_nat @ A @ B ) ) ).
% 5.44/5.70
% 5.44/5.70 % Iic_subset_Iio_iff
% 5.44/5.70 thf(fact_8632_Iic__subset__Iio__iff,axiom,
% 5.44/5.70 ! [A: real,B: real] :
% 5.44/5.70 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.44/5.70 = ( ord_less_real @ A @ B ) ) ).
% 5.44/5.70
% 5.44/5.70 % Iic_subset_Iio_iff
% 5.44/5.70 thf(fact_8633_prod_Ozero__middle,axiom,
% 5.44/5.70 ! [P5: nat,K: nat,G: nat > extended_enat,H2: nat > extended_enat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.70 => ( ( groups7961826882256487087d_enat
% 5.44/5.70 @ ^ [J3: nat] : ( if_Extended_enat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_Extended_enat @ ( J3 = K ) @ one_on7984719198319812577d_enat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.70 = ( groups7961826882256487087d_enat
% 5.44/5.70 @ ^ [J3: nat] : ( if_Extended_enat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.zero_middle
% 5.44/5.70 thf(fact_8634_prod_Ozero__middle,axiom,
% 5.44/5.70 ! [P5: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.44/5.70 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.70 => ( ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [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 ) ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.70 = ( groups6464643781859351333omplex
% 5.44/5.70 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.zero_middle
% 5.44/5.70 thf(fact_8635_prod_Ozero__middle,axiom,
% 5.44/5.70 ! [P5: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.44/5.70 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.70 => ( ( groups129246275422532515t_real
% 5.44/5.70 @ ^ [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 ) ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.70 = ( groups129246275422532515t_real
% 5.44/5.70 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.zero_middle
% 5.44/5.70 thf(fact_8636_prod_Ozero__middle,axiom,
% 5.44/5.70 ! [P5: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.44/5.70 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.70 => ( ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [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 ) ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.70 = ( groups708209901874060359at_nat
% 5.44/5.70 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.zero_middle
% 5.44/5.70 thf(fact_8637_prod_Ozero__middle,axiom,
% 5.44/5.70 ! [P5: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.44/5.70 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.70 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.70 => ( ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [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 ) ) ) ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.70 = ( groups705719431365010083at_int
% 5.44/5.70 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.70 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.zero_middle
% 5.44/5.70 thf(fact_8638_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_real,I2: real,F: real > real] :
% 5.44/5.70 ( ( finite_finite_real @ I6 )
% 5.44/5.70 => ( ( member_real @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: real] :
% 5.44/5.70 ( ( member_real @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8639_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_int,I2: int,F: int > real] :
% 5.44/5.70 ( ( finite_finite_int @ I6 )
% 5.44/5.70 => ( ( member_int @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: int] :
% 5.44/5.70 ( ( member_int @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8640_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_Pr1261947904930325089at_nat,I2: product_prod_nat_nat,F: product_prod_nat_nat > real] :
% 5.44/5.70 ( ( finite6177210948735845034at_nat @ I6 )
% 5.44/5.70 => ( ( member8440522571783428010at_nat @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.70 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups6036352826371341000t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8641_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_nat,I2: nat,F: nat > real] :
% 5.44/5.70 ( ( finite_finite_nat @ I6 )
% 5.44/5.70 => ( ( member_nat @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: nat] :
% 5.44/5.70 ( ( member_nat @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8642_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_complex,I2: complex,F: complex > real] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.70 => ( ( member_complex @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_real @ one_one_real @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: complex] :
% 5.44/5.70 ( ( member_complex @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8643_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_real,I2: real,F: real > int] :
% 5.44/5.70 ( ( finite_finite_real @ I6 )
% 5.44/5.70 => ( ( member_real @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: real] :
% 5.44/5.70 ( ( member_real @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8644_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_Pr1261947904930325089at_nat,I2: product_prod_nat_nat,F: product_prod_nat_nat > int] :
% 5.44/5.70 ( ( finite6177210948735845034at_nat @ I6 )
% 5.44/5.70 => ( ( member8440522571783428010at_nat @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.70 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups4075276357253098568at_int @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8645_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_complex,I2: complex,F: complex > int] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.70 => ( ( member_complex @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: complex] :
% 5.44/5.70 ( ( member_complex @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8646_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_nat,I2: nat,F: nat > int] :
% 5.44/5.70 ( ( finite_finite_nat @ I6 )
% 5.44/5.70 => ( ( member_nat @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: nat] :
% 5.44/5.70 ( ( member_nat @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8647_less__1__prod2,axiom,
% 5.44/5.70 ! [I6: set_int,I2: int,F: int > int] :
% 5.44/5.70 ( ( finite_finite_int @ I6 )
% 5.44/5.70 => ( ( member_int @ I2 @ I6 )
% 5.44/5.70 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.44/5.70 => ( ! [I4: int] :
% 5.44/5.70 ( ( member_int @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_eq_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F @ I6 ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod2
% 5.44/5.70 thf(fact_8648_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > real] :
% 5.44/5.70 ( ( finite6177210948735845034at_nat @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bo2099793752762293965at_nat )
% 5.44/5.70 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.70 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups6036352826371341000t_real @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8649_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_complex,F: complex > real] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bot_set_complex )
% 5.44/5.70 => ( ! [I4: complex] :
% 5.44/5.70 ( ( member_complex @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8650_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_nat,F: nat > real] :
% 5.44/5.70 ( ( finite_finite_nat @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bot_set_nat )
% 5.44/5.70 => ( ! [I4: nat] :
% 5.44/5.70 ( ( member_nat @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8651_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_int,F: int > real] :
% 5.44/5.70 ( ( finite_finite_int @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bot_set_int )
% 5.44/5.70 => ( ! [I4: int] :
% 5.44/5.70 ( ( member_int @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8652_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_real,F: real > real] :
% 5.44/5.70 ( ( finite_finite_real @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bot_set_real )
% 5.44/5.70 => ( ! [I4: real] :
% 5.44/5.70 ( ( member_real @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8653_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > int] :
% 5.44/5.70 ( ( finite6177210948735845034at_nat @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bo2099793752762293965at_nat )
% 5.44/5.70 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.70 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups4075276357253098568at_int @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8654_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_complex,F: complex > int] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bot_set_complex )
% 5.44/5.70 => ( ! [I4: complex] :
% 5.44/5.70 ( ( member_complex @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8655_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_real,F: real > int] :
% 5.44/5.70 ( ( finite_finite_real @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bot_set_real )
% 5.44/5.70 => ( ! [I4: real] :
% 5.44/5.70 ( ( member_real @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8656_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_nat,F: nat > int] :
% 5.44/5.70 ( ( finite_finite_nat @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bot_set_nat )
% 5.44/5.70 => ( ! [I4: nat] :
% 5.44/5.70 ( ( member_nat @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8657_less__1__prod,axiom,
% 5.44/5.70 ! [I6: set_int,F: int > int] :
% 5.44/5.70 ( ( finite_finite_int @ I6 )
% 5.44/5.70 => ( ( I6 != bot_bot_set_int )
% 5.44/5.70 => ( ! [I4: int] :
% 5.44/5.70 ( ( member_int @ I4 @ I6 )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( F @ I4 ) ) )
% 5.44/5.70 => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F @ I6 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % less_1_prod
% 5.44/5.70 thf(fact_8658_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,G: complex > complex] :
% 5.44/5.70 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.44/5.70 = ( times_times_complex @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups3708469109370488835omplex @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8659_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,G: complex > real] :
% 5.44/5.70 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.44/5.70 = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups766887009212190081x_real @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8660_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,G: complex > nat] :
% 5.44/5.70 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.44/5.70 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups861055069439313189ex_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8661_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_complex,A2: set_complex,G: complex > int] :
% 5.44/5.70 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 5.44/5.70 => ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.70 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.44/5.70 = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups858564598930262913ex_int @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8662_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,G: real > complex] :
% 5.44/5.70 ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.70 => ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups713298508707869441omplex @ G @ A2 )
% 5.44/5.70 = ( times_times_complex @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups713298508707869441omplex @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8663_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,G: real > real] :
% 5.44/5.70 ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.70 => ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.44/5.70 = ( times_times_real @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups1681761925125756287l_real @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8664_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,G: real > nat] :
% 5.44/5.70 ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.70 => ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups4696554848551431203al_nat @ G @ A2 )
% 5.44/5.70 = ( times_times_nat @ ( groups4696554848551431203al_nat @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups4696554848551431203al_nat @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8665_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_real,A2: set_real,G: real > int] :
% 5.44/5.70 ( ( ord_less_eq_set_real @ B2 @ A2 )
% 5.44/5.70 => ( ( finite_finite_real @ A2 )
% 5.44/5.70 => ( ( groups4694064378042380927al_int @ G @ A2 )
% 5.44/5.70 = ( times_times_int @ ( groups4694064378042380927al_int @ G @ ( minus_minus_set_real @ A2 @ B2 ) ) @ ( groups4694064378042380927al_int @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8666_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_nat,A2: set_nat,G: nat > complex] :
% 5.44/5.70 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.70 => ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.44/5.70 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups6464643781859351333omplex @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8667_prod_Osubset__diff,axiom,
% 5.44/5.70 ! [B2: set_nat,A2: set_nat,G: nat > real] :
% 5.44/5.70 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 5.44/5.70 => ( ( finite_finite_nat @ A2 )
% 5.44/5.70 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.44/5.70 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups129246275422532515t_real @ G @ B2 ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.subset_diff
% 5.44/5.70 thf(fact_8668_prod_Osame__carrier,axiom,
% 5.44/5.70 ! [C4: set_int,A2: set_int,B2: set_int,G: int > extended_enat,H2: int > extended_enat] :
% 5.44/5.70 ( ( finite_finite_int @ C4 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ( ( groups5078248829458667347d_enat @ G @ A2 )
% 5.44/5.70 = ( groups5078248829458667347d_enat @ H2 @ B2 ) )
% 5.44/5.70 = ( ( groups5078248829458667347d_enat @ G @ C4 )
% 5.44/5.70 = ( groups5078248829458667347d_enat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.same_carrier
% 5.44/5.70 thf(fact_8669_prod_Osame__carrier,axiom,
% 5.44/5.70 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > extended_enat,H2: complex > extended_enat] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_on7984719198319812577d_enat ) )
% 5.44/5.70 => ( ( ( groups8780218893797010257d_enat @ G @ A2 )
% 5.44/5.70 = ( groups8780218893797010257d_enat @ H2 @ B2 ) )
% 5.44/5.70 = ( ( groups8780218893797010257d_enat @ G @ C4 )
% 5.44/5.70 = ( groups8780218893797010257d_enat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.same_carrier
% 5.44/5.70 thf(fact_8670_prod_Osame__carrier,axiom,
% 5.44/5.70 ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 5.44/5.70 ( ( finite_finite_int @ C4 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_complex ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_one_complex ) )
% 5.44/5.70 => ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.44/5.70 = ( groups7440179247065528705omplex @ H2 @ B2 ) )
% 5.44/5.70 = ( ( groups7440179247065528705omplex @ G @ C4 )
% 5.44/5.70 = ( groups7440179247065528705omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.same_carrier
% 5.44/5.70 thf(fact_8671_prod_Osame__carrier,axiom,
% 5.44/5.70 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_complex ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_one_complex ) )
% 5.44/5.70 => ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.44/5.70 = ( groups3708469109370488835omplex @ H2 @ B2 ) )
% 5.44/5.70 = ( ( groups3708469109370488835omplex @ G @ C4 )
% 5.44/5.70 = ( groups3708469109370488835omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.same_carrier
% 5.44/5.70 thf(fact_8672_prod_Osame__carrier,axiom,
% 5.44/5.70 ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 5.44/5.70 ( ( finite_finite_int @ C4 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_real ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_one_real ) )
% 5.44/5.70 => ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.44/5.70 = ( groups2316167850115554303t_real @ H2 @ B2 ) )
% 5.44/5.70 = ( ( groups2316167850115554303t_real @ G @ C4 )
% 5.44/5.70 = ( groups2316167850115554303t_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.same_carrier
% 5.44/5.70 thf(fact_8673_prod_Osame__carrier,axiom,
% 5.44/5.70 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 5.44/5.70 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.70 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.70 => ( ! [A3: complex] :
% 5.44/5.70 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_real ) )
% 5.44/5.70 => ( ! [B3: complex] :
% 5.44/5.70 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_one_real ) )
% 5.44/5.70 => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.44/5.70 = ( groups766887009212190081x_real @ H2 @ B2 ) )
% 5.44/5.70 = ( ( groups766887009212190081x_real @ G @ C4 )
% 5.44/5.70 = ( groups766887009212190081x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.70
% 5.44/5.70 % prod.same_carrier
% 5.44/5.70 thf(fact_8674_prod_Osame__carrier,axiom,
% 5.44/5.70 ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 5.44/5.70 ( ( finite_finite_int @ C4 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.70 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.70 => ( ! [A3: int] :
% 5.44/5.70 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.70 => ( ( G @ A3 )
% 5.44/5.70 = one_one_nat ) )
% 5.44/5.70 => ( ! [B3: int] :
% 5.44/5.70 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.70 => ( ( H2 @ B3 )
% 5.44/5.70 = one_one_nat ) )
% 5.44/5.70 => ( ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 5.44/5.70 = ( groups1707563613775114915nt_nat @ H2 @ B2 ) )
% 5.44/5.70 = ( ( groups1707563613775114915nt_nat @ G @ C4 )
% 5.44/5.70 = ( groups1707563613775114915nt_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrier
% 5.44/5.71 thf(fact_8675_prod_Osame__carrier,axiom,
% 5.44/5.71 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ H2 @ B2 ) )
% 5.44/5.71 = ( ( groups861055069439313189ex_nat @ G @ C4 )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrier
% 5.44/5.71 thf(fact_8676_prod_Osame__carrier,axiom,
% 5.44/5.71 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.44/5.71 = ( groups858564598930262913ex_int @ H2 @ B2 ) )
% 5.44/5.71 = ( ( groups858564598930262913ex_int @ G @ C4 )
% 5.44/5.71 = ( groups858564598930262913ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrier
% 5.44/5.71 thf(fact_8677_prod_Osame__carrier,axiom,
% 5.44/5.71 ! [C4: set_real,A2: set_real,B2: set_real,G: real > extended_enat,H2: real > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: real] :
% 5.44/5.71 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: real] :
% 5.44/5.71 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( ( groups7973222482632965587d_enat @ G @ A2 )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ H2 @ B2 ) )
% 5.44/5.71 = ( ( groups7973222482632965587d_enat @ G @ C4 )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrier
% 5.44/5.71 thf(fact_8678_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_int,A2: set_int,B2: set_int,G: int > extended_enat,H2: int > extended_enat] :
% 5.44/5.71 ( ( finite_finite_int @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: int] :
% 5.44/5.71 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( ( groups5078248829458667347d_enat @ G @ C4 )
% 5.44/5.71 = ( groups5078248829458667347d_enat @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups5078248829458667347d_enat @ G @ A2 )
% 5.44/5.71 = ( groups5078248829458667347d_enat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8679_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > extended_enat,H2: complex > extended_enat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( ( groups8780218893797010257d_enat @ G @ C4 )
% 5.44/5.71 = ( groups8780218893797010257d_enat @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups8780218893797010257d_enat @ G @ A2 )
% 5.44/5.71 = ( groups8780218893797010257d_enat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8680_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_int,A2: set_int,B2: set_int,G: int > complex,H2: int > complex] :
% 5.44/5.71 ( ( finite_finite_int @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ! [B3: int] :
% 5.44/5.71 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ( ( groups7440179247065528705omplex @ G @ C4 )
% 5.44/5.71 = ( groups7440179247065528705omplex @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.44/5.71 = ( groups7440179247065528705omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8681_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > complex,H2: complex > complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ( ( groups3708469109370488835omplex @ G @ C4 )
% 5.44/5.71 = ( groups3708469109370488835omplex @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.44/5.71 = ( groups3708469109370488835omplex @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8682_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_int,A2: set_int,B2: set_int,G: int > real,H2: int > real] :
% 5.44/5.71 ( ( finite_finite_int @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ! [B3: int] :
% 5.44/5.71 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ( ( groups2316167850115554303t_real @ G @ C4 )
% 5.44/5.71 = ( groups2316167850115554303t_real @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.44/5.71 = ( groups2316167850115554303t_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8683_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > real,H2: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ( ( groups766887009212190081x_real @ G @ C4 )
% 5.44/5.71 = ( groups766887009212190081x_real @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.44/5.71 = ( groups766887009212190081x_real @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8684_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_int,A2: set_int,B2: set_int,G: int > nat,H2: int > nat] :
% 5.44/5.71 ( ( finite_finite_int @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ! [B3: int] :
% 5.44/5.71 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ( ( groups1707563613775114915nt_nat @ G @ C4 )
% 5.44/5.71 = ( groups1707563613775114915nt_nat @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 5.44/5.71 = ( groups1707563613775114915nt_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8685_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > nat,H2: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ( ( groups861055069439313189ex_nat @ G @ C4 )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8686_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_complex,A2: set_complex,B2: set_complex,G: complex > int,H2: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ( ( groups858564598930262913ex_int @ G @ C4 )
% 5.44/5.71 = ( groups858564598930262913ex_int @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 5.44/5.71 = ( groups858564598930262913ex_int @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8687_prod_Osame__carrierI,axiom,
% 5.44/5.71 ! [C4: set_real,A2: set_real,B2: set_real,G: real > extended_enat,H2: real > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ B2 @ C4 )
% 5.44/5.71 => ( ! [A3: real] :
% 5.44/5.71 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.44/5.71 => ( ( G @ A3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: real] :
% 5.44/5.71 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B2 ) )
% 5.44/5.71 => ( ( H2 @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( ( groups7973222482632965587d_enat @ G @ C4 )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ H2 @ C4 ) )
% 5.44/5.71 => ( ( groups7973222482632965587d_enat @ G @ A2 )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ H2 @ B2 ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.same_carrierI
% 5.44/5.71 thf(fact_8688_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > extended_enat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups8780218893797010257d_enat @ G @ S )
% 5.44/5.71 = ( groups8780218893797010257d_enat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8689_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ G @ S )
% 5.44/5.71 = ( groups3708469109370488835omplex @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8690_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ G @ S )
% 5.44/5.71 = ( groups766887009212190081x_real @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8691_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ G @ S )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8692_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ( groups858564598930262913ex_int @ G @ S )
% 5.44/5.71 = ( groups858564598930262913ex_int @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8693_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups7973222482632965587d_enat @ G @ S )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8694_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > complex] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ( groups713298508707869441omplex @ G @ S )
% 5.44/5.71 = ( groups713298508707869441omplex @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8695_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > real] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ( groups1681761925125756287l_real @ G @ S )
% 5.44/5.71 = ( groups1681761925125756287l_real @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8696_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > nat] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ( groups4696554848551431203al_nat @ G @ S )
% 5.44/5.71 = ( groups4696554848551431203al_nat @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8697_prod_Omono__neutral__left,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > int] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ( groups4694064378042380927al_int @ G @ S )
% 5.44/5.71 = ( groups4694064378042380927al_int @ G @ T3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_left
% 5.44/5.71 thf(fact_8698_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > extended_enat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups8780218893797010257d_enat @ G @ T3 )
% 5.44/5.71 = ( groups8780218893797010257d_enat @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8699_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ G @ T3 )
% 5.44/5.71 = ( groups3708469109370488835omplex @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8700_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ G @ T3 )
% 5.44/5.71 = ( groups766887009212190081x_real @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8701_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ G @ T3 )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8702_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ( groups858564598930262913ex_int @ G @ T3 )
% 5.44/5.71 = ( groups858564598930262913ex_int @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8703_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups7973222482632965587d_enat @ G @ T3 )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8704_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > complex] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ( groups713298508707869441omplex @ G @ T3 )
% 5.44/5.71 = ( groups713298508707869441omplex @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8705_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > real] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ( groups1681761925125756287l_real @ G @ T3 )
% 5.44/5.71 = ( groups1681761925125756287l_real @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8706_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > nat] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ( groups4696554848551431203al_nat @ G @ T3 )
% 5.44/5.71 = ( groups4696554848551431203al_nat @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8707_prod_Omono__neutral__right,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > int] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ( groups4694064378042380927al_int @ G @ T3 )
% 5.44/5.71 = ( groups4694064378042380927al_int @ G @ S ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_right
% 5.44/5.71 thf(fact_8708_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_int,S: set_int,H2: int > extended_enat,G: int > extended_enat] :
% 5.44/5.71 ( ( finite_finite_int @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups5078248829458667347d_enat @ G @ S )
% 5.44/5.71 = ( groups5078248829458667347d_enat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8709_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,H2: complex > extended_enat,G: complex > extended_enat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups8780218893797010257d_enat @ G @ S )
% 5.44/5.71 = ( groups8780218893797010257d_enat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8710_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_int,S: set_int,H2: int > complex,G: int > complex] :
% 5.44/5.71 ( ( finite_finite_int @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups7440179247065528705omplex @ G @ S )
% 5.44/5.71 = ( groups7440179247065528705omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8711_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,H2: complex > complex,G: complex > complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ G @ S )
% 5.44/5.71 = ( groups3708469109370488835omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8712_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_int,S: set_int,H2: int > real,G: int > real] :
% 5.44/5.71 ( ( finite_finite_int @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups2316167850115554303t_real @ G @ S )
% 5.44/5.71 = ( groups2316167850115554303t_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8713_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,H2: complex > real,G: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ G @ S )
% 5.44/5.71 = ( groups766887009212190081x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8714_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_int,S: set_int,H2: int > nat,G: int > nat] :
% 5.44/5.71 ( ( finite_finite_int @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat @ G @ S )
% 5.44/5.71 = ( groups1707563613775114915nt_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8715_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,H2: complex > nat,G: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ G @ S )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8716_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,H2: complex > int,G: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups858564598930262913ex_int @ G @ S )
% 5.44/5.71 = ( groups858564598930262913ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8717_prod_Omono__neutral__cong__left,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,H2: real > extended_enat,G: real > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( H2 @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups7973222482632965587d_enat @ G @ S )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_left
% 5.44/5.71 thf(fact_8718_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_int,S: set_int,G: int > extended_enat,H2: int > extended_enat] :
% 5.44/5.71 ( ( finite_finite_int @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups5078248829458667347d_enat @ G @ T3 )
% 5.44/5.71 = ( groups5078248829458667347d_enat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8719_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > extended_enat,H2: complex > extended_enat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups8780218893797010257d_enat @ G @ T3 )
% 5.44/5.71 = ( groups8780218893797010257d_enat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8720_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_int,S: set_int,G: int > complex,H2: int > complex] :
% 5.44/5.71 ( ( finite_finite_int @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups7440179247065528705omplex @ G @ T3 )
% 5.44/5.71 = ( groups7440179247065528705omplex @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8721_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > complex,H2: complex > complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_complex ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ G @ T3 )
% 5.44/5.71 = ( groups3708469109370488835omplex @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8722_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_int,S: set_int,G: int > real,H2: int > real] :
% 5.44/5.71 ( ( finite_finite_int @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups2316167850115554303t_real @ G @ T3 )
% 5.44/5.71 = ( groups2316167850115554303t_real @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8723_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > real,H2: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_real ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ G @ T3 )
% 5.44/5.71 = ( groups766887009212190081x_real @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8724_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_int,S: set_int,G: int > nat,H2: int > nat] :
% 5.44/5.71 ( ( finite_finite_int @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ S @ T3 )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ ( minus_minus_set_int @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ! [X5: int] :
% 5.44/5.71 ( ( member_int @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat @ G @ T3 )
% 5.44/5.71 = ( groups1707563613775114915nt_nat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8725_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > nat,H2: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_nat ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ G @ T3 )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8726_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_complex,S: set_complex,G: complex > int,H2: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ T3 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ S @ T3 )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_one_int ) )
% 5.44/5.71 => ( ! [X5: complex] :
% 5.44/5.71 ( ( member_complex @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups858564598930262913ex_int @ G @ T3 )
% 5.44/5.71 = ( groups858564598930262913ex_int @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8727_prod_Omono__neutral__cong__right,axiom,
% 5.44/5.71 ! [T3: set_real,S: set_real,G: real > extended_enat,H2: real > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ T3 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ S @ T3 )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ ( minus_minus_set_real @ T3 @ S ) )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [X5: real] :
% 5.44/5.71 ( ( member_real @ X5 @ S )
% 5.44/5.71 => ( ( G @ X5 )
% 5.44/5.71 = ( H2 @ X5 ) ) )
% 5.44/5.71 => ( ( groups7973222482632965587d_enat @ G @ T3 )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ H2 @ S ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.mono_neutral_cong_right
% 5.44/5.71 thf(fact_8728_prod_OatLeast0__atMost__Suc,axiom,
% 5.44/5.71 ! [G: nat > complex,N2: nat] :
% 5.44/5.71 ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast0_atMost_Suc
% 5.44/5.71 thf(fact_8729_prod_OatLeast0__atMost__Suc,axiom,
% 5.44/5.71 ! [G: nat > real,N2: nat] :
% 5.44/5.71 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast0_atMost_Suc
% 5.44/5.71 thf(fact_8730_prod_OatLeast0__atMost__Suc,axiom,
% 5.44/5.71 ! [G: nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast0_atMost_Suc
% 5.44/5.71 thf(fact_8731_prod_OatLeast0__atMost__Suc,axiom,
% 5.44/5.71 ! [G: nat > int,N2: nat] :
% 5.44/5.71 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast0_atMost_Suc
% 5.44/5.71 thf(fact_8732_prod_OatLeast__Suc__atMost,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > complex] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.71 = ( times_times_complex @ ( G @ M ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast_Suc_atMost
% 5.44/5.71 thf(fact_8733_prod_OatLeast__Suc__atMost,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > real] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.71 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast_Suc_atMost
% 5.44/5.71 thf(fact_8734_prod_OatLeast__Suc__atMost,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.71 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast_Suc_atMost
% 5.44/5.71 thf(fact_8735_prod_OatLeast__Suc__atMost,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > int] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.71 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast_Suc_atMost
% 5.44/5.71 thf(fact_8736_prod_Onat__ivl__Suc_H,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > complex] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.71 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_complex @ ( G @ ( suc @ N2 ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.nat_ivl_Suc'
% 5.44/5.71 thf(fact_8737_prod_Onat__ivl__Suc_H,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > real] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.71 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_real @ ( G @ ( suc @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.nat_ivl_Suc'
% 5.44/5.71 thf(fact_8738_prod_Onat__ivl__Suc_H,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.71 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.nat_ivl_Suc'
% 5.44/5.71 thf(fact_8739_prod_Onat__ivl__Suc_H,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > int] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.44/5.71 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.nat_ivl_Suc'
% 5.44/5.71 thf(fact_8740_prod_OlessThan__Suc__shift,axiom,
% 5.44/5.71 ! [G: nat > complex,N2: nat] :
% 5.44/5.71 ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_complex @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.lessThan_Suc_shift
% 5.44/5.71 thf(fact_8741_prod_OlessThan__Suc__shift,axiom,
% 5.44/5.71 ! [G: nat > real,N2: nat] :
% 5.44/5.71 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.lessThan_Suc_shift
% 5.44/5.71 thf(fact_8742_prod_OlessThan__Suc__shift,axiom,
% 5.44/5.71 ! [G: nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.lessThan_Suc_shift
% 5.44/5.71 thf(fact_8743_prod_OlessThan__Suc__shift,axiom,
% 5.44/5.71 ! [G: nat > int,N2: nat] :
% 5.44/5.71 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.lessThan_Suc_shift
% 5.44/5.71 thf(fact_8744_prod_OSuc__reindex__ivl,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > complex] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_complex @ ( G @ M )
% 5.44/5.71 @ ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.Suc_reindex_ivl
% 5.44/5.71 thf(fact_8745_prod_OSuc__reindex__ivl,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > real] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_real @ ( G @ M )
% 5.44/5.71 @ ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.Suc_reindex_ivl
% 5.44/5.71 thf(fact_8746_prod_OSuc__reindex__ivl,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_nat @ ( G @ M )
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.Suc_reindex_ivl
% 5.44/5.71 thf(fact_8747_prod_OSuc__reindex__ivl,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > int] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( times_times_int @ ( G @ M )
% 5.44/5.71 @ ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.Suc_reindex_ivl
% 5.44/5.71 thf(fact_8748_sum_OatMost__Suc__shift,axiom,
% 5.44/5.71 ! [G: nat > complex,N2: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.atMost_Suc_shift
% 5.44/5.71 thf(fact_8749_sum_OatMost__Suc__shift,axiom,
% 5.44/5.71 ! [G: nat > int,N2: nat] :
% 5.44/5.71 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.atMost_Suc_shift
% 5.44/5.71 thf(fact_8750_sum_OatMost__Suc__shift,axiom,
% 5.44/5.71 ! [G: nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.atMost_Suc_shift
% 5.44/5.71 thf(fact_8751_sum_OatMost__Suc__shift,axiom,
% 5.44/5.71 ! [G: nat > real,N2: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.44/5.71 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.atMost_Suc_shift
% 5.44/5.71 thf(fact_8752_sum__telescope,axiom,
% 5.44/5.71 ! [F: nat > complex,I2: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( minus_minus_complex @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ I2 ) )
% 5.44/5.71 = ( minus_minus_complex @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_telescope
% 5.44/5.71 thf(fact_8753_sum__telescope,axiom,
% 5.44/5.71 ! [F: nat > int,I2: nat] :
% 5.44/5.71 ( ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ I2 ) )
% 5.44/5.71 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_telescope
% 5.44/5.71 thf(fact_8754_sum__telescope,axiom,
% 5.44/5.71 ! [F: nat > real,I2: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ I2 ) )
% 5.44/5.71 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_telescope
% 5.44/5.71 thf(fact_8755_polyfun__eq__coeffs,axiom,
% 5.44/5.71 ! [C: nat > complex,N2: nat,D: nat > complex] :
% 5.44/5.71 ( ( ! [X2: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( D @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 5.44/5.71 = ( ! [I5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.44/5.71 => ( ( C @ I5 )
% 5.44/5.71 = ( D @ I5 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_eq_coeffs
% 5.44/5.71 thf(fact_8756_polyfun__eq__coeffs,axiom,
% 5.44/5.71 ! [C: nat > real,N2: nat,D: nat > real] :
% 5.44/5.71 ( ( ! [X2: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( D @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 5.44/5.71 = ( ! [I5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.44/5.71 => ( ( C @ I5 )
% 5.44/5.71 = ( D @ I5 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_eq_coeffs
% 5.44/5.71 thf(fact_8757_prod_OatLeast1__atMost__eq,axiom,
% 5.44/5.71 ! [G: nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.44/5.71 = ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast1_atMost_eq
% 5.44/5.71 thf(fact_8758_prod_OatLeast1__atMost__eq,axiom,
% 5.44/5.71 ! [G: nat > int,N2: nat] :
% 5.44/5.71 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.44/5.71 = ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.atLeast1_atMost_eq
% 5.44/5.71 thf(fact_8759_bounded__imp__summable,axiom,
% 5.44/5.71 ! [A: nat > int,B2: int] :
% 5.44/5.71 ( ! [N4: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N4 ) )
% 5.44/5.71 => ( ! [N4: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N4 ) ) @ B2 )
% 5.44/5.71 => ( summable_int @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % bounded_imp_summable
% 5.44/5.71 thf(fact_8760_bounded__imp__summable,axiom,
% 5.44/5.71 ! [A: nat > nat,B2: nat] :
% 5.44/5.71 ( ! [N4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N4 ) )
% 5.44/5.71 => ( ! [N4: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N4 ) ) @ B2 )
% 5.44/5.71 => ( summable_nat @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % bounded_imp_summable
% 5.44/5.71 thf(fact_8761_bounded__imp__summable,axiom,
% 5.44/5.71 ! [A: nat > real,B2: real] :
% 5.44/5.71 ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.44/5.71 => ( ! [N4: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N4 ) ) @ B2 )
% 5.44/5.71 => ( summable_real @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % bounded_imp_summable
% 5.44/5.71 thf(fact_8762_fact__prod,axiom,
% 5.44/5.71 ( semiri1406184849735516958ct_int
% 5.44/5.71 = ( ^ [N: nat] :
% 5.44/5.71 ( semiri1314217659103216013at_int
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [X2: nat] : X2
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_prod
% 5.44/5.71 thf(fact_8763_fact__prod,axiom,
% 5.44/5.71 ( semiri5044797733671781792omplex
% 5.44/5.71 = ( ^ [N: nat] :
% 5.44/5.71 ( semiri8010041392384452111omplex
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [X2: nat] : X2
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_prod
% 5.44/5.71 thf(fact_8764_fact__prod,axiom,
% 5.44/5.71 ( semiri3624122377584611663nteger
% 5.44/5.71 = ( ^ [N: nat] :
% 5.44/5.71 ( semiri4939895301339042750nteger
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [X2: nat] : X2
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_prod
% 5.44/5.71 thf(fact_8765_fact__prod,axiom,
% 5.44/5.71 ( semiri2265585572941072030t_real
% 5.44/5.71 = ( ^ [N: nat] :
% 5.44/5.71 ( semiri5074537144036343181t_real
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [X2: nat] : X2
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_prod
% 5.44/5.71 thf(fact_8766_fact__prod,axiom,
% 5.44/5.71 ( semiri1408675320244567234ct_nat
% 5.44/5.71 = ( ^ [N: nat] :
% 5.44/5.71 ( semiri1316708129612266289at_nat
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [X2: nat] : X2
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_prod
% 5.44/5.71 thf(fact_8767_sum_Onested__swap_H,axiom,
% 5.44/5.71 ! [A: nat > nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( groups3542108847815614940at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [J3: nat] :
% 5.44/5.71 ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.nested_swap'
% 5.44/5.71 thf(fact_8768_sum_Onested__swap_H,axiom,
% 5.44/5.71 ! [A: nat > nat > real,N2: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( groups6591440286371151544t_real @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [J3: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.nested_swap'
% 5.44/5.71 thf(fact_8769_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ! [I4: complex] :
% 5.44/5.71 ( ( member_complex @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_complex )
% 5.44/5.71 => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8770_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ! [I4: nat] :
% 5.44/5.71 ( ( member_nat @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_nat )
% 5.44/5.71 => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8771_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_int,F: int > real,G: int > real] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ! [I4: int] :
% 5.44/5.71 ( ( member_int @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_int )
% 5.44/5.71 => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8772_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_real,F: real > real,G: real > real] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ! [I4: real] :
% 5.44/5.71 ( ( member_real @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_real @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_real )
% 5.44/5.71 => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8773_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ! [I4: complex] :
% 5.44/5.71 ( ( member_complex @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_complex )
% 5.44/5.71 => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8774_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ! [I4: int] :
% 5.44/5.71 ( ( member_int @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_int )
% 5.44/5.71 => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8775_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ! [I4: real] :
% 5.44/5.71 ( ( member_real @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_real )
% 5.44/5.71 => ( ord_less_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8776_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ! [I4: complex] :
% 5.44/5.71 ( ( member_complex @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_complex )
% 5.44/5.71 => ( ord_less_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8777_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_real,F: real > int,G: real > int] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ! [I4: real] :
% 5.44/5.71 ( ( member_real @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_real )
% 5.44/5.71 => ( ord_less_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8778_prod__mono__strict,axiom,
% 5.44/5.71 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ! [I4: nat] :
% 5.44/5.71 ( ( member_nat @ I4 @ A2 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) )
% 5.44/5.71 & ( ord_less_nat @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.44/5.71 => ( ( A2 != bot_bot_set_nat )
% 5.44/5.71 => ( ord_less_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ A2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono_strict
% 5.44/5.71 thf(fact_8779_even__prod__iff,axiom,
% 5.44/5.71 ! [A2: set_nat,F: nat > code_integer] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups3455450783089532116nteger @ F @ A2 ) )
% 5.44/5.71 = ( ? [X2: nat] :
% 5.44/5.71 ( ( member_nat @ X2 @ A2 )
% 5.44/5.71 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % even_prod_iff
% 5.44/5.71 thf(fact_8780_even__prod__iff,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > code_integer] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups8682486955453173170nteger @ F @ A2 ) )
% 5.44/5.71 = ( ? [X2: complex] :
% 5.44/5.71 ( ( member_complex @ X2 @ A2 )
% 5.44/5.71 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % even_prod_iff
% 5.44/5.71 thf(fact_8781_even__prod__iff,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 5.44/5.71 = ( ? [X2: complex] :
% 5.44/5.71 ( ( member_complex @ X2 @ A2 )
% 5.44/5.71 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % even_prod_iff
% 5.44/5.71 thf(fact_8782_even__prod__iff,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 5.44/5.71 = ( ? [X2: complex] :
% 5.44/5.71 ( ( member_complex @ X2 @ A2 )
% 5.44/5.71 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % even_prod_iff
% 5.44/5.71 thf(fact_8783_even__prod__iff,axiom,
% 5.44/5.71 ! [A2: set_nat,F: nat > nat] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.44/5.71 = ( ? [X2: nat] :
% 5.44/5.71 ( ( member_nat @ X2 @ A2 )
% 5.44/5.71 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % even_prod_iff
% 5.44/5.71 thf(fact_8784_even__prod__iff,axiom,
% 5.44/5.71 ! [A2: set_nat,F: nat > int] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.44/5.71 = ( ? [X2: nat] :
% 5.44/5.71 ( ( member_nat @ X2 @ A2 )
% 5.44/5.71 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % even_prod_iff
% 5.44/5.71 thf(fact_8785_even__prod__iff,axiom,
% 5.44/5.71 ! [A2: set_int,F: int > int] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.44/5.71 = ( ? [X2: int] :
% 5.44/5.71 ( ( member_int @ X2 @ A2 )
% 5.44/5.71 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % even_prod_iff
% 5.44/5.71 thf(fact_8786_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_complex,X: complex,G: complex > complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( member_complex @ X @ A2 )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.44/5.71 = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8787_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_int,X: int,G: int > complex] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( member_int @ X @ A2 )
% 5.44/5.71 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.44/5.71 = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8788_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_real,X: real,G: real > complex] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ( member_real @ X @ A2 )
% 5.44/5.71 => ( ( groups713298508707869441omplex @ G @ A2 )
% 5.44/5.71 = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8789_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_nat,X: nat,G: nat > complex] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( member_nat @ X @ A2 )
% 5.44/5.71 => ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.44/5.71 = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8790_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( member_complex @ X @ A2 )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.44/5.71 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8791_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_int,X: int,G: int > real] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( member_int @ X @ A2 )
% 5.44/5.71 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.44/5.71 = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8792_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_real,X: real,G: real > real] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ( member_real @ X @ A2 )
% 5.44/5.71 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.44/5.71 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8793_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_nat,X: nat,G: nat > real] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( member_nat @ X @ A2 )
% 5.44/5.71 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.44/5.71 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8794_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_complex,X: complex,G: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( member_complex @ X @ A2 )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.44/5.71 = ( times_times_nat @ ( G @ X ) @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8795_prod_Oremove,axiom,
% 5.44/5.71 ! [A2: set_int,X: int,G: int > nat] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( member_int @ X @ A2 )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 5.44/5.71 = ( times_times_nat @ ( G @ X ) @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.remove
% 5.44/5.71 thf(fact_8796_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_complex,G: complex > complex,X: complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.71 = ( times_times_complex @ ( G @ X ) @ ( groups3708469109370488835omplex @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8797_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_int,G: int > complex,X: int] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( groups7440179247065528705omplex @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.71 = ( times_times_complex @ ( G @ X ) @ ( groups7440179247065528705omplex @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8798_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_real,G: real > complex,X: real] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ( groups713298508707869441omplex @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.71 = ( times_times_complex @ ( G @ X ) @ ( groups713298508707869441omplex @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8799_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_nat,G: nat > complex,X: nat] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( groups6464643781859351333omplex @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.71 = ( times_times_complex @ ( G @ X ) @ ( groups6464643781859351333omplex @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8800_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_complex,G: complex > real,X: complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.71 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8801_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_int,G: int > real,X: int] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.71 = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8802_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_real,G: real > real,X: real] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.44/5.71 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8803_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_nat,G: nat > real,X: nat] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 5.44/5.71 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8804_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_complex,G: complex > nat,X: complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.44/5.71 = ( times_times_nat @ ( G @ X ) @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8805_prod_Oinsert__remove,axiom,
% 5.44/5.71 ! [A2: set_int,G: int > nat,X: int] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.44/5.71 = ( times_times_nat @ ( G @ X ) @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.insert_remove
% 5.44/5.71 thf(fact_8806_prod_Oub__add__nat,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > complex,P5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.44/5.71 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 5.44/5.71 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.ub_add_nat
% 5.44/5.71 thf(fact_8807_prod_Oub__add__nat,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > real,P5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.44/5.71 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 5.44/5.71 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.ub_add_nat
% 5.44/5.71 thf(fact_8808_prod_Oub__add__nat,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > nat,P5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.44/5.71 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 5.44/5.71 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.ub_add_nat
% 5.44/5.71 thf(fact_8809_prod_Oub__add__nat,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,G: nat > int,P5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.44/5.71 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P5 ) ) )
% 5.44/5.71 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P5 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.ub_add_nat
% 5.44/5.71 thf(fact_8810_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.44/5.71 ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y: nat] :
% 5.44/5.71 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 5.44/5.71 = Y )
% 5.44/5.71 => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 5.44/5.71 => ( Y = Xc ) )
% 5.44/5.71 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 5.44/5.71 => ( Y
% 5.44/5.71 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fold_atLeastAtMost_nat.elims
% 5.44/5.71 thf(fact_8811_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.44/5.71 ( set_fo2584398358068434914at_nat
% 5.44/5.71 = ( ^ [F5: nat > nat > nat,A4: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A4 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F5 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B4 @ ( F5 @ A4 @ Acc2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fold_atLeastAtMost_nat.simps
% 5.44/5.71 thf(fact_8812_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_complex,A: complex,B: complex > complex,C: complex > complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.71 => ( ( ( member_complex @ A @ S )
% 5.44/5.71 => ( ( groups3708469109370488835omplex
% 5.44/5.71 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_complex @ ( B @ A ) @ ( groups3708469109370488835omplex @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_complex @ A @ S )
% 5.44/5.71 => ( ( groups3708469109370488835omplex
% 5.44/5.71 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups3708469109370488835omplex @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8813_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_int,A: int,B: int > complex,C: int > complex] :
% 5.44/5.71 ( ( finite_finite_int @ S )
% 5.44/5.71 => ( ( ( member_int @ A @ S )
% 5.44/5.71 => ( ( groups7440179247065528705omplex
% 5.44/5.71 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_complex @ ( B @ A ) @ ( groups7440179247065528705omplex @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_int @ A @ S )
% 5.44/5.71 => ( ( groups7440179247065528705omplex
% 5.44/5.71 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups7440179247065528705omplex @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8814_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_real,A: real,B: real > complex,C: real > complex] :
% 5.44/5.71 ( ( finite_finite_real @ S )
% 5.44/5.71 => ( ( ( member_real @ A @ S )
% 5.44/5.71 => ( ( groups713298508707869441omplex
% 5.44/5.71 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_complex @ ( B @ A ) @ ( groups713298508707869441omplex @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_real @ A @ S )
% 5.44/5.71 => ( ( groups713298508707869441omplex
% 5.44/5.71 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups713298508707869441omplex @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8815_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_nat,A: nat,B: nat > complex,C: nat > complex] :
% 5.44/5.71 ( ( finite_finite_nat @ S )
% 5.44/5.71 => ( ( ( member_nat @ A @ S )
% 5.44/5.71 => ( ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_complex @ ( B @ A ) @ ( groups6464643781859351333omplex @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_nat @ A @ S )
% 5.44/5.71 => ( ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups6464643781859351333omplex @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8816_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_complex,A: complex,B: complex > real,C: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.71 => ( ( ( member_complex @ A @ S )
% 5.44/5.71 => ( ( groups766887009212190081x_real
% 5.44/5.71 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_complex @ A @ S )
% 5.44/5.71 => ( ( groups766887009212190081x_real
% 5.44/5.71 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8817_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_int,A: int,B: int > real,C: int > real] :
% 5.44/5.71 ( ( finite_finite_int @ S )
% 5.44/5.71 => ( ( ( member_int @ A @ S )
% 5.44/5.71 => ( ( groups2316167850115554303t_real
% 5.44/5.71 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_int @ A @ S )
% 5.44/5.71 => ( ( groups2316167850115554303t_real
% 5.44/5.71 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8818_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_real,A: real,B: real > real,C: real > real] :
% 5.44/5.71 ( ( finite_finite_real @ S )
% 5.44/5.71 => ( ( ( member_real @ A @ S )
% 5.44/5.71 => ( ( groups1681761925125756287l_real
% 5.44/5.71 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_real @ A @ S )
% 5.44/5.71 => ( ( groups1681761925125756287l_real
% 5.44/5.71 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8819_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_nat,A: nat,B: nat > real,C: nat > real] :
% 5.44/5.71 ( ( finite_finite_nat @ S )
% 5.44/5.71 => ( ( ( member_nat @ A @ S )
% 5.44/5.71 => ( ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_nat @ A @ S )
% 5.44/5.71 => ( ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8820_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ S )
% 5.44/5.71 => ( ( ( member_complex @ A @ S )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat
% 5.44/5.71 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_nat @ ( B @ A ) @ ( groups861055069439313189ex_nat @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_complex @ A @ S )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat
% 5.44/5.71 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ C @ ( minus_811609699411566653omplex @ S @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8821_prod_Odelta__remove,axiom,
% 5.44/5.71 ! [S: set_int,A: int,B: int > nat,C: int > nat] :
% 5.44/5.71 ( ( finite_finite_int @ S )
% 5.44/5.71 => ( ( ( member_int @ A @ S )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat
% 5.44/5.71 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( times_times_nat @ ( B @ A ) @ ( groups1707563613775114915nt_nat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.44/5.71 & ( ~ ( member_int @ A @ S )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat
% 5.44/5.71 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups1707563613775114915nt_nat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.delta_remove
% 5.44/5.71 thf(fact_8822_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_real,Z: real > real,W: real > real] :
% 5.44/5.71 ( ! [I4: real] :
% 5.44/5.71 ( ( member_real @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: real] :
% 5.44/5.71 ( ( member_real @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups1681761925125756287l_real @ Z @ I6 ) @ ( groups1681761925125756287l_real @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups8097168146408367636l_real
% 5.44/5.71 @ ^ [I5: real] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8823_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_int,Z: int > real,W: int > real] :
% 5.44/5.71 ( ! [I4: int] :
% 5.44/5.71 ( ( member_int @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: int] :
% 5.44/5.71 ( ( member_int @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2316167850115554303t_real @ Z @ I6 ) @ ( groups2316167850115554303t_real @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups8778361861064173332t_real
% 5.44/5.71 @ ^ [I5: int] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8824_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_complex,Z: complex > real,W: complex > real] :
% 5.44/5.71 ( ! [I4: complex] :
% 5.44/5.71 ( ( member_complex @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: complex] :
% 5.44/5.71 ( ( member_complex @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups766887009212190081x_real @ Z @ I6 ) @ ( groups766887009212190081x_real @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups5808333547571424918x_real
% 5.44/5.71 @ ^ [I5: complex] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8825_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_Pr1261947904930325089at_nat,Z: product_prod_nat_nat > real,W: product_prod_nat_nat > real] :
% 5.44/5.71 ( ! [I4: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups6036352826371341000t_real @ Z @ I6 ) @ ( groups6036352826371341000t_real @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups4567486121110086003t_real
% 5.44/5.71 @ ^ [I5: product_prod_nat_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8826_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_real,Z: real > complex,W: real > complex] :
% 5.44/5.71 ( ! [I4: real] :
% 5.44/5.71 ( ( member_real @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: real] :
% 5.44/5.71 ( ( member_real @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I6 ) @ ( groups713298508707869441omplex @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups8097168146408367636l_real
% 5.44/5.71 @ ^ [I5: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8827_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_int,Z: int > complex,W: int > complex] :
% 5.44/5.71 ( ! [I4: int] :
% 5.44/5.71 ( ( member_int @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: int] :
% 5.44/5.71 ( ( member_int @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I6 ) @ ( groups7440179247065528705omplex @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups8778361861064173332t_real
% 5.44/5.71 @ ^ [I5: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8828_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_complex,Z: complex > complex,W: complex > complex] :
% 5.44/5.71 ( ! [I4: complex] :
% 5.44/5.71 ( ( member_complex @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: complex] :
% 5.44/5.71 ( ( member_complex @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups3708469109370488835omplex @ Z @ I6 ) @ ( groups3708469109370488835omplex @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups5808333547571424918x_real
% 5.44/5.71 @ ^ [I5: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8829_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_Pr1261947904930325089at_nat,Z: product_prod_nat_nat > complex,W: product_prod_nat_nat > complex] :
% 5.44/5.71 ( ! [I4: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups8110221916422527690omplex @ Z @ I6 ) @ ( groups8110221916422527690omplex @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups4567486121110086003t_real
% 5.44/5.71 @ ^ [I5: product_prod_nat_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8830_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_nat,Z: nat > real,W: nat > real] :
% 5.44/5.71 ( ! [I4: nat] :
% 5.44/5.71 ( ( member_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: nat] :
% 5.44/5.71 ( ( member_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups129246275422532515t_real @ Z @ I6 ) @ ( groups129246275422532515t_real @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8831_norm__prod__diff,axiom,
% 5.44/5.71 ! [I6: set_nat,Z: nat > complex,W: nat > complex] :
% 5.44/5.71 ( ! [I4: nat] :
% 5.44/5.71 ( ( member_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ! [I4: nat] :
% 5.44/5.71 ( ( member_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I4 ) ) @ one_one_real ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I6 ) @ ( groups6464643781859351333omplex @ W @ I6 ) ) )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_prod_diff
% 5.44/5.71 thf(fact_8832_zero__polynom__imp__zero__coeffs,axiom,
% 5.44/5.71 ! [C: nat > complex,N2: nat,K: nat] :
% 5.44/5.71 ( ! [W2: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ W2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_complex )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( C @ K )
% 5.44/5.71 = zero_zero_complex ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % zero_polynom_imp_zero_coeffs
% 5.44/5.71 thf(fact_8833_zero__polynom__imp__zero__coeffs,axiom,
% 5.44/5.71 ! [C: nat > real,N2: nat,K: nat] :
% 5.44/5.71 ( ! [W2: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ W2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( C @ K )
% 5.44/5.71 = zero_zero_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % zero_polynom_imp_zero_coeffs
% 5.44/5.71 thf(fact_8834_polyfun__eq__0,axiom,
% 5.44/5.71 ! [C: nat > complex,N2: nat] :
% 5.44/5.71 ( ( ! [X2: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_complex ) )
% 5.44/5.71 = ( ! [I5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.44/5.71 => ( ( C @ I5 )
% 5.44/5.71 = zero_zero_complex ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_eq_0
% 5.44/5.71 thf(fact_8835_polyfun__eq__0,axiom,
% 5.44/5.71 ! [C: nat > real,N2: nat] :
% 5.44/5.71 ( ( ! [X2: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_real ) )
% 5.44/5.71 = ( ! [I5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.44/5.71 => ( ( C @ I5 )
% 5.44/5.71 = zero_zero_real ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_eq_0
% 5.44/5.71 thf(fact_8836_sum_OatMost__shift,axiom,
% 5.44/5.71 ! [G: nat > complex,N2: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.atMost_shift
% 5.44/5.71 thf(fact_8837_sum_OatMost__shift,axiom,
% 5.44/5.71 ! [G: nat > int,N2: nat] :
% 5.44/5.71 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.atMost_shift
% 5.44/5.71 thf(fact_8838_sum_OatMost__shift,axiom,
% 5.44/5.71 ! [G: nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.atMost_shift
% 5.44/5.71 thf(fact_8839_sum_OatMost__shift,axiom,
% 5.44/5.71 ! [G: nat > real,N2: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.atMost_shift
% 5.44/5.71 thf(fact_8840_sum__up__index__split,axiom,
% 5.44/5.71 ! [F: nat > complex,M: nat,N2: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.44/5.71 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_up_index_split
% 5.44/5.71 thf(fact_8841_sum__up__index__split,axiom,
% 5.44/5.71 ! [F: nat > int,M: nat,N2: nat] :
% 5.44/5.71 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.44/5.71 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_up_index_split
% 5.44/5.71 thf(fact_8842_sum__up__index__split,axiom,
% 5.44/5.71 ! [F: nat > nat,M: nat,N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.44/5.71 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_up_index_split
% 5.44/5.71 thf(fact_8843_sum__up__index__split,axiom,
% 5.44/5.71 ! [F: nat > real,M: nat,N2: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.44/5.71 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_up_index_split
% 5.44/5.71 thf(fact_8844_atLeast1__atMost__eq__remove0,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.71 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % atLeast1_atMost_eq_remove0
% 5.44/5.71 thf(fact_8845_gbinomial__parallel__sum,axiom,
% 5.44/5.71 ! [A: complex,N2: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_parallel_sum
% 5.44/5.71 thf(fact_8846_gbinomial__parallel__sum,axiom,
% 5.44/5.71 ! [A: real,N2: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_parallel_sum
% 5.44/5.71 thf(fact_8847_sum_Otriangle__reindex__eq,axiom,
% 5.44/5.71 ! [G: nat > nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.44/5.71 @ ( collec3392354462482085612at_nat
% 5.44/5.71 @ ( produc6081775807080527818_nat_o
% 5.44/5.71 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.triangle_reindex_eq
% 5.44/5.71 thf(fact_8848_sum_Otriangle__reindex__eq,axiom,
% 5.44/5.71 ! [G: nat > nat > real,N2: nat] :
% 5.44/5.71 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.44/5.71 @ ( collec3392354462482085612at_nat
% 5.44/5.71 @ ( produc6081775807080527818_nat_o
% 5.44/5.71 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.triangle_reindex_eq
% 5.44/5.71 thf(fact_8849_fact__eq__fact__times,axiom,
% 5.44/5.71 ! [N2: nat,M: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.71 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.44/5.71 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [X2: nat] : X2
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_eq_fact_times
% 5.44/5.71 thf(fact_8850_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_int,A2: set_int,F: int > real] :
% 5.44/5.71 ( ( finite_finite_int @ B2 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: int] :
% 5.44/5.71 ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8851_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > real] :
% 5.44/5.71 ( ( finite6177210948735845034at_nat @ B2 )
% 5.44/5.71 => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ B3 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( groups6036352826371341000t_real @ F @ A2 ) @ ( groups6036352826371341000t_real @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8852_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8853_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > int] :
% 5.44/5.71 ( ( finite6177210948735845034at_nat @ B2 )
% 5.44/5.71 => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ B3 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_int @ ( groups4075276357253098568at_int @ F @ A2 ) @ ( groups4075276357253098568at_int @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8854_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ B2 )
% 5.44/5.71 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8855_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_real,A2: set_real,F: real > real] :
% 5.44/5.71 ( ( finite_finite_real @ B2 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: real] :
% 5.44/5.71 ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: real] :
% 5.44/5.71 ( ( member_real @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8856_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_real,A2: set_real,F: real > int] :
% 5.44/5.71 ( ( finite_finite_real @ B2 )
% 5.44/5.71 => ( ( ord_less_eq_set_real @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: real] :
% 5.44/5.71 ( ( member_real @ B3 @ ( minus_minus_set_real @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: real] :
% 5.44/5.71 ( ( member_real @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8857_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_nat,A2: set_nat,F: nat > real] :
% 5.44/5.71 ( ( finite_finite_nat @ B2 )
% 5.44/5.71 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: nat] :
% 5.44/5.71 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_real @ one_one_real @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: nat] :
% 5.44/5.71 ( ( member_nat @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8858_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_nat,A2: set_nat,F: nat > int] :
% 5.44/5.71 ( ( finite_finite_nat @ B2 )
% 5.44/5.71 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: nat] :
% 5.44/5.71 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: nat] :
% 5.44/5.71 ( ( member_nat @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8859_prod__mono2,axiom,
% 5.44/5.71 ! [B2: set_int,A2: set_int,F: int > int] :
% 5.44/5.71 ( ( finite_finite_int @ B2 )
% 5.44/5.71 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 5.44/5.71 => ( ! [B3: int] :
% 5.44/5.71 ( ( member_int @ B3 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 5.44/5.71 => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ A2 )
% 5.44/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 5.44/5.71 => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ F @ B2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_mono2
% 5.44/5.71 thf(fact_8860_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > nat,A: complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_nat )
% 5.44/5.71 => ( ( ( member_complex @ A @ A2 )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.44/5.71 = ( divide_divide_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_complex @ A @ A2 )
% 5.44/5.71 => ( ( groups861055069439313189ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.44/5.71 = ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8861_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_int,F: int > nat,A: int] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_nat )
% 5.44/5.71 => ( ( ( member_int @ A @ A2 )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.44/5.71 = ( divide_divide_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_int @ A @ A2 )
% 5.44/5.71 => ( ( groups1707563613775114915nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.44/5.71 = ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8862_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_real,F: real > nat,A: real] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_nat )
% 5.44/5.71 => ( ( ( member_real @ A @ A2 )
% 5.44/5.71 => ( ( groups4696554848551431203al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.44/5.71 = ( divide_divide_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_real @ A @ A2 )
% 5.44/5.71 => ( ( groups4696554848551431203al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.44/5.71 = ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8863_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > real,A: complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_real )
% 5.44/5.71 => ( ( ( member_complex @ A @ A2 )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.44/5.71 = ( divide_divide_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_complex @ A @ A2 )
% 5.44/5.71 => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.44/5.71 = ( groups766887009212190081x_real @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8864_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_int,F: int > real,A: int] :
% 5.44/5.71 ( ( finite_finite_int @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_real )
% 5.44/5.71 => ( ( ( member_int @ A @ A2 )
% 5.44/5.71 => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.44/5.71 = ( divide_divide_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_int @ A @ A2 )
% 5.44/5.71 => ( ( groups2316167850115554303t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.44/5.71 = ( groups2316167850115554303t_real @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8865_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_real,F: real > real,A: real] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_real )
% 5.44/5.71 => ( ( ( member_real @ A @ A2 )
% 5.44/5.71 => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.44/5.71 = ( divide_divide_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_real @ A @ A2 )
% 5.44/5.71 => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.44/5.71 = ( groups1681761925125756287l_real @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8866_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_nat,F: nat > real,A: nat] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_real )
% 5.44/5.71 => ( ( ( member_nat @ A @ A2 )
% 5.44/5.71 => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.44/5.71 = ( divide_divide_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_nat @ A @ A2 )
% 5.44/5.71 => ( ( groups129246275422532515t_real @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.44/5.71 = ( groups129246275422532515t_real @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8867_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > int,A: complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_int )
% 5.44/5.71 => ( ( ( member_complex @ A @ A2 )
% 5.44/5.71 => ( ( groups858564598930262913ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.44/5.71 = ( divide_divide_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_complex @ A @ A2 )
% 5.44/5.71 => ( ( groups858564598930262913ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.44/5.71 = ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8868_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_real,F: real > int,A: real] :
% 5.44/5.71 ( ( finite_finite_real @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_int )
% 5.44/5.71 => ( ( ( member_real @ A @ A2 )
% 5.44/5.71 => ( ( groups4694064378042380927al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.44/5.71 = ( divide_divide_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_real @ A @ A2 )
% 5.44/5.71 => ( ( groups4694064378042380927al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.44/5.71 = ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8869_prod__diff1,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > complex,A: complex] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( ( F @ A )
% 5.44/5.71 != zero_zero_complex )
% 5.44/5.71 => ( ( ( member_complex @ A @ A2 )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.44/5.71 = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.44/5.71 & ( ~ ( member_complex @ A @ A2 )
% 5.44/5.71 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.44/5.71 = ( groups3708469109370488835omplex @ F @ A2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_diff1
% 5.44/5.71 thf(fact_8870_sum__gp__basic,axiom,
% 5.44/5.71 ! [X: complex,N2: nat] :
% 5.44/5.71 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_gp_basic
% 5.44/5.71 thf(fact_8871_sum__gp__basic,axiom,
% 5.44/5.71 ! [X: int,N2: nat] :
% 5.44/5.71 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_gp_basic
% 5.44/5.71 thf(fact_8872_sum__gp__basic,axiom,
% 5.44/5.71 ! [X: real,N2: nat] :
% 5.44/5.71 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_gp_basic
% 5.44/5.71 thf(fact_8873_polyfun__roots__finite,axiom,
% 5.44/5.71 ! [C: nat > complex,K: nat,N2: nat] :
% 5.44/5.71 ( ( ( C @ K )
% 5.44/5.71 != zero_zero_complex )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( finite3207457112153483333omplex
% 5.44/5.71 @ ( collect_complex
% 5.44/5.71 @ ^ [Z5: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z5 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_complex ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_roots_finite
% 5.44/5.71 thf(fact_8874_polyfun__roots__finite,axiom,
% 5.44/5.71 ! [C: nat > real,K: nat,N2: nat] :
% 5.44/5.71 ( ( ( C @ K )
% 5.44/5.71 != zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( finite_finite_real
% 5.44/5.71 @ ( collect_real
% 5.44/5.71 @ ^ [Z5: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z5 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_real ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_roots_finite
% 5.44/5.71 thf(fact_8875_polyfun__finite__roots,axiom,
% 5.44/5.71 ! [C: nat > complex,N2: nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex
% 5.44/5.71 @ ( collect_complex
% 5.44/5.71 @ ^ [X2: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_complex ) ) )
% 5.44/5.71 = ( ? [I5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.44/5.71 & ( ( C @ I5 )
% 5.44/5.71 != zero_zero_complex ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_finite_roots
% 5.44/5.71 thf(fact_8876_polyfun__finite__roots,axiom,
% 5.44/5.71 ! [C: nat > real,N2: nat] :
% 5.44/5.71 ( ( finite_finite_real
% 5.44/5.71 @ ( collect_real
% 5.44/5.71 @ ^ [X2: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_real ) ) )
% 5.44/5.71 = ( ? [I5: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.44/5.71 & ( ( C @ I5 )
% 5.44/5.71 != zero_zero_real ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_finite_roots
% 5.44/5.71 thf(fact_8877_pochhammer__Suc__prod,axiom,
% 5.44/5.71 ! [A: real,N2: nat] :
% 5.44/5.71 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod
% 5.44/5.71 thf(fact_8878_pochhammer__Suc__prod,axiom,
% 5.44/5.71 ! [A: complex,N2: nat] :
% 5.44/5.71 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod
% 5.44/5.71 thf(fact_8879_pochhammer__Suc__prod,axiom,
% 5.44/5.71 ! [A: code_integer,N2: nat] :
% 5.44/5.71 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups3455450783089532116nteger
% 5.44/5.71 @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod
% 5.44/5.71 thf(fact_8880_pochhammer__Suc__prod,axiom,
% 5.44/5.71 ! [A: nat,N2: nat] :
% 5.44/5.71 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod
% 5.44/5.71 thf(fact_8881_pochhammer__Suc__prod,axiom,
% 5.44/5.71 ! [A: int,N2: nat] :
% 5.44/5.71 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod
% 5.44/5.71 thf(fact_8882_polyfun__linear__factor__root,axiom,
% 5.44/5.71 ! [C: nat > complex,A: complex,N2: nat] :
% 5.44/5.71 ( ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_complex )
% 5.44/5.71 => ~ ! [B3: nat > complex] :
% 5.44/5.71 ~ ! [Z3: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( times_times_complex @ ( minus_minus_complex @ Z3 @ A )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( B3 @ I5 ) @ ( power_power_complex @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_linear_factor_root
% 5.44/5.71 thf(fact_8883_polyfun__linear__factor__root,axiom,
% 5.44/5.71 ! [C: nat > int,A: int,N2: nat] :
% 5.44/5.71 ( ( ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_int )
% 5.44/5.71 => ~ ! [B3: nat > int] :
% 5.44/5.71 ~ ! [Z3: int] :
% 5.44/5.71 ( ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( times_times_int @ ( minus_minus_int @ Z3 @ A )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( B3 @ I5 ) @ ( power_power_int @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_linear_factor_root
% 5.44/5.71 thf(fact_8884_polyfun__linear__factor__root,axiom,
% 5.44/5.71 ! [C: nat > real,A: real,N2: nat] :
% 5.44/5.71 ( ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_real )
% 5.44/5.71 => ~ ! [B3: nat > real] :
% 5.44/5.71 ~ ! [Z3: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( times_times_real @ ( minus_minus_real @ Z3 @ A )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( B3 @ I5 ) @ ( power_power_real @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_linear_factor_root
% 5.44/5.71 thf(fact_8885_polyfun__linear__factor,axiom,
% 5.44/5.71 ! [C: nat > complex,N2: nat,A: complex] :
% 5.44/5.71 ? [B3: nat > complex] :
% 5.44/5.71 ! [Z3: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( plus_plus_complex
% 5.44/5.71 @ ( times_times_complex @ ( minus_minus_complex @ Z3 @ A )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( B3 @ I5 ) @ ( power_power_complex @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_linear_factor
% 5.44/5.71 thf(fact_8886_polyfun__linear__factor,axiom,
% 5.44/5.71 ! [C: nat > int,N2: nat,A: int] :
% 5.44/5.71 ? [B3: nat > int] :
% 5.44/5.71 ! [Z3: int] :
% 5.44/5.71 ( ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( plus_plus_int
% 5.44/5.71 @ ( times_times_int @ ( minus_minus_int @ Z3 @ A )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( B3 @ I5 ) @ ( power_power_int @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_linear_factor
% 5.44/5.71 thf(fact_8887_polyfun__linear__factor,axiom,
% 5.44/5.71 ! [C: nat > real,N2: nat,A: real] :
% 5.44/5.71 ? [B3: nat > real] :
% 5.44/5.71 ! [Z3: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( plus_plus_real
% 5.44/5.71 @ ( times_times_real @ ( minus_minus_real @ Z3 @ A )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( B3 @ I5 ) @ ( power_power_real @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_linear_factor
% 5.44/5.71 thf(fact_8888_sum__power__shift,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,X: complex] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.71 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_power_shift
% 5.44/5.71 thf(fact_8889_sum__power__shift,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,X: int] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.71 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_power_shift
% 5.44/5.71 thf(fact_8890_sum__power__shift,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,X: real] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.44/5.71 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_power_shift
% 5.44/5.71 thf(fact_8891_pochhammer__prod__rev,axiom,
% 5.44/5.71 ( comm_s7457072308508201937r_real
% 5.44/5.71 = ( ^ [A4: real,N: nat] :
% 5.44/5.71 ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_prod_rev
% 5.44/5.71 thf(fact_8892_pochhammer__prod__rev,axiom,
% 5.44/5.71 ( comm_s2602460028002588243omplex
% 5.44/5.71 = ( ^ [A4: complex,N: nat] :
% 5.44/5.71 ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_prod_rev
% 5.44/5.71 thf(fact_8893_pochhammer__prod__rev,axiom,
% 5.44/5.71 ( comm_s8582702949713902594nteger
% 5.44/5.71 = ( ^ [A4: code_integer,N: nat] :
% 5.44/5.71 ( groups3455450783089532116nteger
% 5.44/5.71 @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A4 @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_prod_rev
% 5.44/5.71 thf(fact_8894_pochhammer__prod__rev,axiom,
% 5.44/5.71 ( comm_s4663373288045622133er_nat
% 5.44/5.71 = ( ^ [A4: nat,N: nat] :
% 5.44/5.71 ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_prod_rev
% 5.44/5.71 thf(fact_8895_pochhammer__prod__rev,axiom,
% 5.44/5.71 ( comm_s4660882817536571857er_int
% 5.44/5.71 = ( ^ [A4: int,N: nat] :
% 5.44/5.71 ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_prod_rev
% 5.44/5.71 thf(fact_8896_fact__div__fact,axiom,
% 5.44/5.71 ! [N2: nat,M: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ N2 @ M )
% 5.44/5.71 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 5.44/5.71 = ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [X2: nat] : X2
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_div_fact
% 5.44/5.71 thf(fact_8897_sum_Otriangle__reindex,axiom,
% 5.44/5.71 ! [G: nat > nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.44/5.71 @ ( collec3392354462482085612at_nat
% 5.44/5.71 @ ( produc6081775807080527818_nat_o
% 5.44/5.71 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.triangle_reindex
% 5.44/5.71 thf(fact_8898_sum_Otriangle__reindex,axiom,
% 5.44/5.71 ! [G: nat > nat > real,N2: nat] :
% 5.44/5.71 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.44/5.71 @ ( collec3392354462482085612at_nat
% 5.44/5.71 @ ( produc6081775807080527818_nat_o
% 5.44/5.71 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.triangle_reindex
% 5.44/5.71 thf(fact_8899_summable__Cauchy__product,axiom,
% 5.44/5.71 ! [A: nat > complex,B: nat > complex] :
% 5.44/5.71 ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.44/5.71 => ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.44/5.71 => ( summable_complex
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_Cauchy_product
% 5.44/5.71 thf(fact_8900_summable__Cauchy__product,axiom,
% 5.44/5.71 ! [A: nat > real,B: nat > real] :
% 5.44/5.71 ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.44/5.71 => ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.44/5.71 => ( summable_real
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_Cauchy_product
% 5.44/5.71 thf(fact_8901_Cauchy__product,axiom,
% 5.44/5.71 ! [A: nat > complex,B: nat > complex] :
% 5.44/5.71 ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.44/5.71 => ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.44/5.71 => ( ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) )
% 5.44/5.71 = ( suminf_complex
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Cauchy_product
% 5.44/5.71 thf(fact_8902_Cauchy__product,axiom,
% 5.44/5.71 ! [A: nat > real,B: nat > real] :
% 5.44/5.71 ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.44/5.71 => ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.44/5.71 => ( ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) )
% 5.44/5.71 = ( suminf_real
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Cauchy_product
% 5.44/5.71 thf(fact_8903_prod_Oin__pairs,axiom,
% 5.44/5.71 ! [G: nat > complex,M: nat,N2: nat] :
% 5.44/5.71 ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.in_pairs
% 5.44/5.71 thf(fact_8904_prod_Oin__pairs,axiom,
% 5.44/5.71 ! [G: nat > real,M: nat,N2: nat] :
% 5.44/5.71 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.in_pairs
% 5.44/5.71 thf(fact_8905_prod_Oin__pairs,axiom,
% 5.44/5.71 ! [G: nat > nat,M: nat,N2: nat] :
% 5.44/5.71 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.in_pairs
% 5.44/5.71 thf(fact_8906_prod_Oin__pairs,axiom,
% 5.44/5.71 ! [G: nat > int,M: nat,N2: nat] :
% 5.44/5.71 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.in_pairs
% 5.44/5.71 thf(fact_8907_sum__atLeastAtMost__code,axiom,
% 5.44/5.71 ! [F: nat > extended_enat,A: nat,B: nat] :
% 5.44/5.71 ( ( groups7108830773950497114d_enat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.71 = ( set_fo2538466533108834004d_enat
% 5.44/5.71 @ ^ [A4: nat] : ( plus_p3455044024723400733d_enat @ ( F @ A4 ) )
% 5.44/5.71 @ A
% 5.44/5.71 @ B
% 5.44/5.71 @ zero_z5237406670263579293d_enat ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_atLeastAtMost_code
% 5.44/5.71 thf(fact_8908_sum__atLeastAtMost__code,axiom,
% 5.44/5.71 ! [F: nat > complex,A: nat,B: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.71 = ( set_fo1517530859248394432omplex
% 5.44/5.71 @ ^ [A4: nat] : ( plus_plus_complex @ ( F @ A4 ) )
% 5.44/5.71 @ A
% 5.44/5.71 @ B
% 5.44/5.71 @ zero_zero_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_atLeastAtMost_code
% 5.44/5.71 thf(fact_8909_sum__atLeastAtMost__code,axiom,
% 5.44/5.71 ! [F: nat > int,A: nat,B: nat] :
% 5.44/5.71 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.71 = ( set_fo2581907887559384638at_int
% 5.44/5.71 @ ^ [A4: nat] : ( plus_plus_int @ ( F @ A4 ) )
% 5.44/5.71 @ A
% 5.44/5.71 @ B
% 5.44/5.71 @ zero_zero_int ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_atLeastAtMost_code
% 5.44/5.71 thf(fact_8910_sum__atLeastAtMost__code,axiom,
% 5.44/5.71 ! [F: nat > nat,A: nat,B: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.71 = ( set_fo2584398358068434914at_nat
% 5.44/5.71 @ ^ [A4: nat] : ( plus_plus_nat @ ( F @ A4 ) )
% 5.44/5.71 @ A
% 5.44/5.71 @ B
% 5.44/5.71 @ zero_zero_nat ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_atLeastAtMost_code
% 5.44/5.71 thf(fact_8911_sum__atLeastAtMost__code,axiom,
% 5.44/5.71 ! [F: nat > real,A: nat,B: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.44/5.71 = ( set_fo3111899725591712190t_real
% 5.44/5.71 @ ^ [A4: nat] : ( plus_plus_real @ ( F @ A4 ) )
% 5.44/5.71 @ A
% 5.44/5.71 @ B
% 5.44/5.71 @ zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_atLeastAtMost_code
% 5.44/5.71 thf(fact_8912_sum_Oin__pairs__0,axiom,
% 5.44/5.71 ! [G: nat > complex,N2: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.in_pairs_0
% 5.44/5.71 thf(fact_8913_sum_Oin__pairs__0,axiom,
% 5.44/5.71 ! [G: nat > int,N2: nat] :
% 5.44/5.71 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.in_pairs_0
% 5.44/5.71 thf(fact_8914_sum_Oin__pairs__0,axiom,
% 5.44/5.71 ! [G: nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.in_pairs_0
% 5.44/5.71 thf(fact_8915_sum_Oin__pairs__0,axiom,
% 5.44/5.71 ! [G: nat > real,N2: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.in_pairs_0
% 5.44/5.71 thf(fact_8916_polynomial__product,axiom,
% 5.44/5.71 ! [M: nat,A: nat > complex,N2: nat,B: nat > complex,X: complex] :
% 5.44/5.71 ( ! [I4: nat] :
% 5.44/5.71 ( ( ord_less_nat @ M @ I4 )
% 5.44/5.71 => ( ( A @ I4 )
% 5.44/5.71 = zero_zero_complex ) )
% 5.44/5.71 => ( ! [J2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ N2 @ J2 )
% 5.44/5.71 => ( ( B @ J2 )
% 5.44/5.71 = zero_zero_complex ) )
% 5.44/5.71 => ( ( times_times_complex
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [R4: nat] :
% 5.44/5.71 ( times_times_complex
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R4 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ R4 ) )
% 5.44/5.71 @ ( power_power_complex @ X @ R4 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polynomial_product
% 5.44/5.71 thf(fact_8917_polynomial__product,axiom,
% 5.44/5.71 ! [M: nat,A: nat > int,N2: nat,B: nat > int,X: int] :
% 5.44/5.71 ( ! [I4: nat] :
% 5.44/5.71 ( ( ord_less_nat @ M @ I4 )
% 5.44/5.71 => ( ( A @ I4 )
% 5.44/5.71 = zero_zero_int ) )
% 5.44/5.71 => ( ! [J2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ N2 @ J2 )
% 5.44/5.71 => ( ( B @ J2 )
% 5.44/5.71 = zero_zero_int ) )
% 5.44/5.71 => ( ( times_times_int
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [R4: nat] :
% 5.44/5.71 ( times_times_int
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R4 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ R4 ) )
% 5.44/5.71 @ ( power_power_int @ X @ R4 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polynomial_product
% 5.44/5.71 thf(fact_8918_polynomial__product,axiom,
% 5.44/5.71 ! [M: nat,A: nat > real,N2: nat,B: nat > real,X: real] :
% 5.44/5.71 ( ! [I4: nat] :
% 5.44/5.71 ( ( ord_less_nat @ M @ I4 )
% 5.44/5.71 => ( ( A @ I4 )
% 5.44/5.71 = zero_zero_real ) )
% 5.44/5.71 => ( ! [J2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ N2 @ J2 )
% 5.44/5.71 => ( ( B @ J2 )
% 5.44/5.71 = zero_zero_real ) )
% 5.44/5.71 => ( ( times_times_real
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [R4: nat] :
% 5.44/5.71 ( times_times_real
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R4 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ R4 ) )
% 5.44/5.71 @ ( power_power_real @ X @ R4 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polynomial_product
% 5.44/5.71 thf(fact_8919_pochhammer__Suc__prod__rev,axiom,
% 5.44/5.71 ! [A: real,N2: nat] :
% 5.44/5.71 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod_rev
% 5.44/5.71 thf(fact_8920_pochhammer__Suc__prod__rev,axiom,
% 5.44/5.71 ! [A: complex,N2: nat] :
% 5.44/5.71 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod_rev
% 5.44/5.71 thf(fact_8921_pochhammer__Suc__prod__rev,axiom,
% 5.44/5.71 ! [A: code_integer,N2: nat] :
% 5.44/5.71 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups3455450783089532116nteger
% 5.44/5.71 @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod_rev
% 5.44/5.71 thf(fact_8922_pochhammer__Suc__prod__rev,axiom,
% 5.44/5.71 ! [A: nat,N2: nat] :
% 5.44/5.71 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod_rev
% 5.44/5.71 thf(fact_8923_pochhammer__Suc__prod__rev,axiom,
% 5.44/5.71 ! [A: int,N2: nat] :
% 5.44/5.71 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.44/5.71 = ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_Suc_prod_rev
% 5.44/5.71 thf(fact_8924_polyfun__eq__const,axiom,
% 5.44/5.71 ! [C: nat > complex,N2: nat,K: complex] :
% 5.44/5.71 ( ( ! [X2: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = K ) )
% 5.44/5.71 = ( ( ( C @ zero_zero_nat )
% 5.44/5.71 = K )
% 5.44/5.71 & ! [X2: nat] :
% 5.44/5.71 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 5.44/5.71 => ( ( C @ X2 )
% 5.44/5.71 = zero_zero_complex ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_eq_const
% 5.44/5.71 thf(fact_8925_polyfun__eq__const,axiom,
% 5.44/5.71 ! [C: nat > real,N2: nat,K: real] :
% 5.44/5.71 ( ( ! [X2: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = K ) )
% 5.44/5.71 = ( ( ( C @ zero_zero_nat )
% 5.44/5.71 = K )
% 5.44/5.71 & ! [X2: nat] :
% 5.44/5.71 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 5.44/5.71 => ( ( C @ X2 )
% 5.44/5.71 = zero_zero_real ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_eq_const
% 5.44/5.71 thf(fact_8926_gbinomial__sum__lower__neg,axiom,
% 5.44/5.71 ! [A: complex,M: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_sum_lower_neg
% 5.44/5.71 thf(fact_8927_gbinomial__sum__lower__neg,axiom,
% 5.44/5.71 ! [A: real,M: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_sum_lower_neg
% 5.44/5.71 thf(fact_8928_polynomial__product__nat,axiom,
% 5.44/5.71 ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X: nat] :
% 5.44/5.71 ( ! [I4: nat] :
% 5.44/5.71 ( ( ord_less_nat @ M @ I4 )
% 5.44/5.71 => ( ( A @ I4 )
% 5.44/5.71 = zero_zero_nat ) )
% 5.44/5.71 => ( ! [J2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ N2 @ J2 )
% 5.44/5.71 => ( ( B @ J2 )
% 5.44/5.71 = zero_zero_nat ) )
% 5.44/5.71 => ( ( times_times_nat
% 5.44/5.71 @ ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( power_power_nat @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 @ ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [R4: nat] :
% 5.44/5.71 ( times_times_nat
% 5.44/5.71 @ ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R4 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ R4 ) )
% 5.44/5.71 @ ( power_power_nat @ X @ R4 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polynomial_product_nat
% 5.44/5.71 thf(fact_8929_Cauchy__product__sums,axiom,
% 5.44/5.71 ! [A: nat > complex,B: nat > complex] :
% 5.44/5.71 ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.44/5.71 => ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.44/5.71 => ( sums_complex
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Cauchy_product_sums
% 5.44/5.71 thf(fact_8930_Cauchy__product__sums,axiom,
% 5.44/5.71 ! [A: nat > real,B: nat > real] :
% 5.44/5.71 ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.44/5.71 => ( ( summable_real
% 5.44/5.71 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.44/5.71 => ( sums_real
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Cauchy_product_sums
% 5.44/5.71 thf(fact_8931_gbinomial__Suc,axiom,
% 5.44/5.71 ! [A: complex,K: nat] :
% 5.44/5.71 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.44/5.71 = ( divide1717551699836669952omplex
% 5.44/5.71 @ ( groups6464643781859351333omplex
% 5.44/5.71 @ ^ [I5: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.44/5.71 @ ( semiri5044797733671781792omplex @ ( suc @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_Suc
% 5.44/5.71 thf(fact_8932_gbinomial__Suc,axiom,
% 5.44/5.71 ! [A: code_integer,K: nat] :
% 5.44/5.71 ( ( gbinom8545251970709558553nteger @ A @ ( suc @ K ) )
% 5.44/5.71 = ( divide6298287555418463151nteger
% 5.44/5.71 @ ( groups3455450783089532116nteger
% 5.44/5.71 @ ^ [I5: nat] : ( minus_8373710615458151222nteger @ A @ ( semiri4939895301339042750nteger @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.44/5.71 @ ( semiri3624122377584611663nteger @ ( suc @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_Suc
% 5.44/5.71 thf(fact_8933_gbinomial__Suc,axiom,
% 5.44/5.71 ! [A: real,K: nat] :
% 5.44/5.71 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.44/5.71 = ( divide_divide_real
% 5.44/5.71 @ ( groups129246275422532515t_real
% 5.44/5.71 @ ^ [I5: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.44/5.71 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_Suc
% 5.44/5.71 thf(fact_8934_gbinomial__Suc,axiom,
% 5.44/5.71 ! [A: nat,K: nat] :
% 5.44/5.71 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.44/5.71 = ( divide_divide_nat
% 5.44/5.71 @ ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.44/5.71 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_Suc
% 5.44/5.71 thf(fact_8935_gbinomial__Suc,axiom,
% 5.44/5.71 ! [A: int,K: nat] :
% 5.44/5.71 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.44/5.71 = ( divide_divide_int
% 5.44/5.71 @ ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I5 ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.44/5.71 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_Suc
% 5.44/5.71 thf(fact_8936_sum_Ozero__middle,axiom,
% 5.44/5.71 ! [P5: nat,K: nat,G: nat > extended_enat,H2: nat > extended_enat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.71 => ( ( groups7108830773950497114d_enat
% 5.44/5.71 @ ^ [J3: nat] : ( if_Extended_enat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_Extended_enat @ ( J3 = K ) @ zero_z5237406670263579293d_enat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.71 = ( groups7108830773950497114d_enat
% 5.44/5.71 @ ^ [J3: nat] : ( if_Extended_enat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.zero_middle
% 5.44/5.71 thf(fact_8937_sum_Ozero__middle,axiom,
% 5.44/5.71 ! [P5: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.71 => ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.zero_middle
% 5.44/5.71 thf(fact_8938_sum_Ozero__middle,axiom,
% 5.44/5.71 ! [P5: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.71 => ( ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.71 = ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.zero_middle
% 5.44/5.71 thf(fact_8939_sum_Ozero__middle,axiom,
% 5.44/5.71 ! [P5: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.71 => ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.71 = ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.zero_middle
% 5.44/5.71 thf(fact_8940_sum_Ozero__middle,axiom,
% 5.44/5.71 ! [P5: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ P5 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K @ P5 )
% 5.44/5.71 => ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P5 ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P5 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum.zero_middle
% 5.44/5.71 thf(fact_8941_gbinomial__partial__sum__poly,axiom,
% 5.44/5.71 ! [M: nat,A: complex,X: complex,Y: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_partial_sum_poly
% 5.44/5.71 thf(fact_8942_gbinomial__partial__sum__poly,axiom,
% 5.44/5.71 ! [M: nat,A: real,X: real,Y: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_partial_sum_poly
% 5.44/5.71 thf(fact_8943_root__polyfun,axiom,
% 5.44/5.71 ! [N2: nat,Z: int,A: int] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( ( power_power_int @ Z @ N2 )
% 5.44/5.71 = A )
% 5.44/5.71 = ( ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( if_int @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I5 = N2 ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_int ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % root_polyfun
% 5.44/5.71 thf(fact_8944_root__polyfun,axiom,
% 5.44/5.71 ! [N2: nat,Z: complex,A: complex] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( ( power_power_complex @ Z @ N2 )
% 5.44/5.71 = A )
% 5.44/5.71 = ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( if_complex @ ( I5 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I5 = N2 ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_complex ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % root_polyfun
% 5.44/5.71 thf(fact_8945_root__polyfun,axiom,
% 5.44/5.71 ! [N2: nat,Z: code_integer,A: code_integer] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( ( power_8256067586552552935nteger @ Z @ N2 )
% 5.44/5.71 = A )
% 5.44/5.71 = ( ( groups7501900531339628137nteger
% 5.44/5.71 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I5 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I5 = N2 ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_z3403309356797280102nteger ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % root_polyfun
% 5.44/5.71 thf(fact_8946_root__polyfun,axiom,
% 5.44/5.71 ! [N2: nat,Z: real,A: real] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( ( power_power_real @ Z @ N2 )
% 5.44/5.71 = A )
% 5.44/5.71 = ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( if_real @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I5 = N2 ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % root_polyfun
% 5.44/5.71 thf(fact_8947_sum__gp0,axiom,
% 5.44/5.71 ! [X: complex,N2: nat] :
% 5.44/5.71 ( ( ( X = one_one_complex )
% 5.44/5.71 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.44/5.71 & ( ( X != one_one_complex )
% 5.44/5.71 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_gp0
% 5.44/5.71 thf(fact_8948_sum__gp0,axiom,
% 5.44/5.71 ! [X: real,N2: nat] :
% 5.44/5.71 ( ( ( X = one_one_real )
% 5.44/5.71 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.44/5.71 & ( ( X != one_one_real )
% 5.44/5.71 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_gp0
% 5.44/5.71 thf(fact_8949_gbinomial__sum__nat__pow2,axiom,
% 5.44/5.71 ! [M: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_sum_nat_pow2
% 5.44/5.71 thf(fact_8950_gbinomial__sum__nat__pow2,axiom,
% 5.44/5.71 ! [M: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_sum_nat_pow2
% 5.44/5.71 thf(fact_8951_gbinomial__partial__sum__poly__xpos,axiom,
% 5.44/5.71 ! [M: nat,A: complex,X: complex,Y: complex] :
% 5.44/5.71 ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_partial_sum_poly_xpos
% 5.44/5.71 thf(fact_8952_gbinomial__partial__sum__poly__xpos,axiom,
% 5.44/5.71 ! [M: nat,A: real,X: real,Y: real] :
% 5.44/5.71 ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_partial_sum_poly_xpos
% 5.44/5.71 thf(fact_8953_polyfun__diff__alt,axiom,
% 5.44/5.71 ! [N2: nat,A: nat > complex,X: complex,Y: complex] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( minus_minus_complex
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [J3: nat] :
% 5.44/5.71 ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K3 ) ) @ ( power_power_complex @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_diff_alt
% 5.44/5.71 thf(fact_8954_polyfun__diff__alt,axiom,
% 5.44/5.71 ! [N2: nat,A: nat > int,X: int,Y: int] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( minus_minus_int
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [J3: nat] :
% 5.44/5.71 ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K3 ) ) @ ( power_power_int @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_diff_alt
% 5.44/5.71 thf(fact_8955_polyfun__diff__alt,axiom,
% 5.44/5.71 ! [N2: nat,A: nat > real,X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( minus_minus_real
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [J3: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K3 ) ) @ ( power_power_real @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_diff_alt
% 5.44/5.71 thf(fact_8956_polyfun__extremal__lemma,axiom,
% 5.44/5.71 ! [E: real,C: nat > complex,N2: nat] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ E )
% 5.44/5.71 => ? [M8: real] :
% 5.44/5.71 ! [Z3: complex] :
% 5.44/5.71 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z3 ) )
% 5.44/5.71 => ( ord_less_eq_real
% 5.44/5.71 @ ( real_V1022390504157884413omplex
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_extremal_lemma
% 5.44/5.71 thf(fact_8957_polyfun__extremal__lemma,axiom,
% 5.44/5.71 ! [E: real,C: nat > real,N2: nat] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ E )
% 5.44/5.71 => ? [M8: real] :
% 5.44/5.71 ! [Z3: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z3 ) )
% 5.44/5.71 => ( ord_less_eq_real
% 5.44/5.71 @ ( real_V7735802525324610683m_real
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z3 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_extremal_lemma
% 5.44/5.71 thf(fact_8958_polyfun__diff,axiom,
% 5.44/5.71 ! [N2: nat,A: nat > complex,X: complex,Y: complex] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( minus_minus_complex
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [J3: nat] :
% 5.44/5.71 ( times_times_complex
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.44/5.71 @ ( power_power_complex @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_diff
% 5.44/5.71 thf(fact_8959_polyfun__diff,axiom,
% 5.44/5.71 ! [N2: nat,A: nat > int,X: int,Y: int] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( minus_minus_int
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [J3: nat] :
% 5.44/5.71 ( times_times_int
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.44/5.71 @ ( power_power_int @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_diff
% 5.44/5.71 thf(fact_8960_polyfun__diff,axiom,
% 5.44/5.71 ! [N2: nat,A: nat > real,X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.44/5.71 => ( ( minus_minus_real
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [J3: nat] :
% 5.44/5.71 ( times_times_real
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 5.44/5.71 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.44/5.71 @ ( power_power_real @ X @ J3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % polyfun_diff
% 5.44/5.71 thf(fact_8961_fact__code,axiom,
% 5.44/5.71 ( semiri1406184849735516958ct_int
% 5.44/5.71 = ( ^ [N: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_code
% 5.44/5.71 thf(fact_8962_fact__code,axiom,
% 5.44/5.71 ( semiri5044797733671781792omplex
% 5.44/5.71 = ( ^ [N: nat] : ( semiri8010041392384452111omplex @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_code
% 5.44/5.71 thf(fact_8963_fact__code,axiom,
% 5.44/5.71 ( semiri3624122377584611663nteger
% 5.44/5.71 = ( ^ [N: nat] : ( semiri4939895301339042750nteger @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_code
% 5.44/5.71 thf(fact_8964_fact__code,axiom,
% 5.44/5.71 ( semiri2265585572941072030t_real
% 5.44/5.71 = ( ^ [N: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_code
% 5.44/5.71 thf(fact_8965_fact__code,axiom,
% 5.44/5.71 ( semiri1408675320244567234ct_nat
% 5.44/5.71 = ( ^ [N: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_code
% 5.44/5.71 thf(fact_8966_gbinomial__r__part__sum,axiom,
% 5.44/5.71 ! [M: nat] :
% 5.44/5.71 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_r_part_sum
% 5.44/5.71 thf(fact_8967_gbinomial__r__part__sum,axiom,
% 5.44/5.71 ! [M: nat] :
% 5.44/5.71 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % gbinomial_r_part_sum
% 5.44/5.71 thf(fact_8968_choose__odd__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] :
% 5.44/5.71 ( if_int
% 5.44/5.71 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.44/5.71 @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) )
% 5.44/5.71 @ zero_zero_int )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_odd_sum
% 5.44/5.71 thf(fact_8969_choose__odd__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] :
% 5.44/5.71 ( if_complex
% 5.44/5.71 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.44/5.71 @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) )
% 5.44/5.71 @ zero_zero_complex )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_odd_sum
% 5.44/5.71 thf(fact_8970_choose__odd__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.44/5.71 @ ( groups7501900531339628137nteger
% 5.44/5.71 @ ^ [I5: nat] :
% 5.44/5.71 ( if_Code_integer
% 5.44/5.71 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.44/5.71 @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) )
% 5.44/5.71 @ zero_z3403309356797280102nteger )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_odd_sum
% 5.44/5.71 thf(fact_8971_choose__odd__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] :
% 5.44/5.71 ( if_real
% 5.44/5.71 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.44/5.71 @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) )
% 5.44/5.71 @ zero_zero_real )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_odd_sum
% 5.44/5.71 thf(fact_8972_choose__even__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.44/5.71 @ ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) @ zero_zero_int )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_even_sum
% 5.44/5.71 thf(fact_8973_choose__even__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) @ zero_zero_complex )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_even_sum
% 5.44/5.71 thf(fact_8974_choose__even__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.44/5.71 @ ( groups7501900531339628137nteger
% 5.44/5.71 @ ^ [I5: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) @ zero_z3403309356797280102nteger )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_even_sum
% 5.44/5.71 thf(fact_8975_choose__even__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) @ zero_zero_real )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.44/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_even_sum
% 5.44/5.71 thf(fact_8976_round__altdef,axiom,
% 5.44/5.71 ( archim8280529875227126926d_real
% 5.44/5.71 = ( ^ [X2: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X2 ) ) @ ( archim7802044766580827645g_real @ X2 ) @ ( archim6058952711729229775r_real @ X2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % round_altdef
% 5.44/5.71 thf(fact_8977_Maclaurin__sin__bound,axiom,
% 5.44/5.71 ! [X: real,N2: nat] :
% 5.44/5.71 ( ord_less_eq_real
% 5.44/5.71 @ ( abs_abs_real
% 5.44/5.71 @ ( minus_minus_real @ ( sin_real @ X )
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.44/5.71 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Maclaurin_sin_bound
% 5.44/5.71 thf(fact_8978_inverse__mult__distrib,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.44/5.71 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_mult_distrib
% 5.44/5.71 thf(fact_8979_inverse__mult__distrib,axiom,
% 5.44/5.71 ! [A: complex,B: complex] :
% 5.44/5.71 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.44/5.71 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_mult_distrib
% 5.44/5.71 thf(fact_8980_inverse__1,axiom,
% 5.44/5.71 ( ( inverse_inverse_real @ one_one_real )
% 5.44/5.71 = one_one_real ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_1
% 5.44/5.71 thf(fact_8981_inverse__1,axiom,
% 5.44/5.71 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.44/5.71 = one_one_complex ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_1
% 5.44/5.71 thf(fact_8982_inverse__eq__1__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ( inverse_inverse_real @ X )
% 5.44/5.71 = one_one_real )
% 5.44/5.71 = ( X = one_one_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_eq_1_iff
% 5.44/5.71 thf(fact_8983_inverse__eq__1__iff,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( ( invers8013647133539491842omplex @ X )
% 5.44/5.71 = one_one_complex )
% 5.44/5.71 = ( X = one_one_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_eq_1_iff
% 5.44/5.71 thf(fact_8984_inverse__divide,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.44/5.71 = ( divide_divide_real @ B @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_divide
% 5.44/5.71 thf(fact_8985_inverse__divide,axiom,
% 5.44/5.71 ! [A: complex,B: complex] :
% 5.44/5.71 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.44/5.71 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_divide
% 5.44/5.71 thf(fact_8986_binomial__Suc__n,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( binomial @ ( suc @ N2 ) @ N2 )
% 5.44/5.71 = ( suc @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_Suc_n
% 5.44/5.71 thf(fact_8987_binomial__n__n,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( binomial @ N2 @ N2 )
% 5.44/5.71 = one_one_nat ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_n_n
% 5.44/5.71 thf(fact_8988_inverse__nonnegative__iff__nonnegative,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.44/5.71 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_nonnegative_iff_nonnegative
% 5.44/5.71 thf(fact_8989_inverse__nonpositive__iff__nonpositive,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.44/5.71 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_nonpositive_iff_nonpositive
% 5.44/5.71 thf(fact_8990_inverse__positive__iff__positive,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.44/5.71 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_positive_iff_positive
% 5.44/5.71 thf(fact_8991_inverse__negative__iff__negative,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.44/5.71 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_negative_iff_negative
% 5.44/5.71 thf(fact_8992_inverse__less__iff__less__neg,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_less_iff_less_neg
% 5.44/5.71 thf(fact_8993_inverse__less__iff__less,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.71 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_less_iff_less
% 5.44/5.71 thf(fact_8994_binomial__0__Suc,axiom,
% 5.44/5.71 ! [K: nat] :
% 5.44/5.71 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.44/5.71 = zero_zero_nat ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_0_Suc
% 5.44/5.71 thf(fact_8995_binomial__1,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 5.44/5.71 = N2 ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_1
% 5.44/5.71 thf(fact_8996_binomial__eq__0__iff,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( ( binomial @ N2 @ K )
% 5.44/5.71 = zero_zero_nat )
% 5.44/5.71 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_eq_0_iff
% 5.44/5.71 thf(fact_8997_binomial__Suc__Suc,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.44/5.71 = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_Suc_Suc
% 5.44/5.71 thf(fact_8998_binomial__n__0,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( binomial @ N2 @ zero_zero_nat )
% 5.44/5.71 = one_one_nat ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_n_0
% 5.44/5.71 thf(fact_8999_prod__eq__1__iff,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 5.44/5.71 = one_one_nat )
% 5.44/5.71 = ( ! [X2: complex] :
% 5.44/5.71 ( ( member_complex @ X2 @ A2 )
% 5.44/5.71 => ( ( F @ X2 )
% 5.44/5.71 = one_one_nat ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_eq_1_iff
% 5.44/5.71 thf(fact_9000_prod__eq__1__iff,axiom,
% 5.44/5.71 ! [A2: set_nat,F: nat > nat] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 5.44/5.71 = one_one_nat )
% 5.44/5.71 = ( ! [X2: nat] :
% 5.44/5.71 ( ( member_nat @ X2 @ A2 )
% 5.44/5.71 => ( ( F @ X2 )
% 5.44/5.71 = one_one_nat ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_eq_1_iff
% 5.44/5.71 thf(fact_9001_inverse__le__iff__le,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_le_iff_le
% 5.44/5.71 thf(fact_9002_inverse__le__iff__le__neg,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_le_iff_le_neg
% 5.44/5.71 thf(fact_9003_right__inverse,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.44/5.71 = one_one_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % right_inverse
% 5.44/5.71 thf(fact_9004_right__inverse,axiom,
% 5.44/5.71 ! [A: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.44/5.71 = one_one_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % right_inverse
% 5.44/5.71 thf(fact_9005_left__inverse,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.44/5.71 = one_one_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % left_inverse
% 5.44/5.71 thf(fact_9006_left__inverse,axiom,
% 5.44/5.71 ! [A: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.44/5.71 = one_one_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % left_inverse
% 5.44/5.71 thf(fact_9007_inverse__eq__divide__numeral,axiom,
% 5.44/5.71 ! [W: num] :
% 5.44/5.71 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 5.44/5.71 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_eq_divide_numeral
% 5.44/5.71 thf(fact_9008_inverse__eq__divide__numeral,axiom,
% 5.44/5.71 ! [W: num] :
% 5.44/5.71 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.44/5.71 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_eq_divide_numeral
% 5.44/5.71 thf(fact_9009_zero__less__binomial__iff,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 5.44/5.71 = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % zero_less_binomial_iff
% 5.44/5.71 thf(fact_9010_prod__pos__nat__iff,axiom,
% 5.44/5.71 ! [A2: set_complex,F: complex > nat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ A2 )
% 5.44/5.71 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 5.44/5.71 = ( ! [X2: complex] :
% 5.44/5.71 ( ( member_complex @ X2 @ A2 )
% 5.44/5.71 => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_pos_nat_iff
% 5.44/5.71 thf(fact_9011_prod__pos__nat__iff,axiom,
% 5.44/5.71 ! [A2: set_nat,F: nat > nat] :
% 5.44/5.71 ( ( finite_finite_nat @ A2 )
% 5.44/5.71 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.44/5.71 = ( ! [X2: nat] :
% 5.44/5.71 ( ( member_nat @ X2 @ A2 )
% 5.44/5.71 => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_pos_nat_iff
% 5.44/5.71 thf(fact_9012_inverse__eq__divide__neg__numeral,axiom,
% 5.44/5.71 ! [W: num] :
% 5.44/5.71 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.44/5.71 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_eq_divide_neg_numeral
% 5.44/5.71 thf(fact_9013_inverse__eq__divide__neg__numeral,axiom,
% 5.44/5.71 ! [W: num] :
% 5.44/5.71 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.71 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_eq_divide_neg_numeral
% 5.44/5.71 thf(fact_9014_real__sqrt__inverse,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 5.44/5.71 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_sqrt_inverse
% 5.44/5.71 thf(fact_9015_power__inverse,axiom,
% 5.44/5.71 ! [A: real,N2: nat] :
% 5.44/5.71 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N2 )
% 5.44/5.71 = ( inverse_inverse_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % power_inverse
% 5.44/5.71 thf(fact_9016_power__inverse,axiom,
% 5.44/5.71 ! [A: complex,N2: nat] :
% 5.44/5.71 ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N2 )
% 5.44/5.71 = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % power_inverse
% 5.44/5.71 thf(fact_9017_mult__commute__imp__mult__inverse__commute,axiom,
% 5.44/5.71 ! [Y: real,X: real] :
% 5.44/5.71 ( ( ( times_times_real @ Y @ X )
% 5.44/5.71 = ( times_times_real @ X @ Y ) )
% 5.44/5.71 => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X )
% 5.44/5.71 = ( times_times_real @ X @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_commute_imp_mult_inverse_commute
% 5.44/5.71 thf(fact_9018_mult__commute__imp__mult__inverse__commute,axiom,
% 5.44/5.71 ! [Y: complex,X: complex] :
% 5.44/5.71 ( ( ( times_times_complex @ Y @ X )
% 5.44/5.71 = ( times_times_complex @ X @ Y ) )
% 5.44/5.71 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y ) @ X )
% 5.44/5.71 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_commute_imp_mult_inverse_commute
% 5.44/5.71 thf(fact_9019_choose__one,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( binomial @ N2 @ one_one_nat )
% 5.44/5.71 = N2 ) ).
% 5.44/5.71
% 5.44/5.71 % choose_one
% 5.44/5.71 thf(fact_9020_norm__inverse__le__norm,axiom,
% 5.44/5.71 ! [R: real,X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ R @ ( real_V7735802525324610683m_real @ X ) )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X ) ) @ ( inverse_inverse_real @ R ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_inverse_le_norm
% 5.44/5.71 thf(fact_9021_norm__inverse__le__norm,axiom,
% 5.44/5.71 ! [R: real,X: complex] :
% 5.44/5.71 ( ( ord_less_eq_real @ R @ ( real_V1022390504157884413omplex @ X ) )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X ) ) @ ( inverse_inverse_real @ R ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_inverse_le_norm
% 5.44/5.71 thf(fact_9022_binomial__eq__0,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( ord_less_nat @ N2 @ K )
% 5.44/5.71 => ( ( binomial @ N2 @ K )
% 5.44/5.71 = zero_zero_nat ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_eq_0
% 5.44/5.71 thf(fact_9023_inverse__less__imp__less,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ord_less_real @ B @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_less_imp_less
% 5.44/5.71 thf(fact_9024_less__imp__inverse__less,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ A @ B )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % less_imp_inverse_less
% 5.44/5.71 thf(fact_9025_inverse__less__imp__less__neg,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.71 => ( ord_less_real @ B @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_less_imp_less_neg
% 5.44/5.71 thf(fact_9026_less__imp__inverse__less__neg,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ A @ B )
% 5.44/5.71 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.71 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % less_imp_inverse_less_neg
% 5.44/5.71 thf(fact_9027_inverse__negative__imp__negative,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.44/5.71 => ( ( A != zero_zero_real )
% 5.44/5.71 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_negative_imp_negative
% 5.44/5.71 thf(fact_9028_inverse__positive__imp__positive,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.44/5.71 => ( ( A != zero_zero_real )
% 5.44/5.71 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_positive_imp_positive
% 5.44/5.71 thf(fact_9029_negative__imp__inverse__negative,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.71 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % negative_imp_inverse_negative
% 5.44/5.71 thf(fact_9030_positive__imp__inverse__positive,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % positive_imp_inverse_positive
% 5.44/5.71 thf(fact_9031_nonzero__inverse__mult__distrib,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( B != zero_zero_real )
% 5.44/5.71 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.44/5.71 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % nonzero_inverse_mult_distrib
% 5.44/5.71 thf(fact_9032_nonzero__inverse__mult__distrib,axiom,
% 5.44/5.71 ! [A: complex,B: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( B != zero_zero_complex )
% 5.44/5.71 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.44/5.71 = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % nonzero_inverse_mult_distrib
% 5.44/5.71 thf(fact_9033_Suc__times__binomial,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) )
% 5.44/5.71 = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Suc_times_binomial
% 5.44/5.71 thf(fact_9034_Suc__times__binomial__eq,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) )
% 5.44/5.71 = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Suc_times_binomial_eq
% 5.44/5.71 thf(fact_9035_inverse__numeral__1,axiom,
% 5.44/5.71 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.44/5.71 = ( numeral_numeral_real @ one ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_numeral_1
% 5.44/5.71 thf(fact_9036_inverse__numeral__1,axiom,
% 5.44/5.71 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.44/5.71 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_numeral_1
% 5.44/5.71 thf(fact_9037_inverse__unique,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ( times_times_real @ A @ B )
% 5.44/5.71 = one_one_real )
% 5.44/5.71 => ( ( inverse_inverse_real @ A )
% 5.44/5.71 = B ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_unique
% 5.44/5.71 thf(fact_9038_inverse__unique,axiom,
% 5.44/5.71 ! [A: complex,B: complex] :
% 5.44/5.71 ( ( ( times_times_complex @ A @ B )
% 5.44/5.71 = one_one_complex )
% 5.44/5.71 => ( ( invers8013647133539491842omplex @ A )
% 5.44/5.71 = B ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_unique
% 5.44/5.71 thf(fact_9039_divide__inverse__commute,axiom,
% 5.44/5.71 ( divide_divide_real
% 5.44/5.71 = ( ^ [A4: real,B4: real] : ( times_times_real @ ( inverse_inverse_real @ B4 ) @ A4 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % divide_inverse_commute
% 5.44/5.71 thf(fact_9040_divide__inverse__commute,axiom,
% 5.44/5.71 ( divide1717551699836669952omplex
% 5.44/5.71 = ( ^ [A4: complex,B4: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B4 ) @ A4 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % divide_inverse_commute
% 5.44/5.71 thf(fact_9041_divide__inverse,axiom,
% 5.44/5.71 ( divide_divide_real
% 5.44/5.71 = ( ^ [A4: real,B4: real] : ( times_times_real @ A4 @ ( inverse_inverse_real @ B4 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % divide_inverse
% 5.44/5.71 thf(fact_9042_divide__inverse,axiom,
% 5.44/5.71 ( divide1717551699836669952omplex
% 5.44/5.71 = ( ^ [A4: complex,B4: complex] : ( times_times_complex @ A4 @ ( invers8013647133539491842omplex @ B4 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % divide_inverse
% 5.44/5.71 thf(fact_9043_field__class_Ofield__divide__inverse,axiom,
% 5.44/5.71 ( divide_divide_real
% 5.44/5.71 = ( ^ [A4: real,B4: real] : ( times_times_real @ A4 @ ( inverse_inverse_real @ B4 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % field_class.field_divide_inverse
% 5.44/5.71 thf(fact_9044_field__class_Ofield__divide__inverse,axiom,
% 5.44/5.71 ( divide1717551699836669952omplex
% 5.44/5.71 = ( ^ [A4: complex,B4: complex] : ( times_times_complex @ A4 @ ( invers8013647133539491842omplex @ B4 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % field_class.field_divide_inverse
% 5.44/5.71 thf(fact_9045_choose__mult__lemma,axiom,
% 5.44/5.71 ! [M: nat,R: nat,K: nat] :
% 5.44/5.71 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.44/5.71 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_mult_lemma
% 5.44/5.71 thf(fact_9046_power__mult__power__inverse__commute,axiom,
% 5.44/5.71 ! [X: real,M: nat,N2: nat] :
% 5.44/5.71 ( ( times_times_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ N2 ) )
% 5.44/5.71 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X ) @ N2 ) @ ( power_power_real @ X @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % power_mult_power_inverse_commute
% 5.44/5.71 thf(fact_9047_power__mult__power__inverse__commute,axiom,
% 5.44/5.71 ! [X: complex,M: nat,N2: nat] :
% 5.44/5.71 ( ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ N2 ) )
% 5.44/5.71 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ N2 ) @ ( power_power_complex @ X @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % power_mult_power_inverse_commute
% 5.44/5.71 thf(fact_9048_power__mult__inverse__distrib,axiom,
% 5.44/5.71 ! [X: real,M: nat] :
% 5.44/5.71 ( ( times_times_real @ ( power_power_real @ X @ M ) @ ( inverse_inverse_real @ X ) )
% 5.44/5.71 = ( times_times_real @ ( inverse_inverse_real @ X ) @ ( power_power_real @ X @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % power_mult_inverse_distrib
% 5.44/5.71 thf(fact_9049_power__mult__inverse__distrib,axiom,
% 5.44/5.71 ! [X: complex,M: nat] :
% 5.44/5.71 ( ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( invers8013647133539491842omplex @ X ) )
% 5.44/5.71 = ( times_times_complex @ ( invers8013647133539491842omplex @ X ) @ ( power_power_complex @ X @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % power_mult_inverse_distrib
% 5.44/5.71 thf(fact_9050_binomial__symmetric,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( binomial @ N2 @ K )
% 5.44/5.71 = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_symmetric
% 5.44/5.71 thf(fact_9051_inverse__eq__divide,axiom,
% 5.44/5.71 ( inverse_inverse_real
% 5.44/5.71 = ( divide_divide_real @ one_one_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_eq_divide
% 5.44/5.71 thf(fact_9052_inverse__eq__divide,axiom,
% 5.44/5.71 ( invers8013647133539491842omplex
% 5.44/5.71 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_eq_divide
% 5.44/5.71 thf(fact_9053_binomial__le__pow,axiom,
% 5.44/5.71 ! [R: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ R @ N2 )
% 5.44/5.71 => ( ord_less_eq_nat @ ( binomial @ N2 @ R ) @ ( power_power_nat @ N2 @ R ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_le_pow
% 5.44/5.71 thf(fact_9054_mult__inverse__of__nat__commute,axiom,
% 5.44/5.71 ! [Xa2: nat,X: real] :
% 5.44/5.71 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa2 ) ) @ X )
% 5.44/5.71 = ( times_times_real @ X @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_inverse_of_nat_commute
% 5.44/5.71 thf(fact_9055_mult__inverse__of__nat__commute,axiom,
% 5.44/5.71 ! [Xa2: nat,X: complex] :
% 5.44/5.71 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa2 ) ) @ X )
% 5.44/5.71 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_inverse_of_nat_commute
% 5.44/5.71 thf(fact_9056_mult__inverse__of__int__commute,axiom,
% 5.44/5.71 ! [Xa2: int,X: real] :
% 5.44/5.71 ( ( times_times_real @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa2 ) ) @ X )
% 5.44/5.71 = ( times_times_real @ X @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_inverse_of_int_commute
% 5.44/5.71 thf(fact_9057_mult__inverse__of__int__commute,axiom,
% 5.44/5.71 ! [Xa2: int,X: complex] :
% 5.44/5.71 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa2 ) ) @ X )
% 5.44/5.71 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_inverse_of_int_commute
% 5.44/5.71 thf(fact_9058_divide__real__def,axiom,
% 5.44/5.71 ( divide_divide_real
% 5.44/5.71 = ( ^ [X2: real,Y3: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y3 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % divide_real_def
% 5.44/5.71 thf(fact_9059_frac__ge__0,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % frac_ge_0
% 5.44/5.71 thf(fact_9060_frac__lt__1,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 5.44/5.71
% 5.44/5.71 % frac_lt_1
% 5.44/5.71 thf(fact_9061_frac__1__eq,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ one_one_real ) )
% 5.44/5.71 = ( archim2898591450579166408c_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % frac_1_eq
% 5.44/5.71 thf(fact_9062_inverse__le__imp__le,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_le_imp_le
% 5.44/5.71 thf(fact_9063_le__imp__inverse__le,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % le_imp_inverse_le
% 5.44/5.71 thf(fact_9064_inverse__le__imp__le__neg,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.71 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_le_imp_le_neg
% 5.44/5.71 thf(fact_9065_le__imp__inverse__le__neg,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.71 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.44/5.71 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % le_imp_inverse_le_neg
% 5.44/5.71 thf(fact_9066_zero__less__binomial,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % zero_less_binomial
% 5.44/5.71 thf(fact_9067_inverse__le__1__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 5.44/5.71 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.71 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_le_1_iff
% 5.44/5.71 thf(fact_9068_one__less__inverse__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 5.44/5.71 = ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % one_less_inverse_iff
% 5.44/5.71 thf(fact_9069_one__less__inverse,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ( ord_less_real @ A @ one_one_real )
% 5.44/5.71 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % one_less_inverse
% 5.44/5.71 thf(fact_9070_division__ring__inverse__add,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( B != zero_zero_real )
% 5.44/5.71 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % division_ring_inverse_add
% 5.44/5.71 thf(fact_9071_division__ring__inverse__add,axiom,
% 5.44/5.71 ! [A: complex,B: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( B != zero_zero_complex )
% 5.44/5.71 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.44/5.71 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % division_ring_inverse_add
% 5.44/5.71 thf(fact_9072_inverse__add,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( B != zero_zero_real )
% 5.44/5.71 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_add
% 5.44/5.71 thf(fact_9073_inverse__add,axiom,
% 5.44/5.71 ! [A: complex,B: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( B != zero_zero_complex )
% 5.44/5.71 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.44/5.71 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_add
% 5.44/5.71 thf(fact_9074_field__class_Ofield__inverse,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.44/5.71 = one_one_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % field_class.field_inverse
% 5.44/5.71 thf(fact_9075_field__class_Ofield__inverse,axiom,
% 5.44/5.71 ! [A: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.44/5.71 = one_one_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % field_class.field_inverse
% 5.44/5.71 thf(fact_9076_division__ring__inverse__diff,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( B != zero_zero_real )
% 5.44/5.71 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % division_ring_inverse_diff
% 5.44/5.71 thf(fact_9077_division__ring__inverse__diff,axiom,
% 5.44/5.71 ! [A: complex,B: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( B != zero_zero_complex )
% 5.44/5.71 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.44/5.71 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % division_ring_inverse_diff
% 5.44/5.71 thf(fact_9078_Suc__times__binomial__add,axiom,
% 5.44/5.71 ! [A: nat,B: nat] :
% 5.44/5.71 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.44/5.71 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Suc_times_binomial_add
% 5.44/5.71 thf(fact_9079_nonzero__inverse__eq__divide,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( inverse_inverse_real @ A )
% 5.44/5.71 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % nonzero_inverse_eq_divide
% 5.44/5.71 thf(fact_9080_nonzero__inverse__eq__divide,axiom,
% 5.44/5.71 ! [A: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( invers8013647133539491842omplex @ A )
% 5.44/5.71 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % nonzero_inverse_eq_divide
% 5.44/5.71 thf(fact_9081_binomial__Suc__Suc__eq__times,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.44/5.71 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) @ ( suc @ K ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_Suc_Suc_eq_times
% 5.44/5.71 thf(fact_9082_choose__mult,axiom,
% 5.44/5.71 ! [K: nat,M: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ M )
% 5.44/5.71 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 5.44/5.71 = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_mult
% 5.44/5.71 thf(fact_9083_binomial__absorb__comp,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 5.44/5.71 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_absorb_comp
% 5.44/5.71 thf(fact_9084_inverse__powr,axiom,
% 5.44/5.71 ! [Y: real,A: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.71 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 5.44/5.71 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_powr
% 5.44/5.71 thf(fact_9085_sum__choose__upper,axiom,
% 5.44/5.71 ! [M: nat,N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_choose_upper
% 5.44/5.71 thf(fact_9086_inverse__less__iff,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.71 => ( ord_less_real @ B @ A ) )
% 5.44/5.71 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.44/5.71 => ( ord_less_real @ A @ B ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_less_iff
% 5.44/5.71 thf(fact_9087_inverse__le__iff,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.44/5.71 => ( ord_less_eq_real @ B @ A ) )
% 5.44/5.71 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.44/5.71 => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_le_iff
% 5.44/5.71 thf(fact_9088_one__le__inverse,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.44/5.71 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % one_le_inverse
% 5.44/5.71 thf(fact_9089_inverse__less__1__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 5.44/5.71 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.71 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_less_1_iff
% 5.44/5.71 thf(fact_9090_one__le__inverse__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 5.44/5.71 = ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 & ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % one_le_inverse_iff
% 5.44/5.71 thf(fact_9091_inverse__diff__inverse,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( A != zero_zero_real )
% 5.44/5.71 => ( ( B != zero_zero_real )
% 5.44/5.71 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.44/5.71 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_diff_inverse
% 5.44/5.71 thf(fact_9092_inverse__diff__inverse,axiom,
% 5.44/5.71 ! [A: complex,B: complex] :
% 5.44/5.71 ( ( A != zero_zero_complex )
% 5.44/5.71 => ( ( B != zero_zero_complex )
% 5.44/5.71 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.44/5.71 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_diff_inverse
% 5.44/5.71 thf(fact_9093_reals__Archimedean,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 => ? [N4: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % reals_Archimedean
% 5.44/5.71 thf(fact_9094_binomial__absorption,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 5.44/5.71 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_absorption
% 5.44/5.71 thf(fact_9095_binomial__fact__lemma,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 5.44/5.71 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_fact_lemma
% 5.44/5.71 thf(fact_9096_forall__pos__mono__1,axiom,
% 5.44/5.71 ! [P: real > $o,E: real] :
% 5.44/5.71 ( ! [D3: real,E2: real] :
% 5.44/5.71 ( ( ord_less_real @ D3 @ E2 )
% 5.44/5.71 => ( ( P @ D3 )
% 5.44/5.71 => ( P @ E2 ) ) )
% 5.44/5.71 => ( ! [N4: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.44/5.71 => ( P @ E ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % forall_pos_mono_1
% 5.44/5.71 thf(fact_9097_forall__pos__mono,axiom,
% 5.44/5.71 ! [P: real > $o,E: real] :
% 5.44/5.71 ( ! [D3: real,E2: real] :
% 5.44/5.71 ( ( ord_less_real @ D3 @ E2 )
% 5.44/5.71 => ( ( P @ D3 )
% 5.44/5.71 => ( P @ E2 ) ) )
% 5.44/5.71 => ( ! [N4: nat] :
% 5.44/5.71 ( ( N4 != zero_zero_nat )
% 5.44/5.71 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) ) )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.44/5.71 => ( P @ E ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % forall_pos_mono
% 5.44/5.71 thf(fact_9098_real__arch__inverse,axiom,
% 5.44/5.71 ! [E: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ E )
% 5.44/5.71 = ( ? [N: nat] :
% 5.44/5.71 ( ( N != zero_zero_nat )
% 5.44/5.71 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.44/5.71 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ E ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_arch_inverse
% 5.44/5.71 thf(fact_9099_sqrt__divide__self__eq,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 5.44/5.71 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sqrt_divide_self_eq
% 5.44/5.71 thf(fact_9100_ln__inverse,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 5.44/5.71 = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % ln_inverse
% 5.44/5.71 thf(fact_9101_prod__int__plus__eq,axiom,
% 5.44/5.71 ! [I2: nat,J: nat] :
% 5.44/5.71 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 5.44/5.71 = ( groups1705073143266064639nt_int
% 5.44/5.71 @ ^ [X2: int] : X2
% 5.44/5.71 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod_int_plus_eq
% 5.44/5.71 thf(fact_9102_summable__exp,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( summable_complex
% 5.44/5.71 @ ^ [N: nat] : ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri5044797733671781792omplex @ N ) ) @ ( power_power_complex @ X @ N ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_exp
% 5.44/5.71 thf(fact_9103_summable__exp,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( summable_real
% 5.44/5.71 @ ^ [N: nat] : ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_exp
% 5.44/5.71 thf(fact_9104_sum__choose__lower,axiom,
% 5.44/5.71 ! [R: nat,N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R @ K3 ) @ K3 )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N2 ) ) @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_choose_lower
% 5.44/5.71 thf(fact_9105_choose__rising__sum_I1_J,axiom,
% 5.44/5.71 ! [N2: nat,M: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_rising_sum(1)
% 5.44/5.71 thf(fact_9106_choose__rising__sum_I2_J,axiom,
% 5.44/5.71 ! [N2: nat,M: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_rising_sum(2)
% 5.44/5.71 thf(fact_9107_binomial__ge__n__over__k__pow__k,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_ge_n_over_k_pow_k
% 5.44/5.71 thf(fact_9108_binomial__maximum_H,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_maximum'
% 5.44/5.71 thf(fact_9109_binomial__mono,axiom,
% 5.44/5.71 ! [K: nat,K6: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ K6 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.44/5.71 => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_mono
% 5.44/5.71 thf(fact_9110_binomial__antimono,axiom,
% 5.44/5.71 ! [K: nat,K6: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ K6 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.44/5.71 => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_antimono
% 5.44/5.71 thf(fact_9111_binomial__maximum,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_maximum
% 5.44/5.71 thf(fact_9112_binomial__le__pow2,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_le_pow2
% 5.44/5.71 thf(fact_9113_choose__reduce__nat,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.71 => ( ( binomial @ N2 @ K )
% 5.44/5.71 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_reduce_nat
% 5.44/5.71 thf(fact_9114_times__binomial__minus1__eq,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.44/5.71 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 5.44/5.71 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % times_binomial_minus1_eq
% 5.44/5.71 thf(fact_9115_ex__inverse__of__nat__less,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 => ? [N4: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.44/5.71 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % ex_inverse_of_nat_less
% 5.44/5.71 thf(fact_9116_power__diff__conv__inverse,axiom,
% 5.44/5.71 ! [X: real,M: nat,N2: nat] :
% 5.44/5.71 ( ( X != zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( power_power_real @ X @ ( minus_minus_nat @ N2 @ M ) )
% 5.44/5.71 = ( times_times_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ M ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % power_diff_conv_inverse
% 5.44/5.71 thf(fact_9117_power__diff__conv__inverse,axiom,
% 5.44/5.71 ! [X: complex,M: nat,N2: nat] :
% 5.44/5.71 ( ( X != zero_zero_complex )
% 5.44/5.71 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ M ) )
% 5.44/5.71 = ( times_times_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ M ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % power_diff_conv_inverse
% 5.44/5.71 thf(fact_9118_binomial__altdef__nat,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( binomial @ N2 @ K )
% 5.44/5.71 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_altdef_nat
% 5.44/5.71 thf(fact_9119_frac__eq,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ( archim2898591450579166408c_real @ X )
% 5.44/5.71 = X )
% 5.44/5.71 = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % frac_eq
% 5.44/5.71 thf(fact_9120_log__inverse,axiom,
% 5.44/5.71 ! [A: real,X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ( A != one_one_real )
% 5.44/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 5.44/5.71 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % log_inverse
% 5.44/5.71 thf(fact_9121_frac__add,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.44/5.71 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 5.44/5.71 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.44/5.71 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.71 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % frac_add
% 5.44/5.71 thf(fact_9122_ln__prod,axiom,
% 5.44/5.71 ! [I6: set_real,F: real > real] :
% 5.44/5.71 ( ( finite_finite_real @ I6 )
% 5.44/5.71 => ( ! [I4: real] :
% 5.44/5.71 ( ( member_real @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.71 => ( ( ln_ln_real @ ( groups1681761925125756287l_real @ F @ I6 ) )
% 5.44/5.71 = ( groups8097168146408367636l_real
% 5.44/5.71 @ ^ [X2: real] : ( ln_ln_real @ ( F @ X2 ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % ln_prod
% 5.44/5.71 thf(fact_9123_ln__prod,axiom,
% 5.44/5.71 ! [I6: set_int,F: int > real] :
% 5.44/5.71 ( ( finite_finite_int @ I6 )
% 5.44/5.71 => ( ! [I4: int] :
% 5.44/5.71 ( ( member_int @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.71 => ( ( ln_ln_real @ ( groups2316167850115554303t_real @ F @ I6 ) )
% 5.44/5.71 = ( groups8778361861064173332t_real
% 5.44/5.71 @ ^ [X2: int] : ( ln_ln_real @ ( F @ X2 ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % ln_prod
% 5.44/5.71 thf(fact_9124_ln__prod,axiom,
% 5.44/5.71 ! [I6: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > real] :
% 5.44/5.71 ( ( finite6177210948735845034at_nat @ I6 )
% 5.44/5.71 => ( ! [I4: product_prod_nat_nat] :
% 5.44/5.71 ( ( member8440522571783428010at_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.71 => ( ( ln_ln_real @ ( groups6036352826371341000t_real @ F @ I6 ) )
% 5.44/5.71 = ( groups4567486121110086003t_real
% 5.44/5.71 @ ^ [X2: product_prod_nat_nat] : ( ln_ln_real @ ( F @ X2 ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % ln_prod
% 5.44/5.71 thf(fact_9125_ln__prod,axiom,
% 5.44/5.71 ! [I6: set_complex,F: complex > real] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ I6 )
% 5.44/5.71 => ( ! [I4: complex] :
% 5.44/5.71 ( ( member_complex @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.71 => ( ( ln_ln_real @ ( groups766887009212190081x_real @ F @ I6 ) )
% 5.44/5.71 = ( groups5808333547571424918x_real
% 5.44/5.71 @ ^ [X2: complex] : ( ln_ln_real @ ( F @ X2 ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % ln_prod
% 5.44/5.71 thf(fact_9126_ln__prod,axiom,
% 5.44/5.71 ! [I6: set_nat,F: nat > real] :
% 5.44/5.71 ( ( finite_finite_nat @ I6 )
% 5.44/5.71 => ( ! [I4: nat] :
% 5.44/5.71 ( ( member_nat @ I4 @ I6 )
% 5.44/5.71 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.44/5.71 => ( ( ln_ln_real @ ( groups129246275422532515t_real @ F @ I6 ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [X2: nat] : ( ln_ln_real @ ( F @ X2 ) )
% 5.44/5.71 @ I6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % ln_prod
% 5.44/5.71 thf(fact_9127_sum__choose__diagonal,axiom,
% 5.44/5.71 ! [M: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.71 => ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sum_choose_diagonal
% 5.44/5.71 thf(fact_9128_vandermonde,axiom,
% 5.44/5.71 ! [M: nat,N2: nat,R: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ R ) )
% 5.44/5.71 = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R ) ) ).
% 5.44/5.71
% 5.44/5.71 % vandermonde
% 5.44/5.71 thf(fact_9129_binomial__less__binomial__Suc,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.71 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_less_binomial_Suc
% 5.44/5.71 thf(fact_9130_binomial__strict__antimono,axiom,
% 5.44/5.71 ! [K: nat,K6: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ K @ K6 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.44/5.71 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.44/5.71 => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_strict_antimono
% 5.44/5.71 thf(fact_9131_binomial__strict__mono,axiom,
% 5.44/5.71 ! [K: nat,K6: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ K @ K6 )
% 5.44/5.71 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.44/5.71 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_strict_mono
% 5.44/5.71 thf(fact_9132_central__binomial__odd,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.71 => ( ( binomial @ N2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.71 = ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % central_binomial_odd
% 5.44/5.71 thf(fact_9133_binomial__addition__formula,axiom,
% 5.44/5.71 ! [N2: nat,K: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( binomial @ N2 @ ( suc @ K ) )
% 5.44/5.71 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_addition_formula
% 5.44/5.71 thf(fact_9134_fact__binomial,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) ) )
% 5.44/5.71 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_binomial
% 5.44/5.71 thf(fact_9135_fact__binomial,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) )
% 5.44/5.71 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % fact_binomial
% 5.44/5.71 thf(fact_9136_binomial__fact,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) )
% 5.44/5.71 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_fact
% 5.44/5.71 thf(fact_9137_binomial__fact,axiom,
% 5.44/5.71 ! [K: nat,N2: nat] :
% 5.44/5.71 ( ( ord_less_eq_nat @ K @ N2 )
% 5.44/5.71 => ( ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) )
% 5.44/5.71 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_fact
% 5.44/5.71 thf(fact_9138_exp__plus__inverse__exp,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_plus_inverse_exp
% 5.44/5.71 thf(fact_9139_prod_Otriangle__reindex__eq,axiom,
% 5.44/5.71 ! [G: nat > nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.44/5.71 @ ( collec3392354462482085612at_nat
% 5.44/5.71 @ ( produc6081775807080527818_nat_o
% 5.44/5.71 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.triangle_reindex_eq
% 5.44/5.71 thf(fact_9140_prod_Otriangle__reindex__eq,axiom,
% 5.44/5.71 ! [G: nat > nat > int,N2: nat] :
% 5.44/5.71 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.44/5.71 @ ( collec3392354462482085612at_nat
% 5.44/5.71 @ ( produc6081775807080527818_nat_o
% 5.44/5.71 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.triangle_reindex_eq
% 5.44/5.71 thf(fact_9141_choose__row__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_row_sum
% 5.44/5.71 thf(fact_9142_binomial,axiom,
% 5.44/5.71 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.71 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial
% 5.44/5.71 thf(fact_9143_choose__two,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_two
% 5.44/5.71 thf(fact_9144_plus__inverse__ge__2,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % plus_inverse_ge_2
% 5.44/5.71 thf(fact_9145_binomial__ring,axiom,
% 5.44/5.71 ! [A: int,B: int,N2: nat] :
% 5.44/5.71 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_ring
% 5.44/5.71 thf(fact_9146_binomial__ring,axiom,
% 5.44/5.71 ! [A: complex,B: complex,N2: nat] :
% 5.44/5.71 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_ring
% 5.44/5.71 thf(fact_9147_binomial__ring,axiom,
% 5.44/5.71 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.44/5.71 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups7501900531339628137nteger
% 5.44/5.71 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K3 ) ) @ ( power_8256067586552552935nteger @ A @ K3 ) ) @ ( power_8256067586552552935nteger @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_ring
% 5.44/5.71 thf(fact_9148_binomial__ring,axiom,
% 5.44/5.71 ! [A: nat,B: nat,N2: nat] :
% 5.44/5.71 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_ring
% 5.44/5.71 thf(fact_9149_binomial__ring,axiom,
% 5.44/5.71 ! [A: real,B: real,N2: nat] :
% 5.44/5.71 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_ring
% 5.44/5.71 thf(fact_9150_real__inv__sqrt__pow2,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( inverse_inverse_real @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_inv_sqrt_pow2
% 5.44/5.71 thf(fact_9151_pochhammer__binomial__sum,axiom,
% 5.44/5.71 ! [A: int,B: int,N2: nat] :
% 5.44/5.71 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_binomial_sum
% 5.44/5.71 thf(fact_9152_pochhammer__binomial__sum,axiom,
% 5.44/5.71 ! [A: complex,B: complex,N2: nat] :
% 5.44/5.71 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( comm_s2602460028002588243omplex @ A @ K3 ) ) @ ( comm_s2602460028002588243omplex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_binomial_sum
% 5.44/5.71 thf(fact_9153_pochhammer__binomial__sum,axiom,
% 5.44/5.71 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.44/5.71 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups7501900531339628137nteger
% 5.44/5.71 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K3 ) ) @ ( comm_s8582702949713902594nteger @ A @ K3 ) ) @ ( comm_s8582702949713902594nteger @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_binomial_sum
% 5.44/5.71 thf(fact_9154_pochhammer__binomial__sum,axiom,
% 5.44/5.71 ! [A: real,B: real,N2: nat] :
% 5.44/5.71 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pochhammer_binomial_sum
% 5.44/5.71 thf(fact_9155_choose__square__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N2 @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_square_sum
% 5.44/5.71 thf(fact_9156_prod_Otriangle__reindex,axiom,
% 5.44/5.71 ! [G: nat > nat > nat,N2: nat] :
% 5.44/5.71 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.44/5.71 @ ( collec3392354462482085612at_nat
% 5.44/5.71 @ ( produc6081775807080527818_nat_o
% 5.44/5.71 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups708209901874060359at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.triangle_reindex
% 5.44/5.71 thf(fact_9157_prod_Otriangle__reindex,axiom,
% 5.44/5.71 ! [G: nat > nat > int,N2: nat] :
% 5.44/5.71 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.44/5.71 @ ( collec3392354462482085612at_nat
% 5.44/5.71 @ ( produc6081775807080527818_nat_o
% 5.44/5.71 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.44/5.71 = ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [K3: nat] :
% 5.44/5.71 ( groups705719431365010083at_int
% 5.44/5.71 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ K3 ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.triangle_reindex
% 5.44/5.71 thf(fact_9158_tan__cot,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.44/5.71 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % tan_cot
% 5.44/5.71 thf(fact_9159_floor__add,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.44/5.71 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 5.44/5.71 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.44/5.71 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % floor_add
% 5.44/5.71 thf(fact_9160_real__le__x__sinh,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_le_x_sinh
% 5.44/5.71 thf(fact_9161_real__le__abs__sinh,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_le_abs_sinh
% 5.44/5.71 thf(fact_9162_tan__sec,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ( cos_real @ X )
% 5.44/5.71 != zero_zero_real )
% 5.44/5.71 => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.71 = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % tan_sec
% 5.44/5.71 thf(fact_9163_tan__sec,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( ( cos_complex @ X )
% 5.44/5.71 != zero_zero_complex )
% 5.44/5.71 => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.71 = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % tan_sec
% 5.44/5.71 thf(fact_9164_choose__alternating__linear__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( N2 != one_one_nat )
% 5.44/5.71 => ( ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I5 ) @ ( semiri1314217659103216013at_int @ I5 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_int ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_alternating_linear_sum
% 5.44/5.71 thf(fact_9165_choose__alternating__linear__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( N2 != one_one_nat )
% 5.44/5.71 => ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I5 ) @ ( semiri8010041392384452111omplex @ I5 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_alternating_linear_sum
% 5.44/5.71 thf(fact_9166_choose__alternating__linear__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( N2 != one_one_nat )
% 5.44/5.71 => ( ( groups7501900531339628137nteger
% 5.44/5.71 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I5 ) @ ( semiri4939895301339042750nteger @ I5 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_alternating_linear_sum
% 5.44/5.71 thf(fact_9167_choose__alternating__linear__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( N2 != one_one_nat )
% 5.44/5.71 => ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( semiri5074537144036343181t_real @ I5 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_alternating_linear_sum
% 5.44/5.71 thf(fact_9168_binomial__r__part__sum,axiom,
% 5.44/5.71 ! [M: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.44/5.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_r_part_sum
% 5.44/5.71 thf(fact_9169_choose__linear__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( groups3542108847815614940at_nat
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_nat @ I5 @ ( binomial @ N2 @ I5 ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_linear_sum
% 5.44/5.71 thf(fact_9170_choose__alternating__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( groups3539618377306564664at_int
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_int ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_alternating_sum
% 5.44/5.71 thf(fact_9171_choose__alternating__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_alternating_sum
% 5.44/5.71 thf(fact_9172_choose__alternating__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( groups7501900531339628137nteger
% 5.44/5.71 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I5 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_z3403309356797280102nteger ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_alternating_sum
% 5.44/5.71 thf(fact_9173_choose__alternating__sum,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.71 = zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % choose_alternating_sum
% 5.44/5.71 thf(fact_9174_binomial__code,axiom,
% 5.44/5.71 ( binomial
% 5.44/5.71 = ( ^ [N: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K3 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % binomial_code
% 5.44/5.71 thf(fact_9175_central__binomial__lower__bound,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % central_binomial_lower_bound
% 5.44/5.71 thf(fact_9176_sin__x__sin__y,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [P4: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [N: nat] :
% 5.44/5.71 ( if_real
% 5.44/5.71 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.44/5.71 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.44/5.71 @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) ) @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P4 @ N ) ) )
% 5.44/5.71 @ zero_zero_real )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P4 ) )
% 5.44/5.71 @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sin_x_sin_y
% 5.44/5.71 thf(fact_9177_sin__x__sin__y,axiom,
% 5.44/5.71 ! [X: complex,Y: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [P4: nat] :
% 5.44/5.71 ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [N: nat] :
% 5.44/5.71 ( if_complex
% 5.44/5.71 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.44/5.71 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.44/5.71 @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) ) @ ( power_power_complex @ X @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P4 @ N ) ) )
% 5.44/5.71 @ zero_zero_complex )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P4 ) )
% 5.44/5.71 @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sin_x_sin_y
% 5.44/5.71 thf(fact_9178_sums__cos__x__plus__y,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [P4: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 ) @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P4 @ N ) ) ) @ zero_zero_real )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P4 ) )
% 5.44/5.71 @ ( cos_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sums_cos_x_plus_y
% 5.44/5.71 thf(fact_9179_sums__cos__x__plus__y,axiom,
% 5.44/5.71 ! [X: complex,Y: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [P4: nat] :
% 5.44/5.71 ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 ) @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_complex @ X @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P4 @ N ) ) ) @ zero_zero_complex )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P4 ) )
% 5.44/5.71 @ ( cos_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sums_cos_x_plus_y
% 5.44/5.71 thf(fact_9180_cos__x__cos__y,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [P4: nat] :
% 5.44/5.71 ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [N: nat] :
% 5.44/5.71 ( if_real
% 5.44/5.71 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.44/5.71 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.44/5.71 @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P4 @ N ) ) )
% 5.44/5.71 @ zero_zero_real )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P4 ) )
% 5.44/5.71 @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cos_x_cos_y
% 5.44/5.71 thf(fact_9181_cos__x__cos__y,axiom,
% 5.44/5.71 ! [X: complex,Y: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [P4: nat] :
% 5.44/5.71 ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [N: nat] :
% 5.44/5.71 ( if_complex
% 5.44/5.71 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P4 )
% 5.44/5.71 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.44/5.71 @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P4 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_complex @ X @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P4 @ N ) ) )
% 5.44/5.71 @ zero_zero_complex )
% 5.44/5.71 @ ( set_ord_atMost_nat @ P4 ) )
% 5.44/5.71 @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cos_x_cos_y
% 5.44/5.71 thf(fact_9182_exp__first__two__terms,axiom,
% 5.44/5.71 ( exp_real
% 5.44/5.71 = ( ^ [X2: real] :
% 5.44/5.71 ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 )
% 5.44/5.71 @ ( suminf_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_first_two_terms
% 5.44/5.71 thf(fact_9183_exp__first__two__terms,axiom,
% 5.44/5.71 ( exp_complex
% 5.44/5.71 = ( ^ [X2: complex] :
% 5.44/5.71 ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ X2 )
% 5.44/5.71 @ ( suminf_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_complex @ X2 @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_first_two_terms
% 5.44/5.71 thf(fact_9184_of__nat__id,axiom,
% 5.44/5.71 ( semiri1316708129612266289at_nat
% 5.44/5.71 = ( ^ [N: nat] : N ) ) ).
% 5.44/5.71
% 5.44/5.71 % of_nat_id
% 5.44/5.71 thf(fact_9185_mult__scaleR__right,axiom,
% 5.44/5.71 ! [X: real,A: real,Y: real] :
% 5.44/5.71 ( ( times_times_real @ X @ ( real_V1485227260804924795R_real @ A @ Y ) )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_scaleR_right
% 5.44/5.71 thf(fact_9186_mult__scaleR__right,axiom,
% 5.44/5.71 ! [X: complex,A: real,Y: complex] :
% 5.44/5.71 ( ( times_times_complex @ X @ ( real_V2046097035970521341omplex @ A @ Y ) )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_scaleR_right
% 5.44/5.71 thf(fact_9187_mult__scaleR__left,axiom,
% 5.44/5.71 ! [A: real,X: real,Y: real] :
% 5.44/5.71 ( ( times_times_real @ ( real_V1485227260804924795R_real @ A @ X ) @ Y )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_scaleR_left
% 5.44/5.71 thf(fact_9188_mult__scaleR__left,axiom,
% 5.44/5.71 ! [A: real,X: complex,Y: complex] :
% 5.44/5.71 ( ( times_times_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ Y )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % mult_scaleR_left
% 5.44/5.71 thf(fact_9189_scaleR__one,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ one_one_real @ X )
% 5.44/5.71 = X ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_one
% 5.44/5.71 thf(fact_9190_scaleR__one,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ one_one_real @ X )
% 5.44/5.71 = X ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_one
% 5.44/5.71 thf(fact_9191_scaleR__scaleR,axiom,
% 5.44/5.71 ! [A: real,B: real,X: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ A @ ( real_V1485227260804924795R_real @ B @ X ) )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_scaleR
% 5.44/5.71 thf(fact_9192_scaleR__scaleR,axiom,
% 5.44/5.71 ! [A: real,B: real,X: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ A @ ( real_V2046097035970521341omplex @ B @ X ) )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_scaleR
% 5.44/5.71 thf(fact_9193_scaleR__eq__iff,axiom,
% 5.44/5.71 ! [B: real,U: real,A: real] :
% 5.44/5.71 ( ( ( plus_plus_real @ B @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.44/5.71 = ( plus_plus_real @ A @ ( real_V1485227260804924795R_real @ U @ B ) ) )
% 5.44/5.71 = ( ( A = B )
% 5.44/5.71 | ( U = one_one_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_eq_iff
% 5.44/5.71 thf(fact_9194_scaleR__eq__iff,axiom,
% 5.44/5.71 ! [B: complex,U: real,A: complex] :
% 5.44/5.71 ( ( ( plus_plus_complex @ B @ ( real_V2046097035970521341omplex @ U @ A ) )
% 5.44/5.71 = ( plus_plus_complex @ A @ ( real_V2046097035970521341omplex @ U @ B ) ) )
% 5.44/5.71 = ( ( A = B )
% 5.44/5.71 | ( U = one_one_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_eq_iff
% 5.44/5.71 thf(fact_9195_scaleR__power,axiom,
% 5.44/5.71 ! [X: real,Y: real,N2: nat] :
% 5.44/5.71 ( ( power_power_real @ ( real_V1485227260804924795R_real @ X @ Y ) @ N2 )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_power
% 5.44/5.71 thf(fact_9196_scaleR__power,axiom,
% 5.44/5.71 ! [X: real,Y: complex,N2: nat] :
% 5.44/5.71 ( ( power_power_complex @ ( real_V2046097035970521341omplex @ X @ Y ) @ N2 )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ ( power_power_real @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_power
% 5.44/5.71 thf(fact_9197_scaleR__minus1__left,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.71 = ( uminus_uminus_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_minus1_left
% 5.44/5.71 thf(fact_9198_scaleR__minus1__left,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.71 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_minus1_left
% 5.44/5.71 thf(fact_9199_scaleR__collapse,axiom,
% 5.44/5.71 ! [U: real,A: real] :
% 5.44/5.71 ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.44/5.71 = A ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_collapse
% 5.44/5.71 thf(fact_9200_scaleR__collapse,axiom,
% 5.44/5.71 ! [U: real,A: complex] :
% 5.44/5.71 ( ( plus_plus_complex @ ( real_V2046097035970521341omplex @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V2046097035970521341omplex @ U @ A ) )
% 5.44/5.71 = A ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_collapse
% 5.44/5.71 thf(fact_9201_norm__scaleR,axiom,
% 5.44/5.71 ! [A: real,X: real] :
% 5.44/5.71 ( ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ A @ X ) )
% 5.44/5.71 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_scaleR
% 5.44/5.71 thf(fact_9202_norm__scaleR,axiom,
% 5.44/5.71 ! [A: real,X: complex] :
% 5.44/5.71 ( ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ A @ X ) )
% 5.44/5.71 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % norm_scaleR
% 5.44/5.71 thf(fact_9203_scaleR__times,axiom,
% 5.44/5.71 ! [U: num,W: num,A: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ U ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_times
% 5.44/5.71 thf(fact_9204_scaleR__times,axiom,
% 5.44/5.71 ! [U: num,W: num,A: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ U ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_times
% 5.44/5.71 thf(fact_9205_inverse__scaleR__times,axiom,
% 5.44/5.71 ! [V: num,W: num,A: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_scaleR_times
% 5.44/5.71 thf(fact_9206_inverse__scaleR__times,axiom,
% 5.44/5.71 ! [V: num,W: num,A: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % inverse_scaleR_times
% 5.44/5.71 thf(fact_9207_fraction__scaleR__times,axiom,
% 5.44/5.71 ! [U: num,V: num,W: num,A: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % fraction_scaleR_times
% 5.44/5.71 thf(fact_9208_fraction__scaleR__times,axiom,
% 5.44/5.71 ! [U: num,V: num,W: num,A: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.44/5.71
% 5.44/5.71 % fraction_scaleR_times
% 5.44/5.71 thf(fact_9209_scaleR__half__double,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 5.44/5.71 = A ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_half_double
% 5.44/5.71 thf(fact_9210_scaleR__half__double,axiom,
% 5.44/5.71 ! [A: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ A @ A ) )
% 5.44/5.71 = A ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_half_double
% 5.44/5.71 thf(fact_9211_real__scaleR__def,axiom,
% 5.44/5.71 real_V1485227260804924795R_real = times_times_real ).
% 5.44/5.71
% 5.44/5.71 % real_scaleR_def
% 5.44/5.71 thf(fact_9212_scaleR__right__distrib,axiom,
% 5.44/5.71 ! [A: real,X: real,Y: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ A @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_right_distrib
% 5.44/5.71 thf(fact_9213_scaleR__right__distrib,axiom,
% 5.44/5.71 ! [A: real,X: complex,Y: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ A @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ ( real_V2046097035970521341omplex @ A @ Y ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_right_distrib
% 5.44/5.71 thf(fact_9214_scaleR__left_Oadd,axiom,
% 5.44/5.71 ! [X: real,Y: real,Xa2: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ X @ Y ) @ Xa2 )
% 5.44/5.71 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ X @ Xa2 ) @ ( real_V1485227260804924795R_real @ Y @ Xa2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_left.add
% 5.44/5.71 thf(fact_9215_scaleR__left_Oadd,axiom,
% 5.44/5.71 ! [X: real,Y: real,Xa2: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ ( plus_plus_real @ X @ Y ) @ Xa2 )
% 5.44/5.71 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ X @ Xa2 ) @ ( real_V2046097035970521341omplex @ Y @ Xa2 ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_left.add
% 5.44/5.71 thf(fact_9216_scaleR__left__distrib,axiom,
% 5.44/5.71 ! [A: real,B: real,X: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ A @ B ) @ X )
% 5.44/5.71 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_left_distrib
% 5.44/5.71 thf(fact_9217_scaleR__left__distrib,axiom,
% 5.44/5.71 ! [A: real,B: real,X: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ ( plus_plus_real @ A @ B ) @ X )
% 5.44/5.71 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ ( real_V2046097035970521341omplex @ B @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_left_distrib
% 5.44/5.71 thf(fact_9218_scaleR__conv__of__real,axiom,
% 5.44/5.71 ( real_V1485227260804924795R_real
% 5.44/5.71 = ( ^ [R4: real] : ( times_times_real @ ( real_V1803761363581548252l_real @ R4 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_conv_of_real
% 5.44/5.71 thf(fact_9219_scaleR__conv__of__real,axiom,
% 5.44/5.71 ( real_V2046097035970521341omplex
% 5.44/5.71 = ( ^ [R4: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R4 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_conv_of_real
% 5.44/5.71 thf(fact_9220_of__real__def,axiom,
% 5.44/5.71 ( real_V1803761363581548252l_real
% 5.44/5.71 = ( ^ [R4: real] : ( real_V1485227260804924795R_real @ R4 @ one_one_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % of_real_def
% 5.44/5.71 thf(fact_9221_of__real__def,axiom,
% 5.44/5.71 ( real_V4546457046886955230omplex
% 5.44/5.71 = ( ^ [R4: real] : ( real_V2046097035970521341omplex @ R4 @ one_one_complex ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % of_real_def
% 5.44/5.71 thf(fact_9222_complex__scaleR,axiom,
% 5.44/5.71 ! [R: real,A: real,B: real] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ R @ ( complex2 @ A @ B ) )
% 5.44/5.71 = ( complex2 @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % complex_scaleR
% 5.44/5.71 thf(fact_9223_scaleR__right__mono__neg,axiom,
% 5.44/5.71 ! [B: real,A: real,C: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.71 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ C ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_right_mono_neg
% 5.44/5.71 thf(fact_9224_scaleR__right__mono,axiom,
% 5.44/5.71 ! [A: real,B: real,X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_right_mono
% 5.44/5.71 thf(fact_9225_scaleR__le__cancel__left,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.44/5.71 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ord_less_eq_real @ A @ B ) )
% 5.44/5.71 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_le_cancel_left
% 5.44/5.71 thf(fact_9226_scaleR__le__cancel__left__neg,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.44/5.71 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_le_cancel_left_neg
% 5.44/5.71 thf(fact_9227_scaleR__le__cancel__left__pos,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.44/5.71 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_le_cancel_left_pos
% 5.44/5.71 thf(fact_9228_scaleR__left__mono__neg,axiom,
% 5.44/5.71 ! [B: real,A: real,C: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ B @ A )
% 5.44/5.71 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_left_mono_neg
% 5.44/5.71 thf(fact_9229_scaleR__left__mono,axiom,
% 5.44/5.71 ! [X: real,Y: real,A: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_left_mono
% 5.44/5.71 thf(fact_9230_vector__fraction__eq__iff,axiom,
% 5.44/5.71 ! [U: real,V: real,A: real,X: real] :
% 5.44/5.71 ( ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ U @ V ) @ A )
% 5.44/5.71 = X )
% 5.44/5.71 = ( ( ( V = zero_zero_real )
% 5.44/5.71 => ( X = zero_zero_real ) )
% 5.44/5.71 & ( ( V != zero_zero_real )
% 5.44/5.71 => ( ( real_V1485227260804924795R_real @ U @ A )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ V @ X ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % vector_fraction_eq_iff
% 5.44/5.71 thf(fact_9231_vector__fraction__eq__iff,axiom,
% 5.44/5.71 ! [U: real,V: real,A: complex,X: complex] :
% 5.44/5.71 ( ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ U @ V ) @ A )
% 5.44/5.71 = X )
% 5.44/5.71 = ( ( ( V = zero_zero_real )
% 5.44/5.71 => ( X = zero_zero_complex ) )
% 5.44/5.71 & ( ( V != zero_zero_real )
% 5.44/5.71 => ( ( real_V2046097035970521341omplex @ U @ A )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ V @ X ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % vector_fraction_eq_iff
% 5.44/5.71 thf(fact_9232_eq__vector__fraction__iff,axiom,
% 5.44/5.71 ! [X: real,U: real,V: real,A: real] :
% 5.44/5.71 ( ( X
% 5.44/5.71 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ U @ V ) @ A ) )
% 5.44/5.71 = ( ( ( V = zero_zero_real )
% 5.44/5.71 => ( X = zero_zero_real ) )
% 5.44/5.71 & ( ( V != zero_zero_real )
% 5.44/5.71 => ( ( real_V1485227260804924795R_real @ V @ X )
% 5.44/5.71 = ( real_V1485227260804924795R_real @ U @ A ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % eq_vector_fraction_iff
% 5.44/5.71 thf(fact_9233_eq__vector__fraction__iff,axiom,
% 5.44/5.71 ! [X: complex,U: real,V: real,A: complex] :
% 5.44/5.71 ( ( X
% 5.44/5.71 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ U @ V ) @ A ) )
% 5.44/5.71 = ( ( ( V = zero_zero_real )
% 5.44/5.71 => ( X = zero_zero_complex ) )
% 5.44/5.71 & ( ( V != zero_zero_real )
% 5.44/5.71 => ( ( real_V2046097035970521341omplex @ V @ X )
% 5.44/5.71 = ( real_V2046097035970521341omplex @ U @ A ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % eq_vector_fraction_iff
% 5.44/5.71 thf(fact_9234_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 5.44/5.71 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E ) @ D ) )
% 5.44/5.71 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Real_Vector_Spaces.le_add_iff2
% 5.44/5.71 thf(fact_9235_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 5.44/5.71 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E ) @ D ) )
% 5.44/5.71 = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.44/5.71
% 5.44/5.71 % Real_Vector_Spaces.le_add_iff1
% 5.44/5.71 thf(fact_9236_zero__le__scaleR__iff,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) )
% 5.44/5.71 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.44/5.71 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.71 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.44/5.71 | ( A = zero_zero_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % zero_le_scaleR_iff
% 5.44/5.71 thf(fact_9237_scaleR__le__0__iff,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B ) @ zero_zero_real )
% 5.44/5.71 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.71 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.44/5.71 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.44/5.71 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.44/5.71 | ( A = zero_zero_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_le_0_iff
% 5.44/5.71 thf(fact_9238_scaleR__mono,axiom,
% 5.44/5.71 ! [A: real,B: real,X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.71 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ Y ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_mono
% 5.44/5.71 thf(fact_9239_scaleR__mono_H,axiom,
% 5.44/5.71 ! [A: real,B: real,C: real,D: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.71 => ( ( ord_less_eq_real @ C @ D )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ D ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_mono'
% 5.44/5.71 thf(fact_9240_split__scaleR__neg__le,axiom,
% 5.44/5.71 ! [A: real,X: real] :
% 5.44/5.71 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.71 & ( ord_less_eq_real @ X @ zero_zero_real ) )
% 5.44/5.71 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.71 & ( ord_less_eq_real @ zero_zero_real @ X ) ) )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % split_scaleR_neg_le
% 5.44/5.71 thf(fact_9241_split__scaleR__pos__le,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.71 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.44/5.71 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.71 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.44/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % split_scaleR_pos_le
% 5.44/5.71 thf(fact_9242_scaleR__nonneg__nonneg,axiom,
% 5.44/5.71 ! [A: real,X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_nonneg_nonneg
% 5.44/5.71 thf(fact_9243_scaleR__nonneg__nonpos,axiom,
% 5.44/5.71 ! [A: real,X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.44/5.71 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_nonneg_nonpos
% 5.44/5.71 thf(fact_9244_scaleR__nonpos__nonneg,axiom,
% 5.44/5.71 ! [A: real,X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_nonpos_nonneg
% 5.44/5.71 thf(fact_9245_scaleR__nonpos__nonpos,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.44/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_nonpos_nonpos
% 5.44/5.71 thf(fact_9246_scaleR__left__le__one__le,axiom,
% 5.44/5.71 ! [X: real,A: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.44/5.71 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_left_le_one_le
% 5.44/5.71 thf(fact_9247_scaleR__2,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 5.44/5.71 = ( plus_plus_real @ X @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_2
% 5.44/5.71 thf(fact_9248_scaleR__2,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 5.44/5.71 = ( plus_plus_complex @ X @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % scaleR_2
% 5.44/5.71 thf(fact_9249_real__vector__affinity__eq,axiom,
% 5.44/5.71 ! [M: real,X: real,C: real,Y: real] :
% 5.44/5.71 ( ( M != zero_zero_real )
% 5.44/5.71 => ( ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X ) @ C )
% 5.44/5.71 = Y )
% 5.44/5.71 = ( X
% 5.44/5.71 = ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_vector_affinity_eq
% 5.44/5.71 thf(fact_9250_real__vector__affinity__eq,axiom,
% 5.44/5.71 ! [M: real,X: complex,C: complex,Y: complex] :
% 5.44/5.71 ( ( M != zero_zero_real )
% 5.44/5.71 => ( ( ( plus_plus_complex @ ( real_V2046097035970521341omplex @ M @ X ) @ C )
% 5.44/5.71 = Y )
% 5.44/5.71 = ( X
% 5.44/5.71 = ( minus_minus_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_vector_affinity_eq
% 5.44/5.71 thf(fact_9251_real__vector__eq__affinity,axiom,
% 5.44/5.71 ! [M: real,Y: real,X: real,C: real] :
% 5.44/5.71 ( ( M != zero_zero_real )
% 5.44/5.71 => ( ( Y
% 5.44/5.71 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X ) @ C ) )
% 5.44/5.71 = ( ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) )
% 5.44/5.71 = X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_vector_eq_affinity
% 5.44/5.71 thf(fact_9252_real__vector__eq__affinity,axiom,
% 5.44/5.71 ! [M: real,Y: complex,X: complex,C: complex] :
% 5.44/5.71 ( ( M != zero_zero_real )
% 5.44/5.71 => ( ( Y
% 5.44/5.71 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ M @ X ) @ C ) )
% 5.44/5.71 = ( ( minus_minus_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ C ) )
% 5.44/5.71 = X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % real_vector_eq_affinity
% 5.44/5.71 thf(fact_9253_neg__le__divideR__eq,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.44/5.71 = ( ord_less_eq_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % neg_le_divideR_eq
% 5.44/5.71 thf(fact_9254_neg__divideR__le__eq,axiom,
% 5.44/5.71 ! [C: real,B: real,A: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.44/5.71 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % neg_divideR_le_eq
% 5.44/5.71 thf(fact_9255_pos__le__divideR__eq,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_eq_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.44/5.71 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pos_le_divideR_eq
% 5.44/5.71 thf(fact_9256_pos__divideR__le__eq,axiom,
% 5.44/5.71 ! [C: real,B: real,A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.44/5.71 = ( ord_less_eq_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pos_divideR_le_eq
% 5.44/5.71 thf(fact_9257_pos__divideR__less__eq,axiom,
% 5.44/5.71 ! [C: real,B: real,A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.44/5.71 = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pos_divideR_less_eq
% 5.44/5.71 thf(fact_9258_pos__less__divideR__eq,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.44/5.71 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pos_less_divideR_eq
% 5.44/5.71 thf(fact_9259_neg__divideR__less__eq,axiom,
% 5.44/5.71 ! [C: real,B: real,A: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.44/5.71 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % neg_divideR_less_eq
% 5.44/5.71 thf(fact_9260_neg__less__divideR__eq,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.44/5.71 = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % neg_less_divideR_eq
% 5.44/5.71 thf(fact_9261_summable__exp__generic,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( summable_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_exp_generic
% 5.44/5.71 thf(fact_9262_summable__exp__generic,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( summable_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_exp_generic
% 5.44/5.71 thf(fact_9263_sin__converges,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X @ N ) )
% 5.44/5.71 @ ( sin_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sin_converges
% 5.44/5.71 thf(fact_9264_sin__converges,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X @ N ) )
% 5.44/5.71 @ ( sin_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sin_converges
% 5.44/5.71 thf(fact_9265_sin__def,axiom,
% 5.44/5.71 ( sin_real
% 5.44/5.71 = ( ^ [X2: real] :
% 5.44/5.71 ( suminf_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sin_def
% 5.44/5.71 thf(fact_9266_sin__def,axiom,
% 5.44/5.71 ( sin_complex
% 5.44/5.71 = ( ^ [X2: complex] :
% 5.44/5.71 ( suminf_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X2 @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sin_def
% 5.44/5.71 thf(fact_9267_cos__converges,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X @ N ) )
% 5.44/5.71 @ ( cos_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cos_converges
% 5.44/5.71 thf(fact_9268_cos__converges,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X @ N ) )
% 5.44/5.71 @ ( cos_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cos_converges
% 5.44/5.71 thf(fact_9269_cos__def,axiom,
% 5.44/5.71 ( cos_real
% 5.44/5.71 = ( ^ [X2: real] :
% 5.44/5.71 ( suminf_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cos_def
% 5.44/5.71 thf(fact_9270_cos__def,axiom,
% 5.44/5.71 ( cos_complex
% 5.44/5.71 = ( ^ [X2: complex] :
% 5.44/5.71 ( suminf_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X2 @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cos_def
% 5.44/5.71 thf(fact_9271_summable__norm__sin,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( summable_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_norm_sin
% 5.44/5.71 thf(fact_9272_summable__norm__sin,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( summable_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_norm_sin
% 5.44/5.71 thf(fact_9273_summable__norm__cos,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( summable_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_norm_cos
% 5.44/5.71 thf(fact_9274_summable__norm__cos,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( summable_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_norm_cos
% 5.44/5.71 thf(fact_9275_pos__le__minus__divideR__eq,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.44/5.71 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pos_le_minus_divideR_eq
% 5.44/5.71 thf(fact_9276_pos__minus__divideR__le__eq,axiom,
% 5.44/5.71 ! [C: real,B: real,A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.44/5.71 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pos_minus_divideR_le_eq
% 5.44/5.71 thf(fact_9277_neg__le__minus__divideR__eq,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.44/5.71 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % neg_le_minus_divideR_eq
% 5.44/5.71 thf(fact_9278_neg__minus__divideR__le__eq,axiom,
% 5.44/5.71 ! [C: real,B: real,A: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.44/5.71 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % neg_minus_divideR_le_eq
% 5.44/5.71 thf(fact_9279_neg__minus__divideR__less__eq,axiom,
% 5.44/5.71 ! [C: real,B: real,A: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.44/5.71 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % neg_minus_divideR_less_eq
% 5.44/5.71 thf(fact_9280_neg__less__minus__divideR__eq,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ C @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.44/5.71 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % neg_less_minus_divideR_eq
% 5.44/5.71 thf(fact_9281_pos__minus__divideR__less__eq,axiom,
% 5.44/5.71 ! [C: real,B: real,A: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.44/5.71 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pos_minus_divideR_less_eq
% 5.44/5.71 thf(fact_9282_pos__less__minus__divideR__eq,axiom,
% 5.44/5.71 ! [C: real,A: real,B: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.71 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.44/5.71 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % pos_less_minus_divideR_eq
% 5.44/5.71 thf(fact_9283_exp__converges,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) )
% 5.44/5.71 @ ( exp_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_converges
% 5.44/5.71 thf(fact_9284_exp__converges,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) )
% 5.44/5.71 @ ( exp_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_converges
% 5.44/5.71 thf(fact_9285_exp__def,axiom,
% 5.44/5.71 ( exp_real
% 5.44/5.71 = ( ^ [X2: real] :
% 5.44/5.71 ( suminf_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_def
% 5.44/5.71 thf(fact_9286_exp__def,axiom,
% 5.44/5.71 ( exp_complex
% 5.44/5.71 = ( ^ [X2: complex] :
% 5.44/5.71 ( suminf_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X2 @ N ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_def
% 5.44/5.71 thf(fact_9287_summable__norm__exp,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( summable_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_norm_exp
% 5.44/5.71 thf(fact_9288_summable__norm__exp,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( summable_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % summable_norm_exp
% 5.44/5.71 thf(fact_9289_sin__minus__converges,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [N: nat] : ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ N ) ) )
% 5.44/5.71 @ ( sin_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sin_minus_converges
% 5.44/5.71 thf(fact_9290_sin__minus__converges,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ N ) ) )
% 5.44/5.71 @ ( sin_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sin_minus_converges
% 5.44/5.71 thf(fact_9291_cos__minus__converges,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ N ) )
% 5.44/5.71 @ ( cos_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cos_minus_converges
% 5.44/5.71 thf(fact_9292_cos__minus__converges,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ N ) )
% 5.44/5.71 @ ( cos_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cos_minus_converges
% 5.44/5.71 thf(fact_9293_complex__inverse,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.44/5.71 = ( 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 ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % complex_inverse
% 5.44/5.71 thf(fact_9294_exp__series__add__commuting,axiom,
% 5.44/5.71 ! [X: real,Y: real,N2: nat] :
% 5.44/5.71 ( ( ( times_times_real @ X @ Y )
% 5.44/5.71 = ( times_times_real @ Y @ X ) )
% 5.44/5.71 => ( ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ N2 ) )
% 5.44/5.71 = ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I5 ) ) @ ( power_power_real @ X @ I5 ) ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ I5 ) ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ I5 ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_series_add_commuting
% 5.44/5.71 thf(fact_9295_exp__series__add__commuting,axiom,
% 5.44/5.71 ! [X: complex,Y: complex,N2: nat] :
% 5.44/5.71 ( ( ( times_times_complex @ X @ Y )
% 5.44/5.71 = ( times_times_complex @ Y @ X ) )
% 5.44/5.71 => ( ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ N2 ) )
% 5.44/5.71 = ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [I5: nat] : ( times_times_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I5 ) ) @ ( power_power_complex @ X @ I5 ) ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ I5 ) ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ I5 ) ) ) )
% 5.44/5.71 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_series_add_commuting
% 5.44/5.71 thf(fact_9296_exp__first__term,axiom,
% 5.44/5.71 ( exp_real
% 5.44/5.71 = ( ^ [X2: real] :
% 5.44/5.71 ( plus_plus_real @ one_one_real
% 5.44/5.71 @ ( suminf_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_first_term
% 5.44/5.71 thf(fact_9297_exp__first__term,axiom,
% 5.44/5.71 ( exp_complex
% 5.44/5.71 = ( ^ [X2: complex] :
% 5.44/5.71 ( plus_plus_complex @ one_one_complex
% 5.44/5.71 @ ( suminf_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N ) ) ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_first_term
% 5.44/5.71 thf(fact_9298_exp__first__terms,axiom,
% 5.44/5.71 ! [K: nat] :
% 5.44/5.71 ( exp_real
% 5.44/5.71 = ( ^ [X2: real] :
% 5.44/5.71 ( plus_plus_real
% 5.44/5.71 @ ( groups6591440286371151544t_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ K ) )
% 5.44/5.71 @ ( suminf_real
% 5.44/5.71 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ K ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ N @ K ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_first_terms
% 5.44/5.71 thf(fact_9299_exp__first__terms,axiom,
% 5.44/5.71 ! [K: nat] :
% 5.44/5.71 ( exp_complex
% 5.44/5.71 = ( ^ [X2: complex] :
% 5.44/5.71 ( plus_plus_complex
% 5.44/5.71 @ ( groups2073611262835488442omplex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X2 @ N ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ K ) )
% 5.44/5.71 @ ( suminf_complex
% 5.44/5.71 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ K ) ) ) @ ( power_power_complex @ X2 @ ( plus_plus_nat @ N @ K ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % exp_first_terms
% 5.44/5.71 thf(fact_9300_sinh__converges,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) )
% 5.44/5.71 @ ( sinh_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_converges
% 5.44/5.71 thf(fact_9301_sinh__converges,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) ) )
% 5.44/5.71 @ ( sinh_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_converges
% 5.44/5.71 thf(fact_9302_cosh__converges,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( sums_real
% 5.44/5.71 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) @ zero_zero_real )
% 5.44/5.71 @ ( cosh_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_converges
% 5.44/5.71 thf(fact_9303_cosh__converges,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( sums_complex
% 5.44/5.71 @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) ) @ zero_zero_complex )
% 5.44/5.71 @ ( cosh_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_converges
% 5.44/5.71 thf(fact_9304_exp__two__pi__i_H,axiom,
% 5.44/5.71 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.44/5.71 = one_one_complex ) ).
% 5.44/5.71
% 5.44/5.71 % exp_two_pi_i'
% 5.44/5.71 thf(fact_9305_exp__two__pi__i,axiom,
% 5.44/5.71 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.44/5.71 = one_one_complex ) ).
% 5.44/5.71
% 5.44/5.71 % exp_two_pi_i
% 5.44/5.71 thf(fact_9306_sinh__real__less__iff,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 5.44/5.71 = ( ord_less_real @ X @ Y ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_real_less_iff
% 5.44/5.71 thf(fact_9307_sinh__real__le__iff,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 5.44/5.71 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_real_le_iff
% 5.44/5.71 thf(fact_9308_sinh__real__neg__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.44/5.71 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_real_neg_iff
% 5.44/5.71 thf(fact_9309_sinh__real__pos__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.44/5.71 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_real_pos_iff
% 5.44/5.71 thf(fact_9310_sinh__real__nonpos__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.44/5.71 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_real_nonpos_iff
% 5.44/5.71 thf(fact_9311_sinh__real__nonneg__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.44/5.71 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_real_nonneg_iff
% 5.44/5.71 thf(fact_9312_cosh__0,axiom,
% 5.44/5.71 ( ( cosh_complex @ zero_zero_complex )
% 5.44/5.71 = one_one_complex ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_0
% 5.44/5.71 thf(fact_9313_cosh__0,axiom,
% 5.44/5.71 ( ( cosh_real @ zero_zero_real )
% 5.44/5.71 = one_one_real ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_0
% 5.44/5.71 thf(fact_9314_norm__ii,axiom,
% 5.44/5.71 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.44/5.71 = one_one_real ) ).
% 5.44/5.71
% 5.44/5.71 % norm_ii
% 5.44/5.71 thf(fact_9315_power2__i,axiom,
% 5.44/5.71 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % power2_i
% 5.44/5.71 thf(fact_9316_i__even__power,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.71 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) ) ).
% 5.44/5.71
% 5.44/5.71 % i_even_power
% 5.44/5.71 thf(fact_9317_tanh__def,axiom,
% 5.44/5.71 ( tanh_real
% 5.44/5.71 = ( ^ [X2: real] : ( divide_divide_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % tanh_def
% 5.44/5.71 thf(fact_9318_tanh__def,axiom,
% 5.44/5.71 ( tanh_complex
% 5.44/5.71 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X2 ) @ ( cosh_complex @ X2 ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % tanh_def
% 5.44/5.71 thf(fact_9319_cosh__plus__sinh,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( plus_plus_complex @ ( cosh_complex @ X ) @ ( sinh_complex @ X ) )
% 5.44/5.71 = ( exp_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_plus_sinh
% 5.44/5.71 thf(fact_9320_cosh__plus__sinh,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( plus_plus_real @ ( cosh_real @ X ) @ ( sinh_real @ X ) )
% 5.44/5.71 = ( exp_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_plus_sinh
% 5.44/5.71 thf(fact_9321_sinh__plus__cosh,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( plus_plus_complex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) )
% 5.44/5.71 = ( exp_complex @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_plus_cosh
% 5.44/5.71 thf(fact_9322_sinh__plus__cosh,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( plus_plus_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) )
% 5.44/5.71 = ( exp_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_plus_cosh
% 5.44/5.71 thf(fact_9323_sinh__le__cosh__real,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_le_cosh_real
% 5.44/5.71 thf(fact_9324_sinh__less__cosh__real,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_less_cosh_real
% 5.44/5.71 thf(fact_9325_cosh__add,axiom,
% 5.44/5.71 ! [X: complex,Y: complex] :
% 5.44/5.71 ( ( cosh_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_complex @ ( times_times_complex @ ( cosh_complex @ X ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( sinh_complex @ X ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_add
% 5.44/5.71 thf(fact_9326_cosh__add,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( cosh_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_add
% 5.44/5.71 thf(fact_9327_sinh__add,axiom,
% 5.44/5.71 ! [X: complex,Y: complex] :
% 5.44/5.71 ( ( sinh_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_complex @ ( times_times_complex @ ( sinh_complex @ X ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( cosh_complex @ X ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_add
% 5.44/5.71 thf(fact_9328_sinh__add,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( sinh_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.71 = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_add
% 5.44/5.71 thf(fact_9329_cosh__diff,axiom,
% 5.44/5.71 ! [X: complex,Y: complex] :
% 5.44/5.71 ( ( cosh_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.44/5.71 = ( minus_minus_complex @ ( times_times_complex @ ( cosh_complex @ X ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( sinh_complex @ X ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_diff
% 5.44/5.71 thf(fact_9330_cosh__diff,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( cosh_real @ ( minus_minus_real @ X @ Y ) )
% 5.44/5.71 = ( minus_minus_real @ ( times_times_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_diff
% 5.44/5.71 thf(fact_9331_sinh__diff,axiom,
% 5.44/5.71 ! [X: complex,Y: complex] :
% 5.44/5.71 ( ( sinh_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.44/5.71 = ( minus_minus_complex @ ( times_times_complex @ ( sinh_complex @ X ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( cosh_complex @ X ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_diff
% 5.44/5.71 thf(fact_9332_sinh__diff,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( sinh_real @ ( minus_minus_real @ X @ Y ) )
% 5.44/5.71 = ( minus_minus_real @ ( times_times_real @ ( sinh_real @ X ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_diff
% 5.44/5.71 thf(fact_9333_cosh__real__pos,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_real_pos
% 5.44/5.71 thf(fact_9334_cosh__real__nonneg,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_real_nonneg
% 5.44/5.71 thf(fact_9335_cosh__real__nonneg__le__iff,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.44/5.71 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_real_nonneg_le_iff
% 5.44/5.71 thf(fact_9336_cosh__real__nonpos__le__iff,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.44/5.71 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_real_nonpos_le_iff
% 5.44/5.71 thf(fact_9337_cosh__real__ge__1,axiom,
% 5.44/5.71 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_real_ge_1
% 5.44/5.71 thf(fact_9338_sinh__double,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.71 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X ) ) @ ( cosh_complex @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_double
% 5.44/5.71 thf(fact_9339_sinh__double,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.71 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X ) ) @ ( cosh_real @ X ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_double
% 5.44/5.71 thf(fact_9340_cosh__real__nonpos__less__iff,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.44/5.71 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.44/5.71 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_real_nonpos_less_iff
% 5.44/5.71 thf(fact_9341_cosh__real__nonneg__less__iff,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.71 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.44/5.71 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_real_nonneg_less_iff
% 5.44/5.71 thf(fact_9342_cosh__real__strict__mono,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( ord_less_real @ X @ Y )
% 5.44/5.71 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_real_strict_mono
% 5.44/5.71 thf(fact_9343_cosh__square__eq,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_square_eq
% 5.44/5.71 thf(fact_9344_cosh__square__eq,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_square_eq
% 5.44/5.71 thf(fact_9345_hyperbolic__pythagoras,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.71 = one_one_complex ) ).
% 5.44/5.71
% 5.44/5.71 % hyperbolic_pythagoras
% 5.44/5.71 thf(fact_9346_hyperbolic__pythagoras,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.71 = one_one_real ) ).
% 5.44/5.71
% 5.44/5.71 % hyperbolic_pythagoras
% 5.44/5.71 thf(fact_9347_sinh__square__eq,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_square_eq
% 5.44/5.71 thf(fact_9348_sinh__square__eq,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_square_eq
% 5.44/5.71 thf(fact_9349_arcosh__cosh__real,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 5.44/5.71 = X ) ) ).
% 5.44/5.71
% 5.44/5.71 % arcosh_cosh_real
% 5.44/5.71 thf(fact_9350_Complex__eq__i,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ( complex2 @ X @ Y )
% 5.44/5.71 = imaginary_unit )
% 5.44/5.71 = ( ( X = zero_zero_real )
% 5.44/5.71 & ( Y = one_one_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Complex_eq_i
% 5.44/5.71 thf(fact_9351_imaginary__unit_Ocode,axiom,
% 5.44/5.71 ( imaginary_unit
% 5.44/5.71 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.44/5.71
% 5.44/5.71 % imaginary_unit.code
% 5.44/5.71 thf(fact_9352_cosh__double,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.71 = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_double
% 5.44/5.71 thf(fact_9353_cosh__double,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.44/5.71 = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_double
% 5.44/5.71 thf(fact_9354_tanh__add,axiom,
% 5.44/5.71 ! [X: real,Y: real] :
% 5.44/5.71 ( ( ( cosh_real @ X )
% 5.44/5.71 != zero_zero_real )
% 5.44/5.71 => ( ( ( cosh_real @ Y )
% 5.44/5.71 != zero_zero_real )
% 5.44/5.71 => ( ( tanh_real @ ( plus_plus_real @ X @ Y ) )
% 5.44/5.71 = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % tanh_add
% 5.44/5.71 thf(fact_9355_tanh__add,axiom,
% 5.44/5.71 ! [X: complex,Y: complex] :
% 5.44/5.71 ( ( ( cosh_complex @ X )
% 5.44/5.71 != zero_zero_complex )
% 5.44/5.71 => ( ( ( cosh_complex @ Y )
% 5.44/5.71 != zero_zero_complex )
% 5.44/5.71 => ( ( tanh_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.71 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X ) @ ( tanh_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X ) @ ( tanh_complex @ Y ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % tanh_add
% 5.44/5.71 thf(fact_9356_sinh__zero__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ( sinh_real @ X )
% 5.44/5.71 = zero_zero_real )
% 5.44/5.71 = ( member_real @ ( exp_real @ X ) @ ( insert_real @ one_one_real @ ( insert_real @ ( uminus_uminus_real @ one_one_real ) @ bot_bot_set_real ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_zero_iff
% 5.44/5.71 thf(fact_9357_sinh__zero__iff,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( ( sinh_complex @ X )
% 5.44/5.71 = zero_zero_complex )
% 5.44/5.71 = ( member_complex @ ( exp_complex @ X ) @ ( insert_complex @ one_one_complex @ ( insert_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ bot_bot_set_complex ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_zero_iff
% 5.44/5.71 thf(fact_9358_cosh__field__def,axiom,
% 5.44/5.71 ( cosh_real
% 5.44/5.71 = ( ^ [Z5: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_field_def
% 5.44/5.71 thf(fact_9359_cosh__field__def,axiom,
% 5.44/5.71 ( cosh_complex
% 5.44/5.71 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_field_def
% 5.44/5.71 thf(fact_9360_sinh__field__def,axiom,
% 5.44/5.71 ( sinh_real
% 5.44/5.71 = ( ^ [Z5: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_field_def
% 5.44/5.71 thf(fact_9361_sinh__field__def,axiom,
% 5.44/5.71 ( sinh_complex
% 5.44/5.71 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_field_def
% 5.44/5.71 thf(fact_9362_cosh__zero__iff,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ( cosh_real @ X )
% 5.44/5.71 = zero_zero_real )
% 5.44/5.71 = ( ( power_power_real @ ( exp_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_zero_iff
% 5.44/5.71 thf(fact_9363_cosh__zero__iff,axiom,
% 5.44/5.71 ! [X: complex] :
% 5.44/5.71 ( ( ( cosh_complex @ X )
% 5.44/5.71 = zero_zero_complex )
% 5.44/5.71 = ( ( power_power_complex @ ( exp_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_zero_iff
% 5.44/5.71 thf(fact_9364_cmod__unit__one,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.44/5.71 = one_one_real ) ).
% 5.44/5.71
% 5.44/5.71 % cmod_unit_one
% 5.44/5.71 thf(fact_9365_cosh__def,axiom,
% 5.44/5.71 ( cosh_real
% 5.44/5.71 = ( ^ [X2: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_def
% 5.44/5.71 thf(fact_9366_cosh__def,axiom,
% 5.44/5.71 ( cosh_complex
% 5.44/5.71 = ( ^ [X2: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_def
% 5.44/5.71 thf(fact_9367_cosh__ln__real,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 5.44/5.71 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cosh_ln_real
% 5.44/5.71 thf(fact_9368_sinh__def,axiom,
% 5.44/5.71 ( sinh_real
% 5.44/5.71 = ( ^ [X2: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_def
% 5.44/5.71 thf(fact_9369_sinh__def,axiom,
% 5.44/5.71 ( sinh_complex
% 5.44/5.71 = ( ^ [X2: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_def
% 5.44/5.71 thf(fact_9370_sinh__ln__real,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 5.44/5.71 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % sinh_ln_real
% 5.44/5.71 thf(fact_9371_Arg__minus__ii,axiom,
% 5.44/5.71 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.44/5.71 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Arg_minus_ii
% 5.44/5.71 thf(fact_9372_csqrt__ii,axiom,
% 5.44/5.71 ( ( csqrt @ imaginary_unit )
% 5.44/5.71 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % csqrt_ii
% 5.44/5.71 thf(fact_9373_Arg__ii,axiom,
% 5.44/5.71 ( ( arg @ imaginary_unit )
% 5.44/5.71 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % Arg_ii
% 5.44/5.71 thf(fact_9374_cis__minus__pi__half,axiom,
% 5.44/5.71 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.44/5.71 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.44/5.71
% 5.44/5.71 % cis_minus_pi_half
% 5.44/5.71 thf(fact_9375_norm__cis,axiom,
% 5.44/5.71 ! [A: real] :
% 5.44/5.71 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.44/5.71 = one_one_real ) ).
% 5.44/5.71
% 5.44/5.71 % norm_cis
% 5.44/5.71 thf(fact_9376_power2__csqrt,axiom,
% 5.44/5.71 ! [Z: complex] :
% 5.44/5.71 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.71 = Z ) ).
% 5.44/5.71
% 5.44/5.71 % power2_csqrt
% 5.44/5.71 thf(fact_9377_cis__pi__half,axiom,
% 5.44/5.71 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.71 = imaginary_unit ) ).
% 5.44/5.71
% 5.44/5.71 % cis_pi_half
% 5.44/5.71 thf(fact_9378_cis__2pi,axiom,
% 5.44/5.71 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.44/5.71 = one_one_complex ) ).
% 5.44/5.71
% 5.44/5.71 % cis_2pi
% 5.44/5.71 thf(fact_9379_cis__mult,axiom,
% 5.44/5.71 ! [A: real,B: real] :
% 5.44/5.71 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.44/5.71 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cis_mult
% 5.44/5.71 thf(fact_9380_DeMoivre,axiom,
% 5.44/5.71 ! [A: real,N2: nat] :
% 5.44/5.71 ( ( power_power_complex @ ( cis @ A ) @ N2 )
% 5.44/5.71 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % DeMoivre
% 5.44/5.71 thf(fact_9381_of__real__sqrt,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.71 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 5.44/5.71 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % of_real_sqrt
% 5.44/5.71 thf(fact_9382_Arg__bounded,axiom,
% 5.44/5.71 ! [Z: complex] :
% 5.44/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.44/5.71 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.44/5.71
% 5.44/5.71 % Arg_bounded
% 5.44/5.71 thf(fact_9383_bij__betw__roots__unity,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.71 => ( bij_betw_nat_complex
% 5.44/5.71 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.44/5.71 @ ( set_ord_lessThan_nat @ N2 )
% 5.44/5.71 @ ( collect_complex
% 5.44/5.71 @ ^ [Z5: complex] :
% 5.44/5.71 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.71 = one_one_complex ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % bij_betw_roots_unity
% 5.44/5.71 thf(fact_9384_cot__less__zero,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.44/5.71 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.71 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % cot_less_zero
% 5.44/5.71 thf(fact_9385_cot__periodic,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.44/5.71 = ( cot_real @ X ) ) ).
% 5.44/5.71
% 5.44/5.71 % cot_periodic
% 5.44/5.71 thf(fact_9386_arctan__def,axiom,
% 5.44/5.71 ( arctan
% 5.44/5.71 = ( ^ [Y3: real] :
% 5.44/5.71 ( the_real
% 5.44/5.71 @ ^ [X2: real] :
% 5.44/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.44/5.71 & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.71 & ( ( tan_real @ X2 )
% 5.44/5.71 = Y3 ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % arctan_def
% 5.44/5.71 thf(fact_9387_cot__npi,axiom,
% 5.44/5.71 ! [N2: nat] :
% 5.44/5.71 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.44/5.71 = zero_zero_real ) ).
% 5.44/5.71
% 5.44/5.71 % cot_npi
% 5.44/5.71 thf(fact_9388_ln__neg__is__const,axiom,
% 5.44/5.71 ! [X: real] :
% 5.44/5.71 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.71 => ( ( ln_ln_real @ X )
% 5.44/5.71 = ( the_real
% 5.44/5.71 @ ^ [X2: real] : $false ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % ln_neg_is_const
% 5.44/5.71 thf(fact_9389_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.71 ! [S5: set_real,T5: set_real,H2: real > real,S: set_real,T3: set_real,G: real > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ S5 )
% 5.44/5.71 => ( ( finite_finite_real @ T5 )
% 5.44/5.71 => ( ( bij_betw_real_real @ H2 @ ( minus_minus_set_real @ S @ S5 ) @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.71 => ( ! [A3: real] :
% 5.44/5.71 ( ( member_real @ A3 @ S5 )
% 5.44/5.71 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: real] :
% 5.44/5.71 ( ( member_real @ B3 @ T5 )
% 5.44/5.71 => ( ( G @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups7973222482632965587d_enat
% 5.44/5.71 @ ^ [X2: real] : ( G @ ( H2 @ X2 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.reindex_bij_betw_not_neutral
% 5.44/5.71 thf(fact_9390_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.71 ! [S5: set_real,T5: set_int,H2: real > int,S: set_real,T3: set_int,G: int > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ S5 )
% 5.44/5.71 => ( ( finite_finite_int @ T5 )
% 5.44/5.71 => ( ( bij_betw_real_int @ H2 @ ( minus_minus_set_real @ S @ S5 ) @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.71 => ( ! [A3: real] :
% 5.44/5.71 ( ( member_real @ A3 @ S5 )
% 5.44/5.71 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: int] :
% 5.44/5.71 ( ( member_int @ B3 @ T5 )
% 5.44/5.71 => ( ( G @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups7973222482632965587d_enat
% 5.44/5.71 @ ^ [X2: real] : ( G @ ( H2 @ X2 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups5078248829458667347d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.reindex_bij_betw_not_neutral
% 5.44/5.71 thf(fact_9391_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.71 ! [S5: set_int,T5: set_real,H2: int > real,S: set_int,T3: set_real,G: real > extended_enat] :
% 5.44/5.71 ( ( finite_finite_int @ S5 )
% 5.44/5.71 => ( ( finite_finite_real @ T5 )
% 5.44/5.71 => ( ( bij_betw_int_real @ H2 @ ( minus_minus_set_int @ S @ S5 ) @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ S5 )
% 5.44/5.71 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: real] :
% 5.44/5.71 ( ( member_real @ B3 @ T5 )
% 5.44/5.71 => ( ( G @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups5078248829458667347d_enat
% 5.44/5.71 @ ^ [X2: int] : ( G @ ( H2 @ X2 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups7973222482632965587d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.reindex_bij_betw_not_neutral
% 5.44/5.71 thf(fact_9392_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.71 ! [S5: set_int,T5: set_int,H2: int > int,S: set_int,T3: set_int,G: int > extended_enat] :
% 5.44/5.71 ( ( finite_finite_int @ S5 )
% 5.44/5.71 => ( ( finite_finite_int @ T5 )
% 5.44/5.71 => ( ( bij_betw_int_int @ H2 @ ( minus_minus_set_int @ S @ S5 ) @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ S5 )
% 5.44/5.71 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: int] :
% 5.44/5.71 ( ( member_int @ B3 @ T5 )
% 5.44/5.71 => ( ( G @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups5078248829458667347d_enat
% 5.44/5.71 @ ^ [X2: int] : ( G @ ( H2 @ X2 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups5078248829458667347d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.reindex_bij_betw_not_neutral
% 5.44/5.71 thf(fact_9393_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.71 ! [S5: set_real,T5: set_complex,H2: real > complex,S: set_real,T3: set_complex,G: complex > extended_enat] :
% 5.44/5.71 ( ( finite_finite_real @ S5 )
% 5.44/5.71 => ( ( finite3207457112153483333omplex @ T5 )
% 5.44/5.71 => ( ( bij_be1067425076133476306omplex @ H2 @ ( minus_minus_set_real @ S @ S5 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.71 => ( ! [A3: real] :
% 5.44/5.71 ( ( member_real @ A3 @ S5 )
% 5.44/5.71 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ T5 )
% 5.44/5.71 => ( ( G @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups7973222482632965587d_enat
% 5.44/5.71 @ ^ [X2: real] : ( G @ ( H2 @ X2 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups8780218893797010257d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.reindex_bij_betw_not_neutral
% 5.44/5.71 thf(fact_9394_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.71 ! [S5: set_int,T5: set_complex,H2: int > complex,S: set_int,T3: set_complex,G: complex > extended_enat] :
% 5.44/5.71 ( ( finite_finite_int @ S5 )
% 5.44/5.71 => ( ( finite3207457112153483333omplex @ T5 )
% 5.44/5.71 => ( ( bij_betw_int_complex @ H2 @ ( minus_minus_set_int @ S @ S5 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.71 => ( ! [A3: int] :
% 5.44/5.71 ( ( member_int @ A3 @ S5 )
% 5.44/5.71 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: complex] :
% 5.44/5.71 ( ( member_complex @ B3 @ T5 )
% 5.44/5.71 => ( ( G @ B3 )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ( groups5078248829458667347d_enat
% 5.44/5.71 @ ^ [X2: int] : ( G @ ( H2 @ X2 ) )
% 5.44/5.71 @ S )
% 5.44/5.71 = ( groups8780218893797010257d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.71
% 5.44/5.71 % prod.reindex_bij_betw_not_neutral
% 5.44/5.71 thf(fact_9395_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.71 ! [S5: set_complex,T5: set_real,H2: complex > real,S: set_complex,T3: set_real,G: real > extended_enat] :
% 5.44/5.71 ( ( finite3207457112153483333omplex @ S5 )
% 5.44/5.71 => ( ( finite_finite_real @ T5 )
% 5.44/5.71 => ( ( bij_be1121013576637796946x_real @ H2 @ ( minus_811609699411566653omplex @ S @ S5 ) @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.71 => ( ! [A3: complex] :
% 5.44/5.71 ( ( member_complex @ A3 @ S5 )
% 5.44/5.71 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.71 = one_on7984719198319812577d_enat ) )
% 5.44/5.71 => ( ! [B3: real] :
% 5.44/5.71 ( ( member_real @ B3 @ T5 )
% 5.44/5.71 => ( ( G @ B3 )
% 5.44/5.72 = one_on7984719198319812577d_enat ) )
% 5.44/5.72 => ( ( groups8780218893797010257d_enat
% 5.44/5.72 @ ^ [X2: complex] : ( G @ ( H2 @ X2 ) )
% 5.44/5.72 @ S )
% 5.44/5.72 = ( groups7973222482632965587d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod.reindex_bij_betw_not_neutral
% 5.44/5.72 thf(fact_9396_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.72 ! [S5: set_complex,T5: set_int,H2: complex > int,S: set_complex,T3: set_int,G: int > extended_enat] :
% 5.44/5.72 ( ( finite3207457112153483333omplex @ S5 )
% 5.44/5.72 => ( ( finite_finite_int @ T5 )
% 5.44/5.72 => ( ( bij_betw_complex_int @ H2 @ ( minus_811609699411566653omplex @ S @ S5 ) @ ( minus_minus_set_int @ T3 @ T5 ) )
% 5.44/5.72 => ( ! [A3: complex] :
% 5.44/5.72 ( ( member_complex @ A3 @ S5 )
% 5.44/5.72 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.72 = one_on7984719198319812577d_enat ) )
% 5.44/5.72 => ( ! [B3: int] :
% 5.44/5.72 ( ( member_int @ B3 @ T5 )
% 5.44/5.72 => ( ( G @ B3 )
% 5.44/5.72 = one_on7984719198319812577d_enat ) )
% 5.44/5.72 => ( ( groups8780218893797010257d_enat
% 5.44/5.72 @ ^ [X2: complex] : ( G @ ( H2 @ X2 ) )
% 5.44/5.72 @ S )
% 5.44/5.72 = ( groups5078248829458667347d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod.reindex_bij_betw_not_neutral
% 5.44/5.72 thf(fact_9397_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.72 ! [S5: set_complex,T5: set_complex,H2: complex > complex,S: set_complex,T3: set_complex,G: complex > extended_enat] :
% 5.44/5.72 ( ( finite3207457112153483333omplex @ S5 )
% 5.44/5.72 => ( ( finite3207457112153483333omplex @ T5 )
% 5.44/5.72 => ( ( bij_be1856998921033663316omplex @ H2 @ ( minus_811609699411566653omplex @ S @ S5 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 5.44/5.72 => ( ! [A3: complex] :
% 5.44/5.72 ( ( member_complex @ A3 @ S5 )
% 5.44/5.72 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.72 = one_on7984719198319812577d_enat ) )
% 5.44/5.72 => ( ! [B3: complex] :
% 5.44/5.72 ( ( member_complex @ B3 @ T5 )
% 5.44/5.72 => ( ( G @ B3 )
% 5.44/5.72 = one_on7984719198319812577d_enat ) )
% 5.44/5.72 => ( ( groups8780218893797010257d_enat
% 5.44/5.72 @ ^ [X2: complex] : ( G @ ( H2 @ X2 ) )
% 5.44/5.72 @ S )
% 5.44/5.72 = ( groups8780218893797010257d_enat @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod.reindex_bij_betw_not_neutral
% 5.44/5.72 thf(fact_9398_prod_Oreindex__bij__betw__not__neutral,axiom,
% 5.44/5.72 ! [S5: set_real,T5: set_real,H2: real > real,S: set_real,T3: set_real,G: real > complex] :
% 5.44/5.72 ( ( finite_finite_real @ S5 )
% 5.44/5.72 => ( ( finite_finite_real @ T5 )
% 5.44/5.72 => ( ( bij_betw_real_real @ H2 @ ( minus_minus_set_real @ S @ S5 ) @ ( minus_minus_set_real @ T3 @ T5 ) )
% 5.44/5.72 => ( ! [A3: real] :
% 5.44/5.72 ( ( member_real @ A3 @ S5 )
% 5.44/5.72 => ( ( G @ ( H2 @ A3 ) )
% 5.44/5.72 = one_one_complex ) )
% 5.44/5.72 => ( ! [B3: real] :
% 5.44/5.72 ( ( member_real @ B3 @ T5 )
% 5.44/5.72 => ( ( G @ B3 )
% 5.44/5.72 = one_one_complex ) )
% 5.44/5.72 => ( ( groups713298508707869441omplex
% 5.44/5.72 @ ^ [X2: real] : ( G @ ( H2 @ X2 ) )
% 5.44/5.72 @ S )
% 5.44/5.72 = ( groups713298508707869441omplex @ G @ T3 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod.reindex_bij_betw_not_neutral
% 5.44/5.72 thf(fact_9399_cot__def,axiom,
% 5.44/5.72 ( cot_real
% 5.44/5.72 = ( ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cot_def
% 5.44/5.72 thf(fact_9400_cot__def,axiom,
% 5.44/5.72 ( cot_complex
% 5.44/5.72 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X2 ) @ ( sin_complex @ X2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cot_def
% 5.44/5.72 thf(fact_9401_arccos__def,axiom,
% 5.44/5.72 ( arccos
% 5.44/5.72 = ( ^ [Y3: real] :
% 5.44/5.72 ( the_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.44/5.72 & ( ord_less_eq_real @ X2 @ pi )
% 5.44/5.72 & ( ( cos_real @ X2 )
% 5.44/5.72 = Y3 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % arccos_def
% 5.44/5.72 thf(fact_9402_pi__half,axiom,
% 5.44/5.72 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.72 = ( the_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.44/5.72 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.72 & ( ( cos_real @ X2 )
% 5.44/5.72 = zero_zero_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % pi_half
% 5.44/5.72 thf(fact_9403_pi__def,axiom,
% 5.44/5.72 ( pi
% 5.44/5.72 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.44/5.72 @ ( the_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.44/5.72 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.44/5.72 & ( ( cos_real @ X2 )
% 5.44/5.72 = zero_zero_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % pi_def
% 5.44/5.72 thf(fact_9404_cot__gt__zero,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.72 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cot_gt_zero
% 5.44/5.72 thf(fact_9405_tan__cot_H,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.44/5.72 = ( cot_real @ X ) ) ).
% 5.44/5.72
% 5.44/5.72 % tan_cot'
% 5.44/5.72 thf(fact_9406_arcsin__def,axiom,
% 5.44/5.72 ( arcsin
% 5.44/5.72 = ( ^ [Y3: real] :
% 5.44/5.72 ( the_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.44/5.72 & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.72 & ( ( sin_real @ X2 )
% 5.44/5.72 = Y3 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % arcsin_def
% 5.44/5.72 thf(fact_9407_modulo__int__unfold,axiom,
% 5.44/5.72 ! [L2: int,K: int,N2: nat,M: nat] :
% 5.44/5.72 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 | ( ( sgn_sgn_int @ K )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 | ( N2 = zero_zero_nat ) )
% 5.44/5.72 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.44/5.72 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.44/5.72 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 | ( ( sgn_sgn_int @ K )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 | ( N2 = zero_zero_nat ) )
% 5.44/5.72 => ( ( ( ( sgn_sgn_int @ K )
% 5.44/5.72 = ( sgn_sgn_int @ L2 ) )
% 5.44/5.72 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.44/5.72 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 5.44/5.72 & ( ( ( sgn_sgn_int @ K )
% 5.44/5.72 != ( sgn_sgn_int @ L2 ) )
% 5.44/5.72 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.44/5.72 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.44/5.72 @ ( minus_minus_int
% 5.44/5.72 @ ( semiri1314217659103216013at_int
% 5.44/5.72 @ ( times_times_nat @ N2
% 5.44/5.72 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.72 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 5.44/5.72 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % modulo_int_unfold
% 5.44/5.72 thf(fact_9408_powr__int,axiom,
% 5.44/5.72 ! [X: real,I2: int] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.44/5.72 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 5.44/5.72 = ( power_power_real @ X @ ( nat2 @ I2 ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.44/5.72 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 5.44/5.72 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % powr_int
% 5.44/5.72 thf(fact_9409_divide__int__unfold,axiom,
% 5.44/5.72 ! [L2: int,K: int,N2: nat,M: nat] :
% 5.44/5.72 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 | ( ( sgn_sgn_int @ K )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 | ( N2 = zero_zero_nat ) )
% 5.44/5.72 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.44/5.72 = zero_zero_int ) )
% 5.44/5.72 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 | ( ( sgn_sgn_int @ K )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 | ( N2 = zero_zero_nat ) )
% 5.44/5.72 => ( ( ( ( sgn_sgn_int @ K )
% 5.44/5.72 = ( sgn_sgn_int @ L2 ) )
% 5.44/5.72 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.44/5.72 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 5.44/5.72 & ( ( ( sgn_sgn_int @ K )
% 5.44/5.72 != ( sgn_sgn_int @ L2 ) )
% 5.44/5.72 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.44/5.72 = ( uminus_uminus_int
% 5.44/5.72 @ ( semiri1314217659103216013at_int
% 5.44/5.72 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 5.44/5.72 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.72 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % divide_int_unfold
% 5.44/5.72 thf(fact_9410_sum__count__set,axiom,
% 5.44/5.72 ! [Xs2: list_int,X8: set_int] :
% 5.44/5.72 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ X8 )
% 5.44/5.72 => ( ( finite_finite_int @ X8 )
% 5.44/5.72 => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs2 ) @ X8 )
% 5.44/5.72 = ( size_size_list_int @ Xs2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sum_count_set
% 5.44/5.72 thf(fact_9411_sum__count__set,axiom,
% 5.44/5.72 ! [Xs2: list_real,X8: set_real] :
% 5.44/5.72 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ X8 )
% 5.44/5.72 => ( ( finite_finite_real @ X8 )
% 5.44/5.72 => ( ( groups1935376822645274424al_nat @ ( count_list_real @ Xs2 ) @ X8 )
% 5.44/5.72 = ( size_size_list_real @ Xs2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sum_count_set
% 5.44/5.72 thf(fact_9412_sum__count__set,axiom,
% 5.44/5.72 ! [Xs2: list_nat,X8: set_nat] :
% 5.44/5.72 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ X8 )
% 5.44/5.72 => ( ( finite_finite_nat @ X8 )
% 5.44/5.72 => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs2 ) @ X8 )
% 5.44/5.72 = ( size_size_list_nat @ Xs2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sum_count_set
% 5.44/5.72 thf(fact_9413_nat__numeral,axiom,
% 5.44/5.72 ! [K: num] :
% 5.44/5.72 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.44/5.72 = ( numeral_numeral_nat @ K ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_numeral
% 5.44/5.72 thf(fact_9414_nat__1,axiom,
% 5.44/5.72 ( ( nat2 @ one_one_int )
% 5.44/5.72 = ( suc @ zero_zero_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_1
% 5.44/5.72 thf(fact_9415_zless__nat__conj,axiom,
% 5.44/5.72 ! [W: int,Z: int] :
% 5.44/5.72 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.44/5.72 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.44/5.72 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % zless_nat_conj
% 5.44/5.72 thf(fact_9416_zero__less__nat__eq,axiom,
% 5.44/5.72 ! [Z: int] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.44/5.72 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.44/5.72
% 5.44/5.72 % zero_less_nat_eq
% 5.44/5.72 thf(fact_9417_diff__nat__numeral,axiom,
% 5.44/5.72 ! [V: num,V3: num] :
% 5.44/5.72 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.44/5.72 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % diff_nat_numeral
% 5.44/5.72 thf(fact_9418_nat__eq__numeral__power__cancel__iff,axiom,
% 5.44/5.72 ! [Y: int,X: num,N2: nat] :
% 5.44/5.72 ( ( ( nat2 @ Y )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.44/5.72 = ( Y
% 5.44/5.72 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_eq_numeral_power_cancel_iff
% 5.44/5.72 thf(fact_9419_numeral__power__eq__nat__cancel__iff,axiom,
% 5.44/5.72 ! [X: num,N2: nat,Y: int] :
% 5.44/5.72 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.44/5.72 = ( nat2 @ Y ) )
% 5.44/5.72 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.44/5.72 = Y ) ) ).
% 5.44/5.72
% 5.44/5.72 % numeral_power_eq_nat_cancel_iff
% 5.44/5.72 thf(fact_9420_nat__ceiling__le__eq,axiom,
% 5.44/5.72 ! [X: real,A: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.44/5.72 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_ceiling_le_eq
% 5.44/5.72 thf(fact_9421_one__less__nat__eq,axiom,
% 5.44/5.72 ! [Z: int] :
% 5.44/5.72 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.44/5.72 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.44/5.72
% 5.44/5.72 % one_less_nat_eq
% 5.44/5.72 thf(fact_9422_nat__numeral__diff__1,axiom,
% 5.44/5.72 ! [V: num] :
% 5.44/5.72 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.44/5.72 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_numeral_diff_1
% 5.44/5.72 thf(fact_9423_nat__less__numeral__power__cancel__iff,axiom,
% 5.44/5.72 ! [A: int,X: num,N2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.44/5.72 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_less_numeral_power_cancel_iff
% 5.44/5.72 thf(fact_9424_numeral__power__less__nat__cancel__iff,axiom,
% 5.44/5.72 ! [X: num,N2: nat,A: int] :
% 5.44/5.72 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 5.44/5.72 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.44/5.72
% 5.44/5.72 % numeral_power_less_nat_cancel_iff
% 5.44/5.72 thf(fact_9425_numeral__power__le__nat__cancel__iff,axiom,
% 5.44/5.72 ! [X: num,N2: nat,A: int] :
% 5.44/5.72 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 5.44/5.72 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.44/5.72
% 5.44/5.72 % numeral_power_le_nat_cancel_iff
% 5.44/5.72 thf(fact_9426_nat__le__numeral__power__cancel__iff,axiom,
% 5.44/5.72 ! [A: int,X: num,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.44/5.72 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_le_numeral_power_cancel_iff
% 5.44/5.72 thf(fact_9427_nat__numeral__as__int,axiom,
% 5.44/5.72 ( numeral_numeral_nat
% 5.44/5.72 = ( ^ [I5: num] : ( nat2 @ ( numeral_numeral_int @ I5 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_numeral_as_int
% 5.44/5.72 thf(fact_9428_nat__mono,axiom,
% 5.44/5.72 ! [X: int,Y: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ X @ Y )
% 5.44/5.72 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_mono
% 5.44/5.72 thf(fact_9429_nat__one__as__int,axiom,
% 5.44/5.72 ( one_one_nat
% 5.44/5.72 = ( nat2 @ one_one_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_one_as_int
% 5.44/5.72 thf(fact_9430_unset__bit__nat__def,axiom,
% 5.44/5.72 ( bit_se4205575877204974255it_nat
% 5.44/5.72 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % unset_bit_nat_def
% 5.44/5.72 thf(fact_9431_nat__mask__eq,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.44/5.72 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_mask_eq
% 5.44/5.72 thf(fact_9432_nat__mono__iff,axiom,
% 5.44/5.72 ! [Z: int,W: int] :
% 5.44/5.72 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.44/5.72 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.44/5.72 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_mono_iff
% 5.44/5.72 thf(fact_9433_zless__nat__eq__int__zless,axiom,
% 5.44/5.72 ! [M: nat,Z: int] :
% 5.44/5.72 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.44/5.72 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.44/5.72
% 5.44/5.72 % zless_nat_eq_int_zless
% 5.44/5.72 thf(fact_9434_nat__le__iff,axiom,
% 5.44/5.72 ! [X: int,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N2 )
% 5.44/5.72 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_le_iff
% 5.44/5.72 thf(fact_9435_nat__int__add,axiom,
% 5.44/5.72 ! [A: nat,B: nat] :
% 5.44/5.72 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.44/5.72 = ( plus_plus_nat @ A @ B ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_int_add
% 5.44/5.72 thf(fact_9436_sgn__mod,axiom,
% 5.44/5.72 ! [L2: int,K: int] :
% 5.44/5.72 ( ( L2 != zero_zero_int )
% 5.44/5.72 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 5.44/5.72 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.44/5.72 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sgn_mod
% 5.44/5.72 thf(fact_9437_nat__abs__mult__distrib,axiom,
% 5.44/5.72 ! [W: int,Z: int] :
% 5.44/5.72 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.44/5.72 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_abs_mult_distrib
% 5.44/5.72 thf(fact_9438_and__nat__def,axiom,
% 5.44/5.72 ( bit_se727722235901077358nd_nat
% 5.44/5.72 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_nat_def
% 5.44/5.72 thf(fact_9439_nat__plus__as__int,axiom,
% 5.44/5.72 ( plus_plus_nat
% 5.44/5.72 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_plus_as_int
% 5.44/5.72 thf(fact_9440_nat__times__as__int,axiom,
% 5.44/5.72 ( times_times_nat
% 5.44/5.72 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_times_as_int
% 5.44/5.72 thf(fact_9441_or__nat__def,axiom,
% 5.44/5.72 ( bit_se1412395901928357646or_nat
% 5.44/5.72 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_nat_def
% 5.44/5.72 thf(fact_9442_real__nat__ceiling__ge,axiom,
% 5.44/5.72 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_nat_ceiling_ge
% 5.44/5.72 thf(fact_9443_nat__div__as__int,axiom,
% 5.44/5.72 ( divide_divide_nat
% 5.44/5.72 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_div_as_int
% 5.44/5.72 thf(fact_9444_nat__less__eq__zless,axiom,
% 5.44/5.72 ! [W: int,Z: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.44/5.72 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.44/5.72 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_less_eq_zless
% 5.44/5.72 thf(fact_9445_nat__le__eq__zle,axiom,
% 5.44/5.72 ! [W: int,Z: int] :
% 5.44/5.72 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.44/5.72 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.44/5.72 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.44/5.72 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_le_eq_zle
% 5.44/5.72 thf(fact_9446_le__nat__iff,axiom,
% 5.44/5.72 ! [K: int,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.72 => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 5.44/5.72 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % le_nat_iff
% 5.44/5.72 thf(fact_9447_nat__add__distrib,axiom,
% 5.44/5.72 ! [Z: int,Z6: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.44/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.44/5.72 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 5.44/5.72 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_add_distrib
% 5.44/5.72 thf(fact_9448_nat__mult__distrib,axiom,
% 5.44/5.72 ! [Z: int,Z6: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.44/5.72 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.44/5.72 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_mult_distrib
% 5.44/5.72 thf(fact_9449_Suc__as__int,axiom,
% 5.44/5.72 ( suc
% 5.44/5.72 = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Suc_as_int
% 5.44/5.72 thf(fact_9450_nat__abs__triangle__ineq,axiom,
% 5.44/5.72 ! [K: int,L2: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L2 ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_abs_triangle_ineq
% 5.44/5.72 thf(fact_9451_nat__div__distrib,axiom,
% 5.44/5.72 ! [X: int,Y: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.72 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.44/5.72 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_div_distrib
% 5.44/5.72 thf(fact_9452_nat__div__distrib_H,axiom,
% 5.44/5.72 ! [Y: int,X: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.72 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.44/5.72 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_div_distrib'
% 5.44/5.72 thf(fact_9453_nat__power__eq,axiom,
% 5.44/5.72 ! [Z: int,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.44/5.72 => ( ( nat2 @ ( power_power_int @ Z @ N2 ) )
% 5.44/5.72 = ( power_power_nat @ ( nat2 @ Z ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_power_eq
% 5.44/5.72 thf(fact_9454_nat__floor__neg,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.44/5.72 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.72 = zero_zero_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_floor_neg
% 5.44/5.72 thf(fact_9455_div__abs__eq__div__nat,axiom,
% 5.44/5.72 ! [K: int,L2: int] :
% 5.44/5.72 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.44/5.72 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % div_abs_eq_div_nat
% 5.44/5.72 thf(fact_9456_nat__mod__distrib,axiom,
% 5.44/5.72 ! [X: int,Y: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.72 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 5.44/5.72 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_mod_distrib
% 5.44/5.72 thf(fact_9457_floor__eq3,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.44/5.72 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.72 = N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % floor_eq3
% 5.44/5.72 thf(fact_9458_le__nat__floor,axiom,
% 5.44/5.72 ! [X: nat,A: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.44/5.72 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % le_nat_floor
% 5.44/5.72 thf(fact_9459_nat__take__bit__eq,axiom,
% 5.44/5.72 ! [K: int,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.72 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.44/5.72 = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_take_bit_eq
% 5.44/5.72 thf(fact_9460_take__bit__nat__eq,axiom,
% 5.44/5.72 ! [K: int,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.72 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) )
% 5.44/5.72 = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_nat_eq
% 5.44/5.72 thf(fact_9461_bit__nat__iff,axiom,
% 5.44/5.72 ! [K: int,N2: nat] :
% 5.44/5.72 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N2 )
% 5.44/5.72 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.72 & ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bit_nat_iff
% 5.44/5.72 thf(fact_9462_divide__int__def,axiom,
% 5.44/5.72 ( divide_divide_int
% 5.44/5.72 = ( ^ [K3: int,L: int] :
% 5.44/5.72 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 5.44/5.72 @ ( if_int
% 5.44/5.72 @ ( ( sgn_sgn_int @ K3 )
% 5.44/5.72 = ( sgn_sgn_int @ L ) )
% 5.44/5.72 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 5.44/5.72 @ ( uminus_uminus_int
% 5.44/5.72 @ ( semiri1314217659103216013at_int
% 5.44/5.72 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 5.44/5.72 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.72 @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % divide_int_def
% 5.44/5.72 thf(fact_9463_modulo__int__def,axiom,
% 5.44/5.72 ( modulo_modulo_int
% 5.44/5.72 = ( ^ [K3: int,L: int] :
% 5.44/5.72 ( if_int @ ( L = zero_zero_int ) @ K3
% 5.44/5.72 @ ( if_int
% 5.44/5.72 @ ( ( sgn_sgn_int @ K3 )
% 5.44/5.72 = ( sgn_sgn_int @ L ) )
% 5.44/5.72 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 5.44/5.72 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 5.44/5.72 @ ( minus_minus_int
% 5.44/5.72 @ ( times_times_int @ ( abs_abs_int @ L )
% 5.44/5.72 @ ( zero_n2684676970156552555ol_int
% 5.44/5.72 @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 5.44/5.72 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % modulo_int_def
% 5.44/5.72 thf(fact_9464_nat__2,axiom,
% 5.44/5.72 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.72 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_2
% 5.44/5.72 thf(fact_9465_Suc__nat__eq__nat__zadd1,axiom,
% 5.44/5.72 ! [Z: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.44/5.72 => ( ( suc @ ( nat2 @ Z ) )
% 5.44/5.72 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Suc_nat_eq_nat_zadd1
% 5.44/5.72 thf(fact_9466_nat__less__iff,axiom,
% 5.44/5.72 ! [W: int,M: nat] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.44/5.72 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.44/5.72 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_less_iff
% 5.44/5.72 thf(fact_9467_nat__mult__distrib__neg,axiom,
% 5.44/5.72 ! [Z: int,Z6: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.44/5.72 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.44/5.72 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_mult_distrib_neg
% 5.44/5.72 thf(fact_9468_nat__abs__int__diff,axiom,
% 5.44/5.72 ! [A: nat,B: nat] :
% 5.44/5.72 ( ( ( ord_less_eq_nat @ A @ B )
% 5.44/5.72 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.44/5.72 = ( minus_minus_nat @ B @ A ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.44/5.72 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.44/5.72 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_abs_int_diff
% 5.44/5.72 thf(fact_9469_floor__eq4,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.44/5.72 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.44/5.72 = N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % floor_eq4
% 5.44/5.72 thf(fact_9470_even__nat__iff,axiom,
% 5.44/5.72 ! [K: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.72 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.44/5.72 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % even_nat_iff
% 5.44/5.72 thf(fact_9471_powr__real__of__int,axiom,
% 5.44/5.72 ! [X: real,N2: int] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.44/5.72 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N2 ) )
% 5.44/5.72 = ( power_power_real @ X @ ( nat2 @ N2 ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.44/5.72 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N2 ) )
% 5.44/5.72 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % powr_real_of_int
% 5.44/5.72 thf(fact_9472_bij__betw__nth__root__unity,axiom,
% 5.44/5.72 ! [C: complex,N2: nat] :
% 5.44/5.72 ( ( C != zero_zero_complex )
% 5.44/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 5.44/5.72 @ ( collect_complex
% 5.44/5.72 @ ^ [Z5: complex] :
% 5.44/5.72 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.72 = one_one_complex ) )
% 5.44/5.72 @ ( collect_complex
% 5.44/5.72 @ ^ [Z5: complex] :
% 5.44/5.72 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.72 = C ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bij_betw_nth_root_unity
% 5.44/5.72 thf(fact_9473_arctan__inverse,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( X != zero_zero_real )
% 5.44/5.72 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.44/5.72 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % arctan_inverse
% 5.44/5.72 thf(fact_9474_cis__multiple__2pi,axiom,
% 5.44/5.72 ! [N2: real] :
% 5.44/5.72 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.44/5.72 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.44/5.72 = one_one_complex ) ) ).
% 5.44/5.72
% 5.44/5.72 % cis_multiple_2pi
% 5.44/5.72 thf(fact_9475_real__root__zero,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( root @ N2 @ zero_zero_real )
% 5.44/5.72 = zero_zero_real ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_zero
% 5.44/5.72 thf(fact_9476_real__root__Suc__0,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.44/5.72 = X ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_Suc_0
% 5.44/5.72 thf(fact_9477_real__root__eq__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ( root @ N2 @ X )
% 5.44/5.72 = ( root @ N2 @ Y ) )
% 5.44/5.72 = ( X = Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_eq_iff
% 5.44/5.72 thf(fact_9478_root__0,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( root @ zero_zero_nat @ X )
% 5.44/5.72 = zero_zero_real ) ).
% 5.44/5.72
% 5.44/5.72 % root_0
% 5.44/5.72 thf(fact_9479_sgn__le__0__iff,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 5.44/5.72 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % sgn_le_0_iff
% 5.44/5.72 thf(fact_9480_zero__le__sgn__iff,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 5.44/5.72 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.44/5.72
% 5.44/5.72 % zero_le_sgn_iff
% 5.44/5.72 thf(fact_9481_real__root__eq__0__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ( root @ N2 @ X )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 = ( X = zero_zero_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_eq_0_iff
% 5.44/5.72 thf(fact_9482_real__root__less__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) )
% 5.44/5.72 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_less_iff
% 5.44/5.72 thf(fact_9483_real__root__le__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) )
% 5.44/5.72 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_le_iff
% 5.44/5.72 thf(fact_9484_real__root__one,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( root @ N2 @ one_one_real )
% 5.44/5.72 = one_one_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_one
% 5.44/5.72 thf(fact_9485_real__root__eq__1__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ( root @ N2 @ X )
% 5.44/5.72 = one_one_real )
% 5.44/5.72 = ( X = one_one_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_eq_1_iff
% 5.44/5.72 thf(fact_9486_real__root__gt__0__iff,axiom,
% 5.44/5.72 ! [N2: nat,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.44/5.72 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_gt_0_iff
% 5.44/5.72 thf(fact_9487_real__root__lt__0__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ ( root @ N2 @ X ) @ zero_zero_real )
% 5.44/5.72 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_lt_0_iff
% 5.44/5.72 thf(fact_9488_real__root__ge__0__iff,axiom,
% 5.44/5.72 ! [N2: nat,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.44/5.72 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_ge_0_iff
% 5.44/5.72 thf(fact_9489_real__root__le__0__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ zero_zero_real )
% 5.44/5.72 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_le_0_iff
% 5.44/5.72 thf(fact_9490_real__root__gt__1__iff,axiom,
% 5.44/5.72 ! [N2: nat,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.44/5.72 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_gt_1_iff
% 5.44/5.72 thf(fact_9491_real__root__lt__1__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ ( root @ N2 @ X ) @ one_one_real )
% 5.44/5.72 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_lt_1_iff
% 5.44/5.72 thf(fact_9492_real__root__ge__1__iff,axiom,
% 5.44/5.72 ! [N2: nat,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.44/5.72 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_ge_1_iff
% 5.44/5.72 thf(fact_9493_real__root__le__1__iff,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ one_one_real )
% 5.44/5.72 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_le_1_iff
% 5.44/5.72 thf(fact_9494_real__root__pow__pos2,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.44/5.72 = X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_pow_pos2
% 5.44/5.72 thf(fact_9495_sgn__root,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( sgn_sgn_real @ ( root @ N2 @ X ) )
% 5.44/5.72 = ( sgn_sgn_real @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sgn_root
% 5.44/5.72 thf(fact_9496_real__root__divide,axiom,
% 5.44/5.72 ! [N2: nat,X: real,Y: real] :
% 5.44/5.72 ( ( root @ N2 @ ( divide_divide_real @ X @ Y ) )
% 5.44/5.72 = ( divide_divide_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_divide
% 5.44/5.72 thf(fact_9497_real__root__minus,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( root @ N2 @ ( uminus_uminus_real @ X ) )
% 5.44/5.72 = ( uminus_uminus_real @ ( root @ N2 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_minus
% 5.44/5.72 thf(fact_9498_real__root__commute,axiom,
% 5.44/5.72 ! [M: nat,N2: nat,X: real] :
% 5.44/5.72 ( ( root @ M @ ( root @ N2 @ X ) )
% 5.44/5.72 = ( root @ N2 @ ( root @ M @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_commute
% 5.44/5.72 thf(fact_9499_real__root__mult,axiom,
% 5.44/5.72 ! [N2: nat,X: real,Y: real] :
% 5.44/5.72 ( ( root @ N2 @ ( times_times_real @ X @ Y ) )
% 5.44/5.72 = ( times_times_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_mult
% 5.44/5.72 thf(fact_9500_real__root__mult__exp,axiom,
% 5.44/5.72 ! [M: nat,N2: nat,X: real] :
% 5.44/5.72 ( ( root @ ( times_times_nat @ M @ N2 ) @ X )
% 5.44/5.72 = ( root @ M @ ( root @ N2 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_mult_exp
% 5.44/5.72 thf(fact_9501_real__root__inverse,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( root @ N2 @ ( inverse_inverse_real @ X ) )
% 5.44/5.72 = ( inverse_inverse_real @ ( root @ N2 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_inverse
% 5.44/5.72 thf(fact_9502_real__root__pos__pos__le,axiom,
% 5.44/5.72 ! [X: real,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_pos_pos_le
% 5.44/5.72 thf(fact_9503_real__sgn__eq,axiom,
% 5.44/5.72 ( sgn_sgn_real
% 5.44/5.72 = ( ^ [X2: real] : ( divide_divide_real @ X2 @ ( abs_abs_real @ X2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_sgn_eq
% 5.44/5.72 thf(fact_9504_root__sgn__power,axiom,
% 5.44/5.72 ! [N2: nat,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 5.44/5.72 = Y ) ) ).
% 5.44/5.72
% 5.44/5.72 % root_sgn_power
% 5.44/5.72 thf(fact_9505_sgn__power__root,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X ) ) @ N2 ) )
% 5.44/5.72 = X ) ) ).
% 5.44/5.72
% 5.44/5.72 % sgn_power_root
% 5.44/5.72 thf(fact_9506_split__root,axiom,
% 5.44/5.72 ! [P: real > $o,N2: nat,X: real] :
% 5.44/5.72 ( ( P @ ( root @ N2 @ X ) )
% 5.44/5.72 = ( ( ( N2 = zero_zero_nat )
% 5.44/5.72 => ( P @ zero_zero_real ) )
% 5.44/5.72 & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ! [Y3: real] :
% 5.44/5.72 ( ( ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N2 ) )
% 5.44/5.72 = X )
% 5.44/5.72 => ( P @ Y3 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % split_root
% 5.44/5.72 thf(fact_9507_real__root__less__mono,axiom,
% 5.44/5.72 ! [N2: nat,X: real,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ X @ Y )
% 5.44/5.72 => ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_less_mono
% 5.44/5.72 thf(fact_9508_real__root__le__mono,axiom,
% 5.44/5.72 ! [N2: nat,X: real,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ X @ Y )
% 5.44/5.72 => ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_le_mono
% 5.44/5.72 thf(fact_9509_real__root__power,axiom,
% 5.44/5.72 ! [N2: nat,X: real,K: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( root @ N2 @ ( power_power_real @ X @ K ) )
% 5.44/5.72 = ( power_power_real @ ( root @ N2 @ X ) @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_power
% 5.44/5.72 thf(fact_9510_real__root__abs,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( root @ N2 @ ( abs_abs_real @ X ) )
% 5.44/5.72 = ( abs_abs_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_abs
% 5.44/5.72 thf(fact_9511_real__root__gt__zero,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_gt_zero
% 5.44/5.72 thf(fact_9512_real__root__strict__decreasing,axiom,
% 5.44/5.72 ! [N2: nat,N3: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_nat @ N2 @ N3 )
% 5.44/5.72 => ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.72 => ( ord_less_real @ ( root @ N3 @ X ) @ ( root @ N2 @ X ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_strict_decreasing
% 5.44/5.72 thf(fact_9513_sqrt__def,axiom,
% 5.44/5.72 ( sqrt
% 5.44/5.72 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sqrt_def
% 5.44/5.72 thf(fact_9514_sgn__real__def,axiom,
% 5.44/5.72 ( sgn_sgn_real
% 5.44/5.72 = ( ^ [A4: real] : ( if_real @ ( A4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sgn_real_def
% 5.44/5.72 thf(fact_9515_root__abs__power,axiom,
% 5.44/5.72 ! [N2: nat,Y: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 5.44/5.72 = ( abs_abs_real @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % root_abs_power
% 5.44/5.72 thf(fact_9516_sin__times__pi__eq__0,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % sin_times_pi_eq_0
% 5.44/5.72 thf(fact_9517_real__root__pos__pos,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_pos_pos
% 5.44/5.72 thf(fact_9518_real__root__strict__increasing,axiom,
% 5.44/5.72 ! [N2: nat,N3: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_nat @ N2 @ N3 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.72 => ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N3 @ X ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_strict_increasing
% 5.44/5.72 thf(fact_9519_real__root__decreasing,axiom,
% 5.44/5.72 ! [N2: nat,N3: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_nat @ N2 @ N3 )
% 5.44/5.72 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.44/5.72 => ( ord_less_eq_real @ ( root @ N3 @ X ) @ ( root @ N2 @ X ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_decreasing
% 5.44/5.72 thf(fact_9520_real__root__pow__pos,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.44/5.72 = X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_pow_pos
% 5.44/5.72 thf(fact_9521_odd__real__root__power__cancel,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( ( root @ N2 @ ( power_power_real @ X @ N2 ) )
% 5.44/5.72 = X ) ) ).
% 5.44/5.72
% 5.44/5.72 % odd_real_root_power_cancel
% 5.44/5.72 thf(fact_9522_odd__real__root__unique,axiom,
% 5.44/5.72 ! [N2: nat,Y: real,X: real] :
% 5.44/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( ( ( power_power_real @ Y @ N2 )
% 5.44/5.72 = X )
% 5.44/5.72 => ( ( root @ N2 @ X )
% 5.44/5.72 = Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % odd_real_root_unique
% 5.44/5.72 thf(fact_9523_odd__real__root__pow,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.44/5.72 = X ) ) ).
% 5.44/5.72
% 5.44/5.72 % odd_real_root_pow
% 5.44/5.72 thf(fact_9524_real__root__pos__unique,axiom,
% 5.44/5.72 ! [N2: nat,Y: real,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.44/5.72 => ( ( ( power_power_real @ Y @ N2 )
% 5.44/5.72 = X )
% 5.44/5.72 => ( ( root @ N2 @ X )
% 5.44/5.72 = Y ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_pos_unique
% 5.44/5.72 thf(fact_9525_real__root__power__cancel,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( root @ N2 @ ( power_power_real @ X @ N2 ) )
% 5.44/5.72 = X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_power_cancel
% 5.44/5.72 thf(fact_9526_sgn__power__injE,axiom,
% 5.44/5.72 ! [A: real,N2: nat,X: real,B: real] :
% 5.44/5.72 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.44/5.72 = X )
% 5.44/5.72 => ( ( X
% 5.44/5.72 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 5.44/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( A = B ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sgn_power_injE
% 5.44/5.72 thf(fact_9527_real__root__increasing,axiom,
% 5.44/5.72 ! [N2: nat,N3: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_eq_nat @ N2 @ N3 )
% 5.44/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.72 => ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N3 @ X ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_root_increasing
% 5.44/5.72 thf(fact_9528_cis__Arg__unique,axiom,
% 5.44/5.72 ! [Z: complex,X: real] :
% 5.44/5.72 ( ( ( sgn_sgn_complex @ Z )
% 5.44/5.72 = ( cis @ X ) )
% 5.44/5.72 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.44/5.72 => ( ( ord_less_eq_real @ X @ pi )
% 5.44/5.72 => ( ( arg @ Z )
% 5.44/5.72 = X ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cis_Arg_unique
% 5.44/5.72 thf(fact_9529_ln__root,axiom,
% 5.44/5.72 ! [N2: nat,B: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.72 => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 5.44/5.72 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % ln_root
% 5.44/5.72 thf(fact_9530_log__root,axiom,
% 5.44/5.72 ! [N2: nat,A: real,B: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.44/5.72 => ( ( log @ B @ ( root @ N2 @ A ) )
% 5.44/5.72 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % log_root
% 5.44/5.72 thf(fact_9531_log__base__root,axiom,
% 5.44/5.72 ! [N2: nat,B: real,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.44/5.72 => ( ( log @ ( root @ N2 @ B ) @ X )
% 5.44/5.72 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % log_base_root
% 5.44/5.72 thf(fact_9532_sin__integer__2pi,axiom,
% 5.44/5.72 ! [N2: real] :
% 5.44/5.72 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.44/5.72 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.44/5.72 = zero_zero_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % sin_integer_2pi
% 5.44/5.72 thf(fact_9533_cos__integer__2pi,axiom,
% 5.44/5.72 ! [N2: real] :
% 5.44/5.72 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.44/5.72 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.44/5.72 = one_one_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % cos_integer_2pi
% 5.44/5.72 thf(fact_9534_Arg__correct,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( Z != zero_zero_complex )
% 5.44/5.72 => ( ( ( sgn_sgn_complex @ Z )
% 5.44/5.72 = ( cis @ ( arg @ Z ) ) )
% 5.44/5.72 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.44/5.72 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Arg_correct
% 5.44/5.72 thf(fact_9535_root__powr__inverse,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( root @ N2 @ X )
% 5.44/5.72 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % root_powr_inverse
% 5.44/5.72 thf(fact_9536_Arg__def,axiom,
% 5.44/5.72 ( arg
% 5.44/5.72 = ( ^ [Z5: complex] :
% 5.44/5.72 ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 5.44/5.72 @ ( fChoice_real
% 5.44/5.72 @ ^ [A4: real] :
% 5.44/5.72 ( ( ( sgn_sgn_complex @ Z5 )
% 5.44/5.72 = ( cis @ A4 ) )
% 5.44/5.72 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 5.44/5.72 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Arg_def
% 5.44/5.72 thf(fact_9537_xor__Suc__0__eq,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.44/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.72 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.72 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_Suc_0_eq
% 5.44/5.72 thf(fact_9538_Suc__0__xor__eq,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.72 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.72 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Suc_0_xor_eq
% 5.44/5.72 thf(fact_9539_horner__sum__of__bool__2__less,axiom,
% 5.44/5.72 ! [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 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % horner_sum_of_bool_2_less
% 5.44/5.72 thf(fact_9540_xor__nat__numerals_I4_J,axiom,
% 5.44/5.72 ! [X: num] :
% 5.44/5.72 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.72 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_nat_numerals(4)
% 5.44/5.72 thf(fact_9541_xor__nat__numerals_I3_J,axiom,
% 5.44/5.72 ! [X: num] :
% 5.44/5.72 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.44/5.72 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_nat_numerals(3)
% 5.44/5.72 thf(fact_9542_xor__nat__numerals_I2_J,axiom,
% 5.44/5.72 ! [Y: num] :
% 5.44/5.72 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.44/5.72 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_nat_numerals(2)
% 5.44/5.72 thf(fact_9543_xor__nat__numerals_I1_J,axiom,
% 5.44/5.72 ! [Y: num] :
% 5.44/5.72 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.44/5.72 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_nat_numerals(1)
% 5.44/5.72 thf(fact_9544_xor__nat__unfold,axiom,
% 5.44/5.72 ( bit_se6528837805403552850or_nat
% 5.44/5.72 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_nat_unfold
% 5.44/5.72 thf(fact_9545_xor__nat__rec,axiom,
% 5.44/5.72 ( bit_se6528837805403552850or_nat
% 5.44/5.72 = ( ^ [M6: nat,N: nat] :
% 5.44/5.72 ( plus_plus_nat
% 5.44/5.72 @ ( zero_n2687167440665602831ol_nat
% 5.44/5.72 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.44/5.72 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.44/5.72 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_nat_rec
% 5.44/5.72 thf(fact_9546_Cauchy__iff2,axiom,
% 5.44/5.72 ( topolo4055970368930404560y_real
% 5.44/5.72 = ( ^ [X4: nat > real] :
% 5.44/5.72 ! [J3: nat] :
% 5.44/5.72 ? [M9: nat] :
% 5.44/5.72 ! [M6: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ M9 @ M6 )
% 5.44/5.72 => ! [N: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ M9 @ N )
% 5.44/5.72 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X4 @ M6 ) @ ( X4 @ N ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Cauchy_iff2
% 5.44/5.72 thf(fact_9547_push__bit__nonnegative__int__iff,axiom,
% 5.44/5.72 ! [N2: nat,K: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.44/5.72 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.44/5.72
% 5.44/5.72 % push_bit_nonnegative_int_iff
% 5.44/5.72 thf(fact_9548_push__bit__negative__int__iff,axiom,
% 5.44/5.72 ! [N2: nat,K: int] :
% 5.44/5.72 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 5.44/5.72 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % push_bit_negative_int_iff
% 5.44/5.72 thf(fact_9549_concat__bit__of__zero__1,axiom,
% 5.44/5.72 ! [N2: nat,L2: int] :
% 5.44/5.72 ( ( bit_concat_bit @ N2 @ zero_zero_int @ L2 )
% 5.44/5.72 = ( bit_se545348938243370406it_int @ N2 @ L2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % concat_bit_of_zero_1
% 5.44/5.72 thf(fact_9550_xor__nonnegative__int__iff,axiom,
% 5.44/5.72 ! [K: int,L2: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 5.44/5.72 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.44/5.72 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_nonnegative_int_iff
% 5.44/5.72 thf(fact_9551_xor__negative__int__iff,axiom,
% 5.44/5.72 ! [K: int,L2: int] :
% 5.44/5.72 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 5.44/5.72 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.44/5.72 != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_negative_int_iff
% 5.44/5.72 thf(fact_9552_push__bit__of__Suc__0,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % push_bit_of_Suc_0
% 5.44/5.72 thf(fact_9553_flip__bit__int__def,axiom,
% 5.44/5.72 ( bit_se2159334234014336723it_int
% 5.44/5.72 = ( ^ [N: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % flip_bit_int_def
% 5.44/5.72 thf(fact_9554_bit__xor__int__iff,axiom,
% 5.44/5.72 ! [K: int,L2: int,N2: nat] :
% 5.44/5.72 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N2 )
% 5.44/5.72 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.44/5.72 != ( bit_se1146084159140164899it_int @ L2 @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bit_xor_int_iff
% 5.44/5.72 thf(fact_9555_push__bit__nat__eq,axiom,
% 5.44/5.72 ! [N2: nat,K: int] :
% 5.44/5.72 ( ( bit_se547839408752420682it_nat @ N2 @ ( nat2 @ K ) )
% 5.44/5.72 = ( nat2 @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % push_bit_nat_eq
% 5.44/5.72 thf(fact_9556_XOR__lower,axiom,
% 5.44/5.72 ! [X: int,Y: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.44/5.72 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % XOR_lower
% 5.44/5.72 thf(fact_9557_set__bit__nat__def,axiom,
% 5.44/5.72 ( bit_se7882103937844011126it_nat
% 5.44/5.72 = ( ^ [M6: nat,N: nat] : ( bit_se1412395901928357646or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % set_bit_nat_def
% 5.44/5.72 thf(fact_9558_flip__bit__nat__def,axiom,
% 5.44/5.72 ( bit_se2161824704523386999it_nat
% 5.44/5.72 = ( ^ [M6: nat,N: nat] : ( bit_se6528837805403552850or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % flip_bit_nat_def
% 5.44/5.72 thf(fact_9559_bit__push__bit__iff__int,axiom,
% 5.44/5.72 ! [M: nat,K: int,N2: nat] :
% 5.44/5.72 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 5.44/5.72 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.72 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bit_push_bit_iff_int
% 5.44/5.72 thf(fact_9560_xor__nat__def,axiom,
% 5.44/5.72 ( bit_se6528837805403552850or_nat
% 5.44/5.72 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_nat_def
% 5.44/5.72 thf(fact_9561_bit__push__bit__iff__nat,axiom,
% 5.44/5.72 ! [M: nat,Q2: nat,N2: nat] :
% 5.44/5.72 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N2 )
% 5.44/5.72 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.72 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bit_push_bit_iff_nat
% 5.44/5.72 thf(fact_9562_concat__bit__eq,axiom,
% 5.44/5.72 ( bit_concat_bit
% 5.44/5.72 = ( ^ [N: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % concat_bit_eq
% 5.44/5.72 thf(fact_9563_concat__bit__def,axiom,
% 5.44/5.72 ( bit_concat_bit
% 5.44/5.72 = ( ^ [N: nat,K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % concat_bit_def
% 5.44/5.72 thf(fact_9564_set__bit__int__def,axiom,
% 5.44/5.72 ( bit_se7879613467334960850it_int
% 5.44/5.72 = ( ^ [N: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % set_bit_int_def
% 5.44/5.72 thf(fact_9565_push__bit__nat__def,axiom,
% 5.44/5.72 ( bit_se547839408752420682it_nat
% 5.44/5.72 = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % push_bit_nat_def
% 5.44/5.72 thf(fact_9566_push__bit__int__def,axiom,
% 5.44/5.72 ( bit_se545348938243370406it_int
% 5.44/5.72 = ( ^ [N: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % push_bit_int_def
% 5.44/5.72 thf(fact_9567_push__bit__minus__one,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.72 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % push_bit_minus_one
% 5.44/5.72 thf(fact_9568_XOR__upper,axiom,
% 5.44/5.72 ! [X: int,N2: nat,Y: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.44/5.72 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.72 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.44/5.72 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % XOR_upper
% 5.44/5.72 thf(fact_9569_xor__int__rec,axiom,
% 5.44/5.72 ( bit_se6526347334894502574or_int
% 5.44/5.72 = ( ^ [K3: int,L: int] :
% 5.44/5.72 ( plus_plus_int
% 5.44/5.72 @ ( zero_n2684676970156552555ol_int
% 5.44/5.72 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.44/5.72 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.44/5.72 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_int_rec
% 5.44/5.72 thf(fact_9570_xor__int__unfold,axiom,
% 5.44/5.72 ( bit_se6526347334894502574or_int
% 5.44/5.72 = ( ^ [K3: int,L: int] :
% 5.44/5.72 ( if_int
% 5.44/5.72 @ ( K3
% 5.44/5.72 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.72 @ ( bit_ri7919022796975470100ot_int @ L )
% 5.44/5.72 @ ( if_int
% 5.44/5.72 @ ( L
% 5.44/5.72 = ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.72 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.44/5.72 @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_int_unfold
% 5.44/5.72 thf(fact_9571_Sum__Ico__nat,axiom,
% 5.44/5.72 ! [M: nat,N2: nat] :
% 5.44/5.72 ( ( groups3542108847815614940at_nat
% 5.44/5.72 @ ^ [X2: nat] : X2
% 5.44/5.72 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.44/5.72 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Sum_Ico_nat
% 5.44/5.72 thf(fact_9572_VEBT_Osize_I3_J,axiom,
% 5.44/5.72 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.44/5.72 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.44/5.72 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT.size(3)
% 5.44/5.72 thf(fact_9573_sum__power2,axiom,
% 5.44/5.72 ! [K: nat] :
% 5.44/5.72 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.44/5.72 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % sum_power2
% 5.44/5.72 thf(fact_9574_not__nonnegative__int__iff,axiom,
% 5.44/5.72 ! [K: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.44/5.72 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % not_nonnegative_int_iff
% 5.44/5.72 thf(fact_9575_not__negative__int__iff,axiom,
% 5.44/5.72 ! [K: int] :
% 5.44/5.72 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.44/5.72 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.44/5.72
% 5.44/5.72 % not_negative_int_iff
% 5.44/5.72 thf(fact_9576_atLeastLessThan__singleton,axiom,
% 5.44/5.72 ! [M: nat] :
% 5.44/5.72 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.44/5.72 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeastLessThan_singleton
% 5.44/5.72 thf(fact_9577_and__minus__minus__numerals,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_minus_minus_numerals
% 5.44/5.72 thf(fact_9578_or__minus__minus__numerals,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_minus_minus_numerals
% 5.44/5.72 thf(fact_9579_bit__not__int__iff,axiom,
% 5.44/5.72 ! [K: int,N2: nat] :
% 5.44/5.72 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N2 )
% 5.44/5.72 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bit_not_int_iff
% 5.44/5.72 thf(fact_9580_all__nat__less__eq,axiom,
% 5.44/5.72 ! [N2: nat,P: nat > $o] :
% 5.44/5.72 ( ( ! [M6: nat] :
% 5.44/5.72 ( ( ord_less_nat @ M6 @ N2 )
% 5.44/5.72 => ( P @ M6 ) ) )
% 5.44/5.72 = ( ! [X2: nat] :
% 5.44/5.72 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.72 => ( P @ X2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % all_nat_less_eq
% 5.44/5.72 thf(fact_9581_ex__nat__less__eq,axiom,
% 5.44/5.72 ! [N2: nat,P: nat > $o] :
% 5.44/5.72 ( ( ? [M6: nat] :
% 5.44/5.72 ( ( ord_less_nat @ M6 @ N2 )
% 5.44/5.72 & ( P @ M6 ) ) )
% 5.44/5.72 = ( ? [X2: nat] :
% 5.44/5.72 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.72 & ( P @ X2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % ex_nat_less_eq
% 5.44/5.72 thf(fact_9582_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.44/5.72 ! [L2: nat,U: nat] :
% 5.44/5.72 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 5.44/5.72 = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeastLessThanSuc_atLeastAtMost
% 5.44/5.72 thf(fact_9583_or__int__def,axiom,
% 5.44/5.72 ( bit_se1409905431419307370or_int
% 5.44/5.72 = ( ^ [K3: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_int_def
% 5.44/5.72 thf(fact_9584_not__int__def,axiom,
% 5.44/5.72 ( bit_ri7919022796975470100ot_int
% 5.44/5.72 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % not_int_def
% 5.44/5.72 thf(fact_9585_and__not__numerals_I1_J,axiom,
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.44/5.72 = zero_zero_int ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(1)
% 5.44/5.72 thf(fact_9586_or__not__numerals_I1_J,axiom,
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(1)
% 5.44/5.72 thf(fact_9587_atLeast0__lessThan__Suc,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.44/5.72 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeast0_lessThan_Suc
% 5.44/5.72 thf(fact_9588_unset__bit__int__def,axiom,
% 5.44/5.72 ( bit_se4203085406695923979it_int
% 5.44/5.72 = ( ^ [N: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % unset_bit_int_def
% 5.44/5.72 thf(fact_9589_xor__int__def,axiom,
% 5.44/5.72 ( bit_se6526347334894502574or_int
% 5.44/5.72 = ( ^ [K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_int_def
% 5.44/5.72 thf(fact_9590_not__int__div__2,axiom,
% 5.44/5.72 ! [K: int] :
% 5.44/5.72 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % not_int_div_2
% 5.44/5.72 thf(fact_9591_even__not__iff__int,axiom,
% 5.44/5.72 ! [K: int] :
% 5.44/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.44/5.72 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % even_not_iff_int
% 5.44/5.72 thf(fact_9592_and__not__numerals_I4_J,axiom,
% 5.44/5.72 ! [M: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.44/5.72 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(4)
% 5.44/5.72 thf(fact_9593_and__not__numerals_I2_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.72 = one_one_int ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(2)
% 5.44/5.72 thf(fact_9594_or__not__numerals_I4_J,axiom,
% 5.44/5.72 ! [M: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(4)
% 5.44/5.72 thf(fact_9595_or__not__numerals_I2_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(2)
% 5.44/5.72 thf(fact_9596_bit__minus__int__iff,axiom,
% 5.44/5.72 ! [K: int,N2: nat] :
% 5.44/5.72 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N2 )
% 5.44/5.72 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % bit_minus_int_iff
% 5.44/5.72 thf(fact_9597_int__numeral__or__not__num__neg,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % int_numeral_or_not_num_neg
% 5.44/5.72 thf(fact_9598_int__numeral__not__or__num__neg,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % int_numeral_not_or_num_neg
% 5.44/5.72 thf(fact_9599_numeral__or__not__num__eq,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) )
% 5.44/5.72 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % numeral_or_not_num_eq
% 5.44/5.72 thf(fact_9600_atLeastLessThanSuc,axiom,
% 5.44/5.72 ! [M: nat,N2: nat] :
% 5.44/5.72 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.72 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.44/5.72 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.72 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.44/5.72 = bot_bot_set_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeastLessThanSuc
% 5.44/5.72 thf(fact_9601_prod__Suc__fact,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.72 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod_Suc_fact
% 5.44/5.72 thf(fact_9602_prod__Suc__Suc__fact,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.44/5.72 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod_Suc_Suc_fact
% 5.44/5.72 thf(fact_9603_and__not__numerals_I5_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.72 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(5)
% 5.44/5.72 thf(fact_9604_and__not__numerals_I7_J,axiom,
% 5.44/5.72 ! [M: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.44/5.72 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(7)
% 5.44/5.72 thf(fact_9605_or__not__numerals_I3_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(3)
% 5.44/5.72 thf(fact_9606_and__not__numerals_I3_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.72 = zero_zero_int ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(3)
% 5.44/5.72 thf(fact_9607_or__not__numerals_I7_J,axiom,
% 5.44/5.72 ! [M: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(7)
% 5.44/5.72 thf(fact_9608_atLeastLessThan__nat__numeral,axiom,
% 5.44/5.72 ! [M: nat,K: num] :
% 5.44/5.72 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.44/5.72 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.44/5.72 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.44/5.72 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.44/5.72 = bot_bot_set_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeastLessThan_nat_numeral
% 5.44/5.72 thf(fact_9609_and__not__numerals_I6_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.72 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(6)
% 5.44/5.72 thf(fact_9610_and__not__numerals_I9_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.72 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(9)
% 5.44/5.72 thf(fact_9611_or__not__numerals_I6_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.72 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(6)
% 5.44/5.72 thf(fact_9612_or__not__numerals_I5_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.72 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(5)
% 5.44/5.72 thf(fact_9613_atLeast1__lessThan__eq__remove0,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.44/5.72 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeast1_lessThan_eq_remove0
% 5.44/5.72 thf(fact_9614_and__not__numerals_I8_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.72 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_numerals(8)
% 5.44/5.72 thf(fact_9615_or__not__numerals_I8_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.72 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(8)
% 5.44/5.72 thf(fact_9616_or__not__numerals_I9_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.72 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % or_not_numerals(9)
% 5.44/5.72 thf(fact_9617_not__int__rec,axiom,
% 5.44/5.72 ( bit_ri7919022796975470100ot_int
% 5.44/5.72 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % not_int_rec
% 5.44/5.72 thf(fact_9618_Chebyshev__sum__upper__nat,axiom,
% 5.44/5.72 ! [N2: nat,A: nat > nat,B: nat > nat] :
% 5.44/5.72 ( ! [I4: nat,J2: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ I4 @ J2 )
% 5.44/5.72 => ( ( ord_less_nat @ J2 @ N2 )
% 5.44/5.72 => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 5.44/5.72 => ( ! [I4: nat,J2: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ I4 @ J2 )
% 5.44/5.72 => ( ( ord_less_nat @ J2 @ N2 )
% 5.44/5.72 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 5.44/5.72 => ( ord_less_eq_nat
% 5.44/5.72 @ ( times_times_nat @ N2
% 5.44/5.72 @ ( groups3542108847815614940at_nat
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( B @ I5 ) )
% 5.44/5.72 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 5.44/5.72 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Chebyshev_sum_upper_nat
% 5.44/5.72 thf(fact_9619_VEBT_Osize__gen_I1_J,axiom,
% 5.44/5.72 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.44/5.72 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.44/5.72 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT.size_gen(1)
% 5.44/5.72 thf(fact_9620_VEBT_Osize__gen_I2_J,axiom,
% 5.44/5.72 ! [X21: $o,X222: $o] :
% 5.44/5.72 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.44/5.72 = zero_zero_nat ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT.size_gen(2)
% 5.44/5.72 thf(fact_9621_valid__eq,axiom,
% 5.44/5.72 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.44/5.72
% 5.44/5.72 % valid_eq
% 5.44/5.72 thf(fact_9622_valid__eq1,axiom,
% 5.44/5.72 ! [T: vEBT_VEBT,D: nat] :
% 5.44/5.72 ( ( vEBT_invar_vebt @ T @ D )
% 5.44/5.72 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.44/5.72
% 5.44/5.72 % valid_eq1
% 5.44/5.72 thf(fact_9623_valid__eq2,axiom,
% 5.44/5.72 ! [T: vEBT_VEBT,D: nat] :
% 5.44/5.72 ( ( vEBT_VEBT_valid @ T @ D )
% 5.44/5.72 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.44/5.72
% 5.44/5.72 % valid_eq2
% 5.44/5.72 thf(fact_9624_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.44/5.72 ! [Uu: $o,Uv: $o,D: nat] :
% 5.44/5.72 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.44/5.72 = ( D = one_one_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.valid'.simps(1)
% 5.44/5.72 thf(fact_9625_csqrt_Osimps_I1_J,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( re @ ( csqrt @ Z ) )
% 5.44/5.72 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt.simps(1)
% 5.44/5.72 thf(fact_9626_divmod__step__integer__def,axiom,
% 5.44/5.72 ( unique4921790084139445826nteger
% 5.44/5.72 = ( ^ [L: num] :
% 5.44/5.72 ( produc6916734918728496179nteger
% 5.44/5.72 @ ^ [Q4: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R4 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % divmod_step_integer_def
% 5.44/5.72 thf(fact_9627_complex__Re__numeral,axiom,
% 5.44/5.72 ! [V: num] :
% 5.44/5.72 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.44/5.72 = ( numeral_numeral_real @ V ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_Re_numeral
% 5.44/5.72 thf(fact_9628_Re__divide__of__nat,axiom,
% 5.44/5.72 ! [Z: complex,N2: nat] :
% 5.44/5.72 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.44/5.72 = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_divide_of_nat
% 5.44/5.72 thf(fact_9629_Re__divide__of__real,axiom,
% 5.44/5.72 ! [Z: complex,R: real] :
% 5.44/5.72 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 5.44/5.72 = ( divide_divide_real @ ( re @ Z ) @ R ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_divide_of_real
% 5.44/5.72 thf(fact_9630_Re__sgn,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( re @ ( sgn_sgn_complex @ Z ) )
% 5.44/5.72 = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_sgn
% 5.44/5.72 thf(fact_9631_Re__divide__numeral,axiom,
% 5.44/5.72 ! [Z: complex,W: num] :
% 5.44/5.72 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.72 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_divide_numeral
% 5.44/5.72 thf(fact_9632_complex__Re__le__cmod,axiom,
% 5.44/5.72 ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_Re_le_cmod
% 5.44/5.72 thf(fact_9633_one__complex_Osimps_I1_J,axiom,
% 5.44/5.72 ( ( re @ one_one_complex )
% 5.44/5.72 = one_one_real ) ).
% 5.44/5.72
% 5.44/5.72 % one_complex.simps(1)
% 5.44/5.72 thf(fact_9634_plus__complex_Osimps_I1_J,axiom,
% 5.44/5.72 ! [X: complex,Y: complex] :
% 5.44/5.72 ( ( re @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.72 = ( plus_plus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % plus_complex.simps(1)
% 5.44/5.72 thf(fact_9635_scaleR__complex_Osimps_I1_J,axiom,
% 5.44/5.72 ! [R: real,X: complex] :
% 5.44/5.72 ( ( re @ ( real_V2046097035970521341omplex @ R @ X ) )
% 5.44/5.72 = ( times_times_real @ R @ ( re @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % scaleR_complex.simps(1)
% 5.44/5.72 thf(fact_9636_abs__Re__le__cmod,axiom,
% 5.44/5.72 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.44/5.72
% 5.44/5.72 % abs_Re_le_cmod
% 5.44/5.72 thf(fact_9637_Re__csqrt,axiom,
% 5.44/5.72 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_csqrt
% 5.44/5.72 thf(fact_9638_one__natural_Orsp,axiom,
% 5.44/5.72 one_one_nat = one_one_nat ).
% 5.44/5.72
% 5.44/5.72 % one_natural.rsp
% 5.44/5.72 thf(fact_9639_cmod__plus__Re__le__0__iff,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.44/5.72 = ( ( re @ Z )
% 5.44/5.72 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cmod_plus_Re_le_0_iff
% 5.44/5.72 thf(fact_9640_cos__n__Re__cis__pow__n,axiom,
% 5.44/5.72 ! [N2: nat,A: real] :
% 5.44/5.72 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) )
% 5.44/5.72 = ( re @ ( power_power_complex @ ( cis @ A ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cos_n_Re_cis_pow_n
% 5.44/5.72 thf(fact_9641_csqrt_Ocode,axiom,
% 5.44/5.72 ( csqrt
% 5.44/5.72 = ( ^ [Z5: complex] :
% 5.44/5.72 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.72 @ ( times_times_real
% 5.44/5.72 @ ( if_real
% 5.44/5.72 @ ( ( im @ Z5 )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 @ one_one_real
% 5.44/5.72 @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 5.44/5.72 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt.code
% 5.44/5.72 thf(fact_9642_csqrt_Osimps_I2_J,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( im @ ( csqrt @ Z ) )
% 5.44/5.72 = ( times_times_real
% 5.44/5.72 @ ( if_real
% 5.44/5.72 @ ( ( im @ Z )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 @ one_one_real
% 5.44/5.72 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.44/5.72 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt.simps(2)
% 5.44/5.72 thf(fact_9643_integer__of__int__code,axiom,
% 5.44/5.72 ( code_integer_of_int
% 5.44/5.72 = ( ^ [K3: int] :
% 5.44/5.72 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.44/5.72 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.44/5.72 @ ( if_Code_integer
% 5.44/5.72 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.44/5.72 = zero_zero_int )
% 5.44/5.72 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % integer_of_int_code
% 5.44/5.72 thf(fact_9644_Im__divide__of__real,axiom,
% 5.44/5.72 ! [Z: complex,R: real] :
% 5.44/5.72 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 5.44/5.72 = ( divide_divide_real @ ( im @ Z ) @ R ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_divide_of_real
% 5.44/5.72 thf(fact_9645_Im__sgn,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( im @ ( sgn_sgn_complex @ Z ) )
% 5.44/5.72 = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_sgn
% 5.44/5.72 thf(fact_9646_Re__power__real,axiom,
% 5.44/5.72 ! [X: complex,N2: nat] :
% 5.44/5.72 ( ( ( im @ X )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 => ( ( re @ ( power_power_complex @ X @ N2 ) )
% 5.44/5.72 = ( power_power_real @ ( re @ X ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_power_real
% 5.44/5.72 thf(fact_9647_Im__divide__numeral,axiom,
% 5.44/5.72 ! [Z: complex,W: num] :
% 5.44/5.72 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.44/5.72 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_divide_numeral
% 5.44/5.72 thf(fact_9648_Im__divide__of__nat,axiom,
% 5.44/5.72 ! [Z: complex,N2: nat] :
% 5.44/5.72 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.44/5.72 = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_divide_of_nat
% 5.44/5.72 thf(fact_9649_csqrt__of__real__nonneg,axiom,
% 5.44/5.72 ! [X: complex] :
% 5.44/5.72 ( ( ( im @ X )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 5.44/5.72 => ( ( csqrt @ X )
% 5.44/5.72 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt_of_real_nonneg
% 5.44/5.72 thf(fact_9650_csqrt__minus,axiom,
% 5.44/5.72 ! [X: complex] :
% 5.44/5.72 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.44/5.72 | ( ( ( im @ X )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.44/5.72 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.44/5.72 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt_minus
% 5.44/5.72 thf(fact_9651_csqrt__of__real__nonpos,axiom,
% 5.44/5.72 ! [X: complex] :
% 5.44/5.72 ( ( ( im @ X )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 5.44/5.72 => ( ( csqrt @ X )
% 5.44/5.72 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt_of_real_nonpos
% 5.44/5.72 thf(fact_9652_imaginary__unit_Osimps_I2_J,axiom,
% 5.44/5.72 ( ( im @ imaginary_unit )
% 5.44/5.72 = one_one_real ) ).
% 5.44/5.72
% 5.44/5.72 % imaginary_unit.simps(2)
% 5.44/5.72 thf(fact_9653_plus__complex_Osimps_I2_J,axiom,
% 5.44/5.72 ! [X: complex,Y: complex] :
% 5.44/5.72 ( ( im @ ( plus_plus_complex @ X @ Y ) )
% 5.44/5.72 = ( plus_plus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % plus_complex.simps(2)
% 5.44/5.72 thf(fact_9654_scaleR__complex_Osimps_I2_J,axiom,
% 5.44/5.72 ! [R: real,X: complex] :
% 5.44/5.72 ( ( im @ ( real_V2046097035970521341omplex @ R @ X ) )
% 5.44/5.72 = ( times_times_real @ R @ ( im @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % scaleR_complex.simps(2)
% 5.44/5.72 thf(fact_9655_abs__Im__le__cmod,axiom,
% 5.44/5.72 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.44/5.72
% 5.44/5.72 % abs_Im_le_cmod
% 5.44/5.72 thf(fact_9656_times__complex_Osimps_I2_J,axiom,
% 5.44/5.72 ! [X: complex,Y: complex] :
% 5.44/5.72 ( ( im @ ( times_times_complex @ X @ Y ) )
% 5.44/5.72 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % times_complex.simps(2)
% 5.44/5.72 thf(fact_9657_cmod__Im__le__iff,axiom,
% 5.44/5.72 ! [X: complex,Y: complex] :
% 5.44/5.72 ( ( ( re @ X )
% 5.44/5.72 = ( re @ Y ) )
% 5.44/5.72 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.44/5.72 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cmod_Im_le_iff
% 5.44/5.72 thf(fact_9658_cmod__Re__le__iff,axiom,
% 5.44/5.72 ! [X: complex,Y: complex] :
% 5.44/5.72 ( ( ( im @ X )
% 5.44/5.72 = ( im @ Y ) )
% 5.44/5.72 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.44/5.72 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cmod_Re_le_iff
% 5.44/5.72 thf(fact_9659_times__complex_Osimps_I1_J,axiom,
% 5.44/5.72 ! [X: complex,Y: complex] :
% 5.44/5.72 ( ( re @ ( times_times_complex @ X @ Y ) )
% 5.44/5.72 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % times_complex.simps(1)
% 5.44/5.72 thf(fact_9660_plus__complex_Ocode,axiom,
% 5.44/5.72 ( plus_plus_complex
% 5.44/5.72 = ( ^ [X2: complex,Y3: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y3 ) ) @ ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y3 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % plus_complex.code
% 5.44/5.72 thf(fact_9661_scaleR__complex_Ocode,axiom,
% 5.44/5.72 ( real_V2046097035970521341omplex
% 5.44/5.72 = ( ^ [R4: real,X2: complex] : ( complex2 @ ( times_times_real @ R4 @ ( re @ X2 ) ) @ ( times_times_real @ R4 @ ( im @ X2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % scaleR_complex.code
% 5.44/5.72 thf(fact_9662_csqrt__principal,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.44/5.72 | ( ( ( re @ ( csqrt @ Z ) )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt_principal
% 5.44/5.72 thf(fact_9663_cmod__le,axiom,
% 5.44/5.72 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cmod_le
% 5.44/5.72 thf(fact_9664_sin__n__Im__cis__pow__n,axiom,
% 5.44/5.72 ! [N2: nat,A: real] :
% 5.44/5.72 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) )
% 5.44/5.72 = ( im @ ( power_power_complex @ ( cis @ A ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sin_n_Im_cis_pow_n
% 5.44/5.72 thf(fact_9665_Re__exp,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( re @ ( exp_complex @ Z ) )
% 5.44/5.72 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_exp
% 5.44/5.72 thf(fact_9666_Im__exp,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( im @ ( exp_complex @ Z ) )
% 5.44/5.72 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_exp
% 5.44/5.72 thf(fact_9667_times__complex_Ocode,axiom,
% 5.44/5.72 ( times_times_complex
% 5.44/5.72 = ( ^ [X2: complex,Y3: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y3 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y3 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % times_complex.code
% 5.44/5.72 thf(fact_9668_cmod__power2,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.72 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cmod_power2
% 5.44/5.72 thf(fact_9669_Im__power2,axiom,
% 5.44/5.72 ! [X: complex] :
% 5.44/5.72 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.72 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_power2
% 5.44/5.72 thf(fact_9670_Re__power2,axiom,
% 5.44/5.72 ! [X: complex] :
% 5.44/5.72 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.72 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_power2
% 5.44/5.72 thf(fact_9671_complex__eq__0,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( Z = zero_zero_complex )
% 5.44/5.72 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.72 = zero_zero_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_eq_0
% 5.44/5.72 thf(fact_9672_norm__complex__def,axiom,
% 5.44/5.72 ( real_V1022390504157884413omplex
% 5.44/5.72 = ( ^ [Z5: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % norm_complex_def
% 5.44/5.72 thf(fact_9673_inverse__complex_Osimps_I1_J,axiom,
% 5.44/5.72 ! [X: complex] :
% 5.44/5.72 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 5.44/5.72 = ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % inverse_complex.simps(1)
% 5.44/5.72 thf(fact_9674_complex__neq__0,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( Z != zero_zero_complex )
% 5.44/5.72 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_neq_0
% 5.44/5.72 thf(fact_9675_Re__divide,axiom,
% 5.44/5.72 ! [X: complex,Y: complex] :
% 5.44/5.72 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.44/5.72 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_divide
% 5.44/5.72 thf(fact_9676_csqrt__square,axiom,
% 5.44/5.72 ! [B: complex] :
% 5.44/5.72 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.44/5.72 | ( ( ( re @ B )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.44/5.72 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.72 = B ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt_square
% 5.44/5.72 thf(fact_9677_csqrt__unique,axiom,
% 5.44/5.72 ! [W: complex,Z: complex] :
% 5.44/5.72 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.44/5.72 = Z )
% 5.44/5.72 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.44/5.72 | ( ( ( re @ W )
% 5.44/5.72 = zero_zero_real )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.44/5.72 => ( ( csqrt @ Z )
% 5.44/5.72 = W ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % csqrt_unique
% 5.44/5.72 thf(fact_9678_inverse__complex_Osimps_I2_J,axiom,
% 5.44/5.72 ! [X: complex] :
% 5.44/5.72 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 5.44/5.72 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % inverse_complex.simps(2)
% 5.44/5.72 thf(fact_9679_Im__divide,axiom,
% 5.44/5.72 ! [X: complex,Y: complex] :
% 5.44/5.72 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.44/5.72 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_divide
% 5.44/5.72 thf(fact_9680_complex__abs__le__norm,axiom,
% 5.44/5.72 ! [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 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_abs_le_norm
% 5.44/5.72 thf(fact_9681_complex__unit__circle,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( Z != zero_zero_complex )
% 5.44/5.72 => ( ( 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 ) ) ) )
% 5.44/5.72 = one_one_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_unit_circle
% 5.44/5.72 thf(fact_9682_inverse__complex_Ocode,axiom,
% 5.44/5.72 ( invers8013647133539491842omplex
% 5.44/5.72 = ( ^ [X2: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % inverse_complex.code
% 5.44/5.72 thf(fact_9683_Complex__divide,axiom,
% 5.44/5.72 ( divide1717551699836669952omplex
% 5.44/5.72 = ( ^ [X2: complex,Y3: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Complex_divide
% 5.44/5.72 thf(fact_9684_Im__Reals__divide,axiom,
% 5.44/5.72 ! [R: complex,Z: complex] :
% 5.44/5.72 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.44/5.72 => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.44/5.72 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_Reals_divide
% 5.44/5.72 thf(fact_9685_Re__Reals__divide,axiom,
% 5.44/5.72 ! [R: complex,Z: complex] :
% 5.44/5.72 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.44/5.72 => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.44/5.72 = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_Reals_divide
% 5.44/5.72 thf(fact_9686_Re__divide__Reals,axiom,
% 5.44/5.72 ! [R: complex,Z: complex] :
% 5.44/5.72 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.44/5.72 => ( ( re @ ( divide1717551699836669952omplex @ Z @ R ) )
% 5.44/5.72 = ( divide_divide_real @ ( re @ Z ) @ ( re @ R ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_divide_Reals
% 5.44/5.72 thf(fact_9687_Im__divide__Reals,axiom,
% 5.44/5.72 ! [R: complex,Z: complex] :
% 5.44/5.72 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.44/5.72 => ( ( im @ ( divide1717551699836669952omplex @ Z @ R ) )
% 5.44/5.72 = ( divide_divide_real @ ( im @ Z ) @ ( re @ R ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_divide_Reals
% 5.44/5.72 thf(fact_9688_complex__mult__cnj,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.44/5.72 = ( 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 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_mult_cnj
% 5.44/5.72 thf(fact_9689_num__of__integer__code,axiom,
% 5.44/5.72 ( code_num_of_integer
% 5.44/5.72 = ( ^ [K3: code_integer] :
% 5.44/5.72 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.44/5.72 @ ( produc7336495610019696514er_num
% 5.44/5.72 @ ^ [L: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ one ) )
% 5.44/5.72 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % num_of_integer_code
% 5.44/5.72 thf(fact_9690_Re__complex__div__gt__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.44/5.72 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_complex_div_gt_0
% 5.44/5.72 thf(fact_9691_Re__complex__div__lt__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.44/5.72 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_complex_div_lt_0
% 5.44/5.72 thf(fact_9692_Re__complex__div__ge__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.44/5.72 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_complex_div_ge_0
% 5.44/5.72 thf(fact_9693_Re__complex__div__le__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.44/5.72 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % Re_complex_div_le_0
% 5.44/5.72 thf(fact_9694_Im__complex__div__gt__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.44/5.72 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_complex_div_gt_0
% 5.44/5.72 thf(fact_9695_Im__complex__div__lt__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.44/5.72 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_complex_div_lt_0
% 5.44/5.72 thf(fact_9696_Im__complex__div__ge__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.44/5.72 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_complex_div_ge_0
% 5.44/5.72 thf(fact_9697_Im__complex__div__le__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.44/5.72 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % Im_complex_div_le_0
% 5.44/5.72 thf(fact_9698_complex__mod__mult__cnj,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.44/5.72 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_mod_mult_cnj
% 5.44/5.72 thf(fact_9699_complex__div__gt__0,axiom,
% 5.44/5.72 ! [A: complex,B: complex] :
% 5.44/5.72 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.44/5.72 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.44/5.72 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.44/5.72 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_div_gt_0
% 5.44/5.72 thf(fact_9700_complex__norm__square,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.72 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_norm_square
% 5.44/5.72 thf(fact_9701_complex__add__cnj,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.44/5.72 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_add_cnj
% 5.44/5.72 thf(fact_9702_complex__diff__cnj,axiom,
% 5.44/5.72 ! [Z: complex] :
% 5.44/5.72 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.44/5.72 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_diff_cnj
% 5.44/5.72 thf(fact_9703_complex__div__cnj,axiom,
% 5.44/5.72 ( divide1717551699836669952omplex
% 5.44/5.72 = ( ^ [A4: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % complex_div_cnj
% 5.44/5.72 thf(fact_9704_cnj__add__mult__eq__Re,axiom,
% 5.44/5.72 ! [Z: complex,W: complex] :
% 5.44/5.72 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.44/5.72 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % cnj_add_mult_eq_Re
% 5.44/5.72 thf(fact_9705_nat__of__integer__code,axiom,
% 5.44/5.72 ( code_nat_of_integer
% 5.44/5.72 = ( ^ [K3: code_integer] :
% 5.44/5.72 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.44/5.72 @ ( produc1555791787009142072er_nat
% 5.44/5.72 @ ^ [L: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ one_one_nat ) )
% 5.44/5.72 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_of_integer_code
% 5.44/5.72 thf(fact_9706_int__of__integer__code,axiom,
% 5.44/5.72 ( code_int_of_integer
% 5.44/5.72 = ( ^ [K3: code_integer] :
% 5.44/5.72 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.44/5.72 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.44/5.72 @ ( produc1553301316500091796er_int
% 5.44/5.72 @ ^ [L: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ one_one_int ) )
% 5.44/5.72 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % int_of_integer_code
% 5.44/5.72 thf(fact_9707_card__Collect__less__nat,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( finite_card_nat
% 5.44/5.72 @ ( collect_nat
% 5.44/5.72 @ ^ [I5: nat] : ( ord_less_nat @ I5 @ N2 ) ) )
% 5.44/5.72 = N2 ) ).
% 5.44/5.72
% 5.44/5.72 % card_Collect_less_nat
% 5.44/5.72 thf(fact_9708_card__atMost,axiom,
% 5.44/5.72 ! [U: nat] :
% 5.44/5.72 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.44/5.72 = ( suc @ U ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_atMost
% 5.44/5.72 thf(fact_9709_card__Collect__le__nat,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( finite_card_nat
% 5.44/5.72 @ ( collect_nat
% 5.44/5.72 @ ^ [I5: nat] : ( ord_less_eq_nat @ I5 @ N2 ) ) )
% 5.44/5.72 = ( suc @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_Collect_le_nat
% 5.44/5.72 thf(fact_9710_of__nat__of__integer,axiom,
% 5.44/5.72 ! [K: code_integer] :
% 5.44/5.72 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 5.44/5.72 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 5.44/5.72
% 5.44/5.72 % of_nat_of_integer
% 5.44/5.72 thf(fact_9711_int__of__integer__max,axiom,
% 5.44/5.72 ! [K: code_integer,L2: code_integer] :
% 5.44/5.72 ( ( code_int_of_integer @ ( ord_max_Code_integer @ K @ L2 ) )
% 5.44/5.72 = ( ord_max_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % int_of_integer_max
% 5.44/5.72 thf(fact_9712_card__atLeastAtMost,axiom,
% 5.44/5.72 ! [L2: nat,U: nat] :
% 5.44/5.72 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.44/5.72 = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_atLeastAtMost
% 5.44/5.72 thf(fact_9713_card__less__Suc2,axiom,
% 5.44/5.72 ! [M7: set_nat,I2: nat] :
% 5.44/5.72 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.44/5.72 => ( ( finite_card_nat
% 5.44/5.72 @ ( collect_nat
% 5.44/5.72 @ ^ [K3: nat] :
% 5.44/5.72 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.44/5.72 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 5.44/5.72 = ( finite_card_nat
% 5.44/5.72 @ ( collect_nat
% 5.44/5.72 @ ^ [K3: nat] :
% 5.44/5.72 ( ( member_nat @ K3 @ M7 )
% 5.44/5.72 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_less_Suc2
% 5.44/5.72 thf(fact_9714_card__less__Suc,axiom,
% 5.44/5.72 ! [M7: set_nat,I2: nat] :
% 5.44/5.72 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.44/5.72 => ( ( suc
% 5.44/5.72 @ ( finite_card_nat
% 5.44/5.72 @ ( collect_nat
% 5.44/5.72 @ ^ [K3: nat] :
% 5.44/5.72 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.44/5.72 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 5.44/5.72 = ( finite_card_nat
% 5.44/5.72 @ ( collect_nat
% 5.44/5.72 @ ^ [K3: nat] :
% 5.44/5.72 ( ( member_nat @ K3 @ M7 )
% 5.44/5.72 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_less_Suc
% 5.44/5.72 thf(fact_9715_card__less,axiom,
% 5.44/5.72 ! [M7: set_nat,I2: nat] :
% 5.44/5.72 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.44/5.72 => ( ( finite_card_nat
% 5.44/5.72 @ ( collect_nat
% 5.44/5.72 @ ^ [K3: nat] :
% 5.44/5.72 ( ( member_nat @ K3 @ M7 )
% 5.44/5.72 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 5.44/5.72 != zero_zero_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_less
% 5.44/5.72 thf(fact_9716_subset__card__intvl__is__intvl,axiom,
% 5.44/5.72 ! [A2: set_nat,K: nat] :
% 5.44/5.72 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.44/5.72 => ( A2
% 5.44/5.72 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % subset_card_intvl_is_intvl
% 5.44/5.72 thf(fact_9717_nat__of__integer__code__post_I3_J,axiom,
% 5.44/5.72 ! [K: num] :
% 5.44/5.72 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.44/5.72 = ( numeral_numeral_nat @ K ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_of_integer_code_post(3)
% 5.44/5.72 thf(fact_9718_nat__of__integer__code__post_I2_J,axiom,
% 5.44/5.72 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.44/5.72 = one_one_nat ) ).
% 5.44/5.72
% 5.44/5.72 % nat_of_integer_code_post(2)
% 5.44/5.72 thf(fact_9719_subset__eq__atLeast0__lessThan__card,axiom,
% 5.44/5.72 ! [N3: set_nat,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_set_nat @ N3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.44/5.72 => ( ord_less_eq_nat @ ( finite_card_nat @ N3 ) @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % subset_eq_atLeast0_lessThan_card
% 5.44/5.72 thf(fact_9720_card__sum__le__nat__sum,axiom,
% 5.44/5.72 ! [S: set_nat] :
% 5.44/5.72 ( ord_less_eq_nat
% 5.44/5.72 @ ( groups3542108847815614940at_nat
% 5.44/5.72 @ ^ [X2: nat] : X2
% 5.44/5.72 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 5.44/5.72 @ ( groups3542108847815614940at_nat
% 5.44/5.72 @ ^ [X2: nat] : X2
% 5.44/5.72 @ S ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_sum_le_nat_sum
% 5.44/5.72 thf(fact_9721_card__nth__roots,axiom,
% 5.44/5.72 ! [C: complex,N2: nat] :
% 5.44/5.72 ( ( C != zero_zero_complex )
% 5.44/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( finite_card_complex
% 5.44/5.72 @ ( collect_complex
% 5.44/5.72 @ ^ [Z5: complex] :
% 5.44/5.72 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.72 = C ) ) )
% 5.44/5.72 = N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_nth_roots
% 5.44/5.72 thf(fact_9722_card__roots__unity__eq,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( finite_card_complex
% 5.44/5.72 @ ( collect_complex
% 5.44/5.72 @ ^ [Z5: complex] :
% 5.44/5.72 ( ( power_power_complex @ Z5 @ N2 )
% 5.44/5.72 = one_one_complex ) ) )
% 5.44/5.72 = N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_roots_unity_eq
% 5.44/5.72 thf(fact_9723_floor__real__def,axiom,
% 5.44/5.72 ( archim6058952711729229775r_real
% 5.44/5.72 = ( ^ [X2: real] :
% 5.44/5.72 ( the_int
% 5.44/5.72 @ ^ [Z5: int] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X2 )
% 5.44/5.72 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % floor_real_def
% 5.44/5.72 thf(fact_9724_drop__bit__numeral__minus__bit1,axiom,
% 5.44/5.72 ! [L2: num,K: num] :
% 5.44/5.72 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.44/5.72 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_numeral_minus_bit1
% 5.44/5.72 thf(fact_9725_drop__bit__nonnegative__int__iff,axiom,
% 5.44/5.72 ! [N2: nat,K: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) )
% 5.44/5.72 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_nonnegative_int_iff
% 5.44/5.72 thf(fact_9726_drop__bit__negative__int__iff,axiom,
% 5.44/5.72 ! [N2: nat,K: int] :
% 5.44/5.72 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 5.44/5.72 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_negative_int_iff
% 5.44/5.72 thf(fact_9727_drop__bit__minus__one,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.44/5.72 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_minus_one
% 5.44/5.72 thf(fact_9728_drop__bit__Suc__minus__bit0,axiom,
% 5.44/5.72 ! [N2: nat,K: num] :
% 5.44/5.72 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.44/5.72 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_Suc_minus_bit0
% 5.44/5.72 thf(fact_9729_drop__bit__numeral__minus__bit0,axiom,
% 5.44/5.72 ! [L2: num,K: num] :
% 5.44/5.72 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.44/5.72 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_numeral_minus_bit0
% 5.44/5.72 thf(fact_9730_drop__bit__Suc__minus__bit1,axiom,
% 5.44/5.72 ! [N2: nat,K: num] :
% 5.44/5.72 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.44/5.72 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_Suc_minus_bit1
% 5.44/5.72 thf(fact_9731_nat_Odisc__eq__case_I1_J,axiom,
% 5.44/5.72 ! [Nat: nat] :
% 5.44/5.72 ( ( Nat = zero_zero_nat )
% 5.44/5.72 = ( case_nat_o @ $true
% 5.44/5.72 @ ^ [Uu3: nat] : $false
% 5.44/5.72 @ Nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat.disc_eq_case(1)
% 5.44/5.72 thf(fact_9732_nat_Odisc__eq__case_I2_J,axiom,
% 5.44/5.72 ! [Nat: nat] :
% 5.44/5.72 ( ( Nat != zero_zero_nat )
% 5.44/5.72 = ( case_nat_o @ $false
% 5.44/5.72 @ ^ [Uu3: nat] : $true
% 5.44/5.72 @ Nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat.disc_eq_case(2)
% 5.44/5.72 thf(fact_9733_drop__bit__push__bit__int,axiom,
% 5.44/5.72 ! [M: nat,N2: nat,K: int] :
% 5.44/5.72 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.44/5.72 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N2 @ M ) @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_push_bit_int
% 5.44/5.72 thf(fact_9734_less__eq__nat_Osimps_I2_J,axiom,
% 5.44/5.72 ! [M: nat,N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.44/5.72 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % less_eq_nat.simps(2)
% 5.44/5.72 thf(fact_9735_max__Suc2,axiom,
% 5.44/5.72 ! [M: nat,N2: nat] :
% 5.44/5.72 ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 5.44/5.72 = ( case_nat_nat @ ( suc @ N2 )
% 5.44/5.72 @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ M3 @ N2 ) )
% 5.44/5.72 @ M ) ) ).
% 5.44/5.72
% 5.44/5.72 % max_Suc2
% 5.44/5.72 thf(fact_9736_max__Suc1,axiom,
% 5.44/5.72 ! [N2: nat,M: nat] :
% 5.44/5.72 ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 5.44/5.72 = ( case_nat_nat @ ( suc @ N2 )
% 5.44/5.72 @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ N2 @ M3 ) )
% 5.44/5.72 @ M ) ) ).
% 5.44/5.72
% 5.44/5.72 % max_Suc1
% 5.44/5.72 thf(fact_9737_diff__Suc,axiom,
% 5.44/5.72 ! [M: nat,N2: nat] :
% 5.44/5.72 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.44/5.72 = ( case_nat_nat @ zero_zero_nat
% 5.44/5.72 @ ^ [K3: nat] : K3
% 5.44/5.72 @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % diff_Suc
% 5.44/5.72 thf(fact_9738_drop__bit__int__def,axiom,
% 5.44/5.72 ( bit_se8568078237143864401it_int
% 5.44/5.72 = ( ^ [N: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_int_def
% 5.44/5.72 thf(fact_9739_drop__bit__of__Suc__0,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.44/5.72 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_of_Suc_0
% 5.44/5.72 thf(fact_9740_drop__bit__nat__eq,axiom,
% 5.44/5.72 ! [N2: nat,K: int] :
% 5.44/5.72 ( ( bit_se8570568707652914677it_nat @ N2 @ ( nat2 @ K ) )
% 5.44/5.72 = ( nat2 @ ( bit_se8568078237143864401it_int @ N2 @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_nat_eq
% 5.44/5.72 thf(fact_9741_pred__def,axiom,
% 5.44/5.72 ( pred
% 5.44/5.72 = ( case_nat_nat @ zero_zero_nat
% 5.44/5.72 @ ^ [X24: nat] : X24 ) ) ).
% 5.44/5.72
% 5.44/5.72 % pred_def
% 5.44/5.72 thf(fact_9742_drop__bit__nat__def,axiom,
% 5.44/5.72 ( bit_se8570568707652914677it_nat
% 5.44/5.72 = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % drop_bit_nat_def
% 5.44/5.72 thf(fact_9743_Suc__0__mod__numeral,axiom,
% 5.44/5.72 ! [K: num] :
% 5.44/5.72 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.44/5.72 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Suc_0_mod_numeral
% 5.44/5.72 thf(fact_9744_prod__decode__aux_Oelims,axiom,
% 5.44/5.72 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.44/5.72 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod_decode_aux.elims
% 5.44/5.72 thf(fact_9745_prod__decode__aux_Osimps,axiom,
% 5.44/5.72 ( nat_prod_decode_aux
% 5.44/5.72 = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod_decode_aux.simps
% 5.44/5.72 thf(fact_9746_Suc__0__div__numeral,axiom,
% 5.44/5.72 ! [K: num] :
% 5.44/5.72 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.44/5.72 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Suc_0_div_numeral
% 5.44/5.72 thf(fact_9747_vebt__maxt_Opelims,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.44/5.72 ( ( ( vEBT_vebt_maxt @ X )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 5.44/5.72 => ( ! [A3: $o,B3: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.72 => ( ( ( B3
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.72 & ( ~ B3
% 5.44/5.72 => ( ( A3
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.72 & ( ~ A3
% 5.44/5.72 => ( Y = none_nat ) ) ) ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.44/5.72 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.72 => ( ( Y = none_nat )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.44/5.72 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.44/5.72 => ( ( Y
% 5.44/5.72 = ( some_nat @ Ma2 ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % vebt_maxt.pelims
% 5.44/5.72 thf(fact_9748_vebt__mint_Opelims,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.44/5.72 ( ( ( vEBT_vebt_mint @ X )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 5.44/5.72 => ( ! [A3: $o,B3: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.44/5.72 => ( ( ( A3
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( some_nat @ zero_zero_nat ) ) )
% 5.44/5.72 & ( ~ A3
% 5.44/5.72 => ( ( B3
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( some_nat @ one_one_nat ) ) )
% 5.44/5.72 & ( ~ B3
% 5.44/5.72 => ( Y = none_nat ) ) ) ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 5.44/5.72 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.44/5.72 => ( ( Y = none_nat )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.44/5.72 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.44/5.72 => ( ( Y
% 5.44/5.72 = ( some_nat @ Mi2 ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % vebt_mint.pelims
% 5.44/5.72 thf(fact_9749_fst__divmod__nat,axiom,
% 5.44/5.72 ! [M: nat,N2: nat] :
% 5.44/5.72 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 5.44/5.72 = ( divide_divide_nat @ M @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % fst_divmod_nat
% 5.44/5.72 thf(fact_9750_one__mod__minus__numeral,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % one_mod_minus_numeral
% 5.44/5.72 thf(fact_9751_minus__one__mod__numeral,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % minus_one_mod_numeral
% 5.44/5.72 thf(fact_9752_bezw_Oelims,axiom,
% 5.44/5.72 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.44/5.72 ( ( ( bezw @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.44/5.72 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bezw.elims
% 5.44/5.72 thf(fact_9753_bezw_Osimps,axiom,
% 5.44/5.72 ( bezw
% 5.44/5.72 = ( ^ [X2: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y3 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bezw.simps
% 5.44/5.72 thf(fact_9754_bezw__non__0,axiom,
% 5.44/5.72 ! [Y: nat,X: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.44/5.72 => ( ( bezw @ X @ Y )
% 5.44/5.72 = ( 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 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bezw_non_0
% 5.44/5.72 thf(fact_9755_bezw_Opelims,axiom,
% 5.44/5.72 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.44/5.72 ( ( ( bezw @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.44/5.72 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.44/5.72 & ( ( Xa2 != zero_zero_nat )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 5.44/5.72 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bezw.pelims
% 5.44/5.72 thf(fact_9756_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Y: $o] :
% 5.44/5.72 ( ( ( vEBT_VEBT_minNull @ X )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.44/5.72 => ( ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ $false @ $false ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.44/5.72 => ( ! [Uv2: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.44/5.72 => ( ~ Y
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.44/5.72 => ( ! [Uu2: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.44/5.72 => ( ~ Y
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.44/5.72 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.44/5.72 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.44/5.72 => ( ~ Y
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.minNull.pelims(1)
% 5.44/5.72 thf(fact_9757_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT] :
% 5.44/5.72 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.44/5.72 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.44/5.72 => ( ! [Uv2: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.44/5.72 => ( ! [Uu2: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.44/5.72 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.minNull.pelims(3)
% 5.44/5.72 thf(fact_9758_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT] :
% 5.44/5.72 ( ( vEBT_VEBT_minNull @ X )
% 5.44/5.72 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.44/5.72 => ( ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ $false @ $false ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.44/5.72 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.44/5.72 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.minNull.pelims(2)
% 5.44/5.72 thf(fact_9759_prod__decode__aux_Opelims,axiom,
% 5.44/5.72 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.44/5.72 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.44/5.72 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 5.44/5.72 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % prod_decode_aux.pelims
% 5.44/5.72 thf(fact_9760_bit__cut__integer__code,axiom,
% 5.44/5.72 ( code_bit_cut_integer
% 5.44/5.72 = ( ^ [K3: code_integer] :
% 5.44/5.72 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.44/5.72 @ ( produc9125791028180074456eger_o
% 5.44/5.72 @ ^ [R4: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R4 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 5.44/5.72 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bit_cut_integer_code
% 5.44/5.72 thf(fact_9761_bit__cut__integer__def,axiom,
% 5.44/5.72 ( code_bit_cut_integer
% 5.44/5.72 = ( ^ [K3: code_integer] :
% 5.44/5.72 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.44/5.72 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % bit_cut_integer_def
% 5.44/5.72 thf(fact_9762_nat__descend__induct,axiom,
% 5.44/5.72 ! [N2: nat,P: nat > $o,M: nat] :
% 5.44/5.72 ( ! [K2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ N2 @ K2 )
% 5.44/5.72 => ( P @ K2 ) )
% 5.44/5.72 => ( ! [K2: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.44/5.72 => ( ! [I: nat] :
% 5.44/5.72 ( ( ord_less_nat @ K2 @ I )
% 5.44/5.72 => ( P @ I ) )
% 5.44/5.72 => ( P @ K2 ) ) )
% 5.44/5.72 => ( P @ M ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_descend_induct
% 5.44/5.72 thf(fact_9763_infinite__nat__iff__unbounded__le,axiom,
% 5.44/5.72 ! [S: set_nat] :
% 5.44/5.72 ( ( ~ ( finite_finite_nat @ S ) )
% 5.44/5.72 = ( ! [M6: nat] :
% 5.44/5.72 ? [N: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ M6 @ N )
% 5.44/5.72 & ( member_nat @ N @ S ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % infinite_nat_iff_unbounded_le
% 5.44/5.72 thf(fact_9764_unbounded__k__infinite,axiom,
% 5.44/5.72 ! [K: nat,S: set_nat] :
% 5.44/5.72 ( ! [M5: nat] :
% 5.44/5.72 ( ( ord_less_nat @ K @ M5 )
% 5.44/5.72 => ? [N9: nat] :
% 5.44/5.72 ( ( ord_less_nat @ M5 @ N9 )
% 5.44/5.72 & ( member_nat @ N9 @ S ) ) )
% 5.44/5.72 => ~ ( finite_finite_nat @ S ) ) ).
% 5.44/5.72
% 5.44/5.72 % unbounded_k_infinite
% 5.44/5.72 thf(fact_9765_infinite__nat__iff__unbounded,axiom,
% 5.44/5.72 ! [S: set_nat] :
% 5.44/5.72 ( ( ~ ( finite_finite_nat @ S ) )
% 5.44/5.72 = ( ! [M6: nat] :
% 5.44/5.72 ? [N: nat] :
% 5.44/5.72 ( ( ord_less_nat @ M6 @ N )
% 5.44/5.72 & ( member_nat @ N @ S ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % infinite_nat_iff_unbounded
% 5.44/5.72 thf(fact_9766_finite__enumerate,axiom,
% 5.44/5.72 ! [S: set_nat] :
% 5.44/5.72 ( ( finite_finite_nat @ S )
% 5.44/5.72 => ? [R3: nat > nat] :
% 5.44/5.72 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S ) ) )
% 5.44/5.72 & ! [N9: nat] :
% 5.44/5.72 ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S ) )
% 5.44/5.72 => ( member_nat @ ( R3 @ N9 ) @ S ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % finite_enumerate
% 5.44/5.72 thf(fact_9767_xor__minus__numerals_I2_J,axiom,
% 5.44/5.72 ! [K: int,N2: num] :
% 5.44/5.72 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_minus_numerals(2)
% 5.44/5.72 thf(fact_9768_xor__minus__numerals_I1_J,axiom,
% 5.44/5.72 ! [N2: num,K: int] :
% 5.44/5.72 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ K )
% 5.44/5.72 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N2 @ one ) @ K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_minus_numerals(1)
% 5.44/5.72 thf(fact_9769_sub__BitM__One__eq,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 5.44/5.72 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sub_BitM_One_eq
% 5.44/5.72 thf(fact_9770_Suc__funpow,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( compow_nat_nat @ N2 @ suc )
% 5.44/5.72 = ( plus_plus_nat @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % Suc_funpow
% 5.44/5.72 thf(fact_9771_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.44/5.72 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X2 )
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % max_nat.semilattice_neutr_order_axioms
% 5.44/5.72 thf(fact_9772_times__int_Oabs__eq,axiom,
% 5.44/5.72 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.44/5.72 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.44/5.72 = ( abs_Integ
% 5.44/5.72 @ ( produc27273713700761075at_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.72 ( produc2626176000494625587at_nat
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) )
% 5.44/5.72 @ Xa2
% 5.44/5.72 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % times_int.abs_eq
% 5.44/5.72 thf(fact_9773_eq__Abs__Integ,axiom,
% 5.44/5.72 ! [Z: int] :
% 5.44/5.72 ~ ! [X5: nat,Y5: nat] :
% 5.44/5.72 ( Z
% 5.44/5.72 != ( abs_Integ @ ( product_Pair_nat_nat @ X5 @ Y5 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % eq_Abs_Integ
% 5.44/5.72 thf(fact_9774_zero__int__def,axiom,
% 5.44/5.72 ( zero_zero_int
% 5.44/5.72 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % zero_int_def
% 5.44/5.72 thf(fact_9775_int__def,axiom,
% 5.44/5.72 ( semiri1314217659103216013at_int
% 5.44/5.72 = ( ^ [N: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N @ zero_zero_nat ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % int_def
% 5.44/5.72 thf(fact_9776_uminus__int_Oabs__eq,axiom,
% 5.44/5.72 ! [X: product_prod_nat_nat] :
% 5.44/5.72 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.44/5.72 = ( abs_Integ
% 5.44/5.72 @ ( produc2626176000494625587at_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X2 )
% 5.44/5.72 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % uminus_int.abs_eq
% 5.44/5.72 thf(fact_9777_one__int__def,axiom,
% 5.44/5.72 ( one_one_int
% 5.44/5.72 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % one_int_def
% 5.44/5.72 thf(fact_9778_less__int_Oabs__eq,axiom,
% 5.44/5.72 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.44/5.72 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.44/5.72 = ( produc8739625826339149834_nat_o
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.72 ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 5.44/5.72 @ Xa2
% 5.44/5.72 @ X ) ) ).
% 5.44/5.72
% 5.44/5.72 % less_int.abs_eq
% 5.44/5.72 thf(fact_9779_less__eq__int_Oabs__eq,axiom,
% 5.44/5.72 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.44/5.72 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.44/5.72 = ( produc8739625826339149834_nat_o
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.72 ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 5.44/5.72 @ Xa2
% 5.44/5.72 @ X ) ) ).
% 5.44/5.72
% 5.44/5.72 % less_eq_int.abs_eq
% 5.44/5.72 thf(fact_9780_plus__int_Oabs__eq,axiom,
% 5.44/5.72 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.44/5.72 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.44/5.72 = ( abs_Integ
% 5.44/5.72 @ ( produc27273713700761075at_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.72 ( produc2626176000494625587at_nat
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y3 @ V4 ) ) )
% 5.44/5.72 @ Xa2
% 5.44/5.72 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % plus_int.abs_eq
% 5.44/5.72 thf(fact_9781_minus__int_Oabs__eq,axiom,
% 5.44/5.72 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.44/5.72 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.44/5.72 = ( abs_Integ
% 5.44/5.72 @ ( produc27273713700761075at_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.72 ( produc2626176000494625587at_nat
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) )
% 5.44/5.72 @ Xa2
% 5.44/5.72 @ X ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % minus_int.abs_eq
% 5.44/5.72 thf(fact_9782_less__eq__int_Orep__eq,axiom,
% 5.44/5.72 ( ord_less_eq_int
% 5.44/5.72 = ( ^ [X2: int,Xa3: int] :
% 5.44/5.72 ( produc8739625826339149834_nat_o
% 5.44/5.72 @ ^ [Y3: nat,Z5: nat] :
% 5.44/5.72 ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y3 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 5.44/5.72 @ ( rep_Integ @ X2 )
% 5.44/5.72 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % less_eq_int.rep_eq
% 5.44/5.72 thf(fact_9783_less__int_Orep__eq,axiom,
% 5.44/5.72 ( ord_less_int
% 5.44/5.72 = ( ^ [X2: int,Xa3: int] :
% 5.44/5.72 ( produc8739625826339149834_nat_o
% 5.44/5.72 @ ^ [Y3: nat,Z5: nat] :
% 5.44/5.72 ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y3 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 5.44/5.72 @ ( rep_Integ @ X2 )
% 5.44/5.72 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % less_int.rep_eq
% 5.44/5.72 thf(fact_9784_num__of__nat_Osimps_I2_J,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.44/5.72 = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.44/5.72 = one ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % num_of_nat.simps(2)
% 5.44/5.72 thf(fact_9785_num__of__nat__numeral__eq,axiom,
% 5.44/5.72 ! [Q2: num] :
% 5.44/5.72 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.44/5.72 = Q2 ) ).
% 5.44/5.72
% 5.44/5.72 % num_of_nat_numeral_eq
% 5.44/5.72 thf(fact_9786_num__of__nat_Osimps_I1_J,axiom,
% 5.44/5.72 ( ( num_of_nat @ zero_zero_nat )
% 5.44/5.72 = one ) ).
% 5.44/5.72
% 5.44/5.72 % num_of_nat.simps(1)
% 5.44/5.72 thf(fact_9787_numeral__num__of__nat,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 5.44/5.72 = N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % numeral_num_of_nat
% 5.44/5.72 thf(fact_9788_num__of__nat__One,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 5.44/5.72 => ( ( num_of_nat @ N2 )
% 5.44/5.72 = one ) ) ).
% 5.44/5.72
% 5.44/5.72 % num_of_nat_One
% 5.44/5.72 thf(fact_9789_num__of__nat__double,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 5.44/5.72 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % num_of_nat_double
% 5.44/5.72 thf(fact_9790_num__of__nat__plus__distrib,axiom,
% 5.44/5.72 ! [M: nat,N2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.44/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.44/5.72 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % num_of_nat_plus_distrib
% 5.44/5.72 thf(fact_9791_uminus__int__def,axiom,
% 5.44/5.72 ( uminus_uminus_int
% 5.44/5.72 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.44/5.72 @ ( produc2626176000494625587at_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % uminus_int_def
% 5.44/5.72 thf(fact_9792_times__int__def,axiom,
% 5.44/5.72 ( times_times_int
% 5.44/5.72 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.44/5.72 @ ( produc27273713700761075at_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.72 ( produc2626176000494625587at_nat
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % times_int_def
% 5.44/5.72 thf(fact_9793_minus__int__def,axiom,
% 5.44/5.72 ( minus_minus_int
% 5.44/5.72 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.44/5.72 @ ( produc27273713700761075at_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.72 ( produc2626176000494625587at_nat
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % minus_int_def
% 5.44/5.72 thf(fact_9794_plus__int__def,axiom,
% 5.44/5.72 ( plus_plus_int
% 5.44/5.72 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.44/5.72 @ ( produc27273713700761075at_nat
% 5.44/5.72 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.72 ( produc2626176000494625587at_nat
% 5.44/5.72 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y3 @ V4 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % plus_int_def
% 5.44/5.72 thf(fact_9795_pow_Osimps_I3_J,axiom,
% 5.44/5.72 ! [X: num,Y: num] :
% 5.44/5.72 ( ( pow @ X @ ( bit1 @ Y ) )
% 5.44/5.72 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 5.44/5.72
% 5.44/5.72 % pow.simps(3)
% 5.44/5.72 thf(fact_9796_sqr_Osimps_I2_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( sqr @ ( bit0 @ N2 ) )
% 5.44/5.72 = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sqr.simps(2)
% 5.44/5.72 thf(fact_9797_sqr_Osimps_I1_J,axiom,
% 5.44/5.72 ( ( sqr @ one )
% 5.44/5.72 = one ) ).
% 5.44/5.72
% 5.44/5.72 % sqr.simps(1)
% 5.44/5.72 thf(fact_9798_sqr__conv__mult,axiom,
% 5.44/5.72 ( sqr
% 5.44/5.72 = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sqr_conv_mult
% 5.44/5.72 thf(fact_9799_pow_Osimps_I2_J,axiom,
% 5.44/5.72 ! [X: num,Y: num] :
% 5.44/5.72 ( ( pow @ X @ ( bit0 @ Y ) )
% 5.44/5.72 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % pow.simps(2)
% 5.44/5.72 thf(fact_9800_sqr_Osimps_I3_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( sqr @ ( bit1 @ N2 ) )
% 5.44/5.72 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sqr.simps(3)
% 5.44/5.72 thf(fact_9801_integer__of__num__triv_I2_J,axiom,
% 5.44/5.72 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.44/5.72 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % integer_of_num_triv(2)
% 5.44/5.72 thf(fact_9802_image__minus__const__atLeastLessThan__nat,axiom,
% 5.44/5.72 ! [C: nat,Y: nat,X: nat] :
% 5.44/5.72 ( ( ( ord_less_nat @ C @ Y )
% 5.44/5.72 => ( ( image_nat_nat
% 5.44/5.72 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.44/5.72 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.44/5.72 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_nat @ C @ Y )
% 5.44/5.72 => ( ( ( ord_less_nat @ X @ Y )
% 5.44/5.72 => ( ( image_nat_nat
% 5.44/5.72 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.44/5.72 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.44/5.72 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.44/5.72 & ( ~ ( ord_less_nat @ X @ Y )
% 5.44/5.72 => ( ( image_nat_nat
% 5.44/5.72 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.44/5.72 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.44/5.72 = bot_bot_set_nat ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % image_minus_const_atLeastLessThan_nat
% 5.44/5.72 thf(fact_9803_bij__betw__Suc,axiom,
% 5.44/5.72 ! [M7: set_nat,N3: set_nat] :
% 5.44/5.72 ( ( bij_betw_nat_nat @ suc @ M7 @ N3 )
% 5.44/5.72 = ( ( image_nat_nat @ suc @ M7 )
% 5.44/5.72 = N3 ) ) ).
% 5.44/5.72
% 5.44/5.72 % bij_betw_Suc
% 5.44/5.72 thf(fact_9804_image__Suc__atLeastAtMost,axiom,
% 5.44/5.72 ! [I2: nat,J: nat] :
% 5.44/5.72 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.44/5.72 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % image_Suc_atLeastAtMost
% 5.44/5.72 thf(fact_9805_image__Suc__atLeastLessThan,axiom,
% 5.44/5.72 ! [I2: nat,J: nat] :
% 5.44/5.72 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 5.44/5.72 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % image_Suc_atLeastLessThan
% 5.44/5.72 thf(fact_9806_zero__notin__Suc__image,axiom,
% 5.44/5.72 ! [A2: set_nat] :
% 5.44/5.72 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % zero_notin_Suc_image
% 5.44/5.72 thf(fact_9807_image__Suc__lessThan,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % image_Suc_lessThan
% 5.44/5.72 thf(fact_9808_image__Suc__atMost,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 5.44/5.72 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % image_Suc_atMost
% 5.44/5.72 thf(fact_9809_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.44/5.72 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeast0_atMost_Suc_eq_insert_0
% 5.44/5.72 thf(fact_9810_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.44/5.72 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeast0_lessThan_Suc_eq_insert_0
% 5.44/5.72 thf(fact_9811_lessThan__Suc__eq__insert__0,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 5.44/5.72 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lessThan_Suc_eq_insert_0
% 5.44/5.72 thf(fact_9812_atMost__Suc__eq__insert__0,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 5.44/5.72 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atMost_Suc_eq_insert_0
% 5.44/5.72 thf(fact_9813_integer__of__num__triv_I1_J,axiom,
% 5.44/5.72 ( ( code_integer_of_num @ one )
% 5.44/5.72 = one_one_Code_integer ) ).
% 5.44/5.72
% 5.44/5.72 % integer_of_num_triv(1)
% 5.44/5.72 thf(fact_9814_integer__of__num_I2_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 5.44/5.72 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % integer_of_num(2)
% 5.44/5.72 thf(fact_9815_Inf__real__def,axiom,
% 5.44/5.72 ( comple4887499456419720421f_real
% 5.44/5.72 = ( ^ [X4: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X4 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Inf_real_def
% 5.44/5.72 thf(fact_9816_suminf__eq__SUP__real,axiom,
% 5.44/5.72 ! [X8: nat > real] :
% 5.44/5.72 ( ( summable_real @ X8 )
% 5.44/5.72 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 5.44/5.72 => ( ( suminf_real @ X8 )
% 5.44/5.72 = ( comple1385675409528146559p_real
% 5.44/5.72 @ ( image_nat_real
% 5.44/5.72 @ ^ [I5: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I5 ) )
% 5.44/5.72 @ top_top_set_nat ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % suminf_eq_SUP_real
% 5.44/5.72 thf(fact_9817_range__mod,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( image_nat_nat
% 5.44/5.72 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N2 )
% 5.44/5.72 @ top_top_set_nat )
% 5.44/5.72 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % range_mod
% 5.44/5.72 thf(fact_9818_UNIV__nat__eq,axiom,
% 5.44/5.72 ( top_top_set_nat
% 5.44/5.72 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % UNIV_nat_eq
% 5.44/5.72 thf(fact_9819_card__UNIV__unit,axiom,
% 5.44/5.72 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.44/5.72 = one_one_nat ) ).
% 5.44/5.72
% 5.44/5.72 % card_UNIV_unit
% 5.44/5.72 thf(fact_9820_card__UNIV__bool,axiom,
% 5.44/5.72 ( ( finite_card_o @ top_top_set_o )
% 5.44/5.72 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_UNIV_bool
% 5.44/5.72 thf(fact_9821_range__mult,axiom,
% 5.44/5.72 ! [A: real] :
% 5.44/5.72 ( ( ( A = zero_zero_real )
% 5.44/5.72 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.44/5.72 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.44/5.72 & ( ( A != zero_zero_real )
% 5.44/5.72 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.44/5.72 = top_top_set_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % range_mult
% 5.44/5.72 thf(fact_9822_root__def,axiom,
% 5.44/5.72 ( root
% 5.44/5.72 = ( ^ [N: nat,X2: real] :
% 5.44/5.72 ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 5.44/5.72 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.44/5.72 @ ^ [Y3: real] : ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) )
% 5.44/5.72 @ X2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % root_def
% 5.44/5.72 thf(fact_9823_card__UNIV__char,axiom,
% 5.44/5.72 ( ( finite_card_char @ top_top_set_char )
% 5.44/5.72 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_UNIV_char
% 5.44/5.72 thf(fact_9824_UNIV__char__of__nat,axiom,
% 5.44/5.72 ( top_top_set_char
% 5.44/5.72 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % UNIV_char_of_nat
% 5.44/5.72 thf(fact_9825_char_Osize_I2_J,axiom,
% 5.44/5.72 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.44/5.72 ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.44/5.72 = zero_zero_nat ) ).
% 5.44/5.72
% 5.44/5.72 % char.size(2)
% 5.44/5.72 thf(fact_9826_nat__of__char__less__256,axiom,
% 5.44/5.72 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nat_of_char_less_256
% 5.44/5.72 thf(fact_9827_range__nat__of__char,axiom,
% 5.44/5.72 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.44/5.72 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % range_nat_of_char
% 5.44/5.72 thf(fact_9828_integer__of__char__code,axiom,
% 5.44/5.72 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.44/5.72 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.44/5.72 = ( 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 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % integer_of_char_code
% 5.44/5.72 thf(fact_9829_String_Ochar__of__ascii__of,axiom,
% 5.44/5.72 ! [C: char] :
% 5.44/5.72 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.44/5.72 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % String.char_of_ascii_of
% 5.44/5.72 thf(fact_9830_DERIV__real__root__generic,axiom,
% 5.44/5.72 ! [N2: nat,X: real,D4: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( X != zero_zero_real )
% 5.44/5.72 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( D4
% 5.44/5.72 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.44/5.72 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.72 => ( D4
% 5.44/5.72 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.44/5.72 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( D4
% 5.44/5.72 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_real_root_generic
% 5.44/5.72 thf(fact_9831_sorted__list__of__set__lessThan__Suc,axiom,
% 5.44/5.72 ! [K: nat] :
% 5.44/5.72 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.44/5.72 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sorted_list_of_set_lessThan_Suc
% 5.44/5.72 thf(fact_9832_sorted__list__of__set__atMost__Suc,axiom,
% 5.44/5.72 ! [K: nat] :
% 5.44/5.72 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.44/5.72 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sorted_list_of_set_atMost_Suc
% 5.44/5.72 thf(fact_9833_has__real__derivative__neg__dec__left,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real,S: set_real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.44/5.72 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.44/5.72 => ? [D3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.72 & ! [H4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.44/5.72 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S )
% 5.44/5.72 => ( ( ord_less_real @ H4 @ D3 )
% 5.44/5.72 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % has_real_derivative_neg_dec_left
% 5.44/5.72 thf(fact_9834_has__real__derivative__pos__inc__left,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real,S: set_real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.44/5.72 => ? [D3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.72 & ! [H4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.44/5.72 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S )
% 5.44/5.72 => ( ( ord_less_real @ H4 @ D3 )
% 5.44/5.72 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % has_real_derivative_pos_inc_left
% 5.44/5.72 thf(fact_9835_has__real__derivative__pos__inc__right,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real,S: set_real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.44/5.72 => ? [D3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.72 & ! [H4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.44/5.72 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S )
% 5.44/5.72 => ( ( ord_less_real @ H4 @ D3 )
% 5.44/5.72 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % has_real_derivative_pos_inc_right
% 5.44/5.72 thf(fact_9836_has__real__derivative__neg__dec__right,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real,S: set_real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.44/5.72 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.44/5.72 => ? [D3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.72 & ! [H4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.44/5.72 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S )
% 5.44/5.72 => ( ( ord_less_real @ H4 @ D3 )
% 5.44/5.72 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % has_real_derivative_neg_dec_right
% 5.44/5.72 thf(fact_9837_DERIV__const__ratio__const2,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real,K: real] :
% 5.44/5.72 ( ( A != B )
% 5.44/5.72 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.44/5.72 = K ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_const_ratio_const2
% 5.44/5.72 thf(fact_9838_DERIV__const__ratio__const,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real,K: real] :
% 5.44/5.72 ( ( A != B )
% 5.44/5.72 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.44/5.72 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_const_ratio_const
% 5.44/5.72 thf(fact_9839_DERIV__neg__dec__left,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.44/5.72 => ? [D3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.72 & ! [H4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.44/5.72 => ( ( ord_less_real @ H4 @ D3 )
% 5.44/5.72 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_neg_dec_left
% 5.44/5.72 thf(fact_9840_DERIV__pos__inc__left,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.44/5.72 => ? [D3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.72 & ! [H4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.44/5.72 => ( ( ord_less_real @ H4 @ D3 )
% 5.44/5.72 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_pos_inc_left
% 5.44/5.72 thf(fact_9841_DERIV__pos__inc__right,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.44/5.72 => ? [D3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.72 & ! [H4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.44/5.72 => ( ( ord_less_real @ H4 @ D3 )
% 5.44/5.72 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_pos_inc_right
% 5.44/5.72 thf(fact_9842_DERIV__neg__dec__right,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.44/5.72 => ? [D3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.44/5.72 & ! [H4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.44/5.72 => ( ( ord_less_real @ H4 @ D3 )
% 5.44/5.72 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_neg_dec_right
% 5.44/5.72 thf(fact_9843_DERIV__neg__imp__decreasing,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_eq_real @ X5 @ B )
% 5.44/5.72 => ? [Y2: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_real @ Y2 @ zero_zero_real ) ) ) )
% 5.44/5.72 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_neg_imp_decreasing
% 5.44/5.72 thf(fact_9844_DERIV__pos__imp__increasing,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_eq_real @ X5 @ B )
% 5.44/5.72 => ? [Y2: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_real @ zero_zero_real @ Y2 ) ) ) )
% 5.44/5.72 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_pos_imp_increasing
% 5.44/5.72 thf(fact_9845_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_eq_real @ X5 @ B )
% 5.44/5.72 => ? [Y2: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_eq_real @ Y2 @ zero_zero_real ) ) ) )
% 5.44/5.72 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_nonpos_imp_nonincreasing
% 5.44/5.72 thf(fact_9846_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_eq_real @ X5 @ B )
% 5.44/5.72 => ? [Y2: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) )
% 5.44/5.72 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_nonneg_imp_nondecreasing
% 5.44/5.72 thf(fact_9847_deriv__nonneg__imp__mono,axiom,
% 5.44/5.72 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.44/5.72 ( ! [X5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.44/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X5 ) ) )
% 5.44/5.72 => ( ( ord_less_eq_real @ A @ B )
% 5.44/5.72 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % deriv_nonneg_imp_mono
% 5.44/5.72 thf(fact_9848_MVT2,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real,F6: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_eq_real @ X5 @ B )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ? [Z4: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ Z4 )
% 5.44/5.72 & ( ord_less_real @ Z4 @ B )
% 5.44/5.72 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.44/5.72 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F6 @ Z4 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % MVT2
% 5.44/5.72 thf(fact_9849_DERIV__local__const,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real,D: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.44/5.72 => ( ! [Y5: real] :
% 5.44/5.72 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.44/5.72 => ( ( F @ X )
% 5.44/5.72 = ( F @ Y5 ) ) )
% 5.44/5.72 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_local_const
% 5.44/5.72 thf(fact_9850_DERIV__ln,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_ln
% 5.44/5.72 thf(fact_9851_DERIV__const__average,axiom,
% 5.44/5.72 ! [A: real,B: real,V: real > real,K: real] :
% 5.44/5.72 ( ( A != B )
% 5.44/5.72 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.44/5.72 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_const_average
% 5.44/5.72 thf(fact_9852_DERIV__local__max,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real,D: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.44/5.72 => ( ! [Y5: real] :
% 5.44/5.72 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.44/5.72 => ( ord_less_eq_real @ ( F @ Y5 ) @ ( F @ X ) ) )
% 5.44/5.72 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_local_max
% 5.44/5.72 thf(fact_9853_DERIV__local__min,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,X: real,D: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.44/5.72 => ( ! [Y5: real] :
% 5.44/5.72 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.44/5.72 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y5 ) ) )
% 5.44/5.72 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_local_min
% 5.44/5.72 thf(fact_9854_DERIV__ln__divide,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_ln_divide
% 5.44/5.72 thf(fact_9855_DERIV__pow,axiom,
% 5.44/5.72 ! [N2: nat,X: real,S3: set_real] :
% 5.44/5.72 ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [X2: real] : ( power_power_real @ X2 @ N2 )
% 5.44/5.72 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ S3 ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_pow
% 5.44/5.72 thf(fact_9856_DERIV__fun__pow,axiom,
% 5.44/5.72 ! [G: real > real,M: real,X: real,N2: nat] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N2 )
% 5.44/5.72 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) @ M )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_fun_pow
% 5.44/5.72 thf(fact_9857_has__real__derivative__powr,axiom,
% 5.44/5.72 ! [Z: real,R: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.44/5.72 => ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [Z5: real] : ( powr_real @ Z5 @ R )
% 5.44/5.72 @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % has_real_derivative_powr
% 5.44/5.72 thf(fact_9858_DERIV__log,axiom,
% 5.44/5.72 ! [X: real,B: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_log
% 5.44/5.72 thf(fact_9859_DERIV__fun__powr,axiom,
% 5.44/5.72 ! [G: real > real,M: real,X: real,R: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R )
% 5.44/5.72 @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_fun_powr
% 5.44/5.72 thf(fact_9860_DERIV__powr,axiom,
% 5.44/5.72 ! [G: real > real,M: real,X: real,F: real > real,R: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.44/5.72 => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 5.44/5.72 @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_powr
% 5.44/5.72 thf(fact_9861_DERIV__real__sqrt,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_real_sqrt
% 5.44/5.72 thf(fact_9862_DERIV__arctan,axiom,
% 5.44/5.72 ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_arctan
% 5.44/5.72 thf(fact_9863_arsinh__real__has__field__derivative,axiom,
% 5.44/5.72 ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % arsinh_real_has_field_derivative
% 5.44/5.72 thf(fact_9864_DERIV__real__sqrt__generic,axiom,
% 5.44/5.72 ! [X: real,D4: real] :
% 5.44/5.72 ( ( X != zero_zero_real )
% 5.44/5.72 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( D4
% 5.44/5.72 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.72 => ( D4
% 5.44/5.72 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_real_sqrt_generic
% 5.44/5.72 thf(fact_9865_arcosh__real__has__field__derivative,axiom,
% 5.44/5.72 ! [X: real,A2: set_real] :
% 5.44/5.72 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % arcosh_real_has_field_derivative
% 5.44/5.72 thf(fact_9866_artanh__real__has__field__derivative,axiom,
% 5.44/5.72 ! [X: real,A2: set_real] :
% 5.44/5.72 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % artanh_real_has_field_derivative
% 5.44/5.72 thf(fact_9867_DERIV__real__root,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_real_root
% 5.44/5.72 thf(fact_9868_DERIV__arccos,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_arccos
% 5.44/5.72 thf(fact_9869_DERIV__arcsin,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_arcsin
% 5.44/5.72 thf(fact_9870_Maclaurin__all__le,axiom,
% 5.44/5.72 ! [Diff: nat > real > real,F: real > real,X: real,N2: nat] :
% 5.44/5.72 ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.44/5.72 & ( ( F @ X )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Maclaurin_all_le
% 5.44/5.72 thf(fact_9871_Maclaurin__all__le__objl,axiom,
% 5.44/5.72 ! [Diff: nat > real > real,F: real > real,X: real,N2: nat] :
% 5.44/5.72 ( ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 & ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.44/5.72 & ( ( F @ X )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Maclaurin_all_le_objl
% 5.44/5.72 thf(fact_9872_DERIV__odd__real__root,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( ( X != zero_zero_real )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_odd_real_root
% 5.44/5.72 thf(fact_9873_Maclaurin,axiom,
% 5.44/5.72 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.44/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ! [M5: nat,T4: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.44/5.72 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.44/5.72 & ( ord_less_real @ T4 @ H2 )
% 5.44/5.72 & ( ( F @ H2 )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Maclaurin
% 5.44/5.72 thf(fact_9874_Maclaurin2,axiom,
% 5.44/5.72 ! [H2: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.44/5.72 => ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ! [M5: nat,T4: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.44/5.72 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.44/5.72 & ( ord_less_eq_real @ T4 @ H2 )
% 5.44/5.72 & ( ( F @ H2 )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Maclaurin2
% 5.44/5.72 thf(fact_9875_Maclaurin__minus,axiom,
% 5.44/5.72 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.44/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ! [M5: nat,T4: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ H2 @ T4 )
% 5.44/5.72 & ( ord_less_eq_real @ T4 @ zero_zero_real ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_real @ H2 @ T4 )
% 5.44/5.72 & ( ord_less_real @ T4 @ zero_zero_real )
% 5.44/5.72 & ( ( F @ H2 )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Maclaurin_minus
% 5.44/5.72 thf(fact_9876_Maclaurin__all__lt,axiom,
% 5.44/5.72 ! [Diff: nat > real > real,F: real > real,N2: nat,X: real] :
% 5.44/5.72 ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( X != zero_zero_real )
% 5.44/5.72 => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T4 ) )
% 5.44/5.72 & ( ord_less_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.44/5.72 & ( ( F @ X )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Maclaurin_all_lt
% 5.44/5.72 thf(fact_9877_Maclaurin__bi__le,axiom,
% 5.44/5.72 ! [Diff: nat > real > real,F: real > real,N2: nat,X: real] :
% 5.44/5.72 ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ! [M5: nat,T4: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X ) )
% 5.44/5.72 & ( ( F @ X )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Maclaurin_bi_le
% 5.44/5.72 thf(fact_9878_Taylor,axiom,
% 5.44/5.72 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ! [M5: nat,T4: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ A @ T4 )
% 5.44/5.72 & ( ord_less_eq_real @ T4 @ B ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.44/5.72 => ( ( ord_less_eq_real @ A @ C )
% 5.44/5.72 => ( ( ord_less_eq_real @ C @ B )
% 5.44/5.72 => ( ( ord_less_eq_real @ A @ X )
% 5.44/5.72 => ( ( ord_less_eq_real @ X @ B )
% 5.44/5.72 => ( ( X != C )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ( ord_less_real @ X @ C )
% 5.44/5.72 => ( ( ord_less_real @ X @ T4 )
% 5.44/5.72 & ( ord_less_real @ T4 @ C ) ) )
% 5.44/5.72 & ( ~ ( ord_less_real @ X @ C )
% 5.44/5.72 => ( ( ord_less_real @ C @ T4 )
% 5.44/5.72 & ( ord_less_real @ T4 @ X ) ) )
% 5.44/5.72 & ( ( F @ X )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Taylor
% 5.44/5.72 thf(fact_9879_Taylor__up,axiom,
% 5.44/5.72 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ! [M5: nat,T4: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ A @ T4 )
% 5.44/5.72 & ( ord_less_eq_real @ T4 @ B ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.44/5.72 => ( ( ord_less_eq_real @ A @ C )
% 5.44/5.72 => ( ( ord_less_real @ C @ B )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_real @ C @ T4 )
% 5.44/5.72 & ( ord_less_real @ T4 @ B )
% 5.44/5.72 & ( ( F @ B )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Taylor_up
% 5.44/5.72 thf(fact_9880_Taylor__down,axiom,
% 5.44/5.72 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( ( Diff @ zero_zero_nat )
% 5.44/5.72 = F )
% 5.44/5.72 => ( ! [M5: nat,T4: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ A @ T4 )
% 5.44/5.72 & ( ord_less_eq_real @ T4 @ B ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.44/5.72 => ( ( ord_less_real @ A @ C )
% 5.44/5.72 => ( ( ord_less_eq_real @ C @ B )
% 5.44/5.72 => ? [T4: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ T4 )
% 5.44/5.72 & ( ord_less_real @ T4 @ C )
% 5.44/5.72 & ( ( F @ A )
% 5.44/5.72 = ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.44/5.72 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T4 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Taylor_down
% 5.44/5.72 thf(fact_9881_Maclaurin__lemma2,axiom,
% 5.44/5.72 ! [N2: nat,H2: real,Diff: nat > real > real,K: nat,B2: real] :
% 5.44/5.72 ( ! [M5: nat,T4: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.44/5.72 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.44/5.72 => ( ( N2
% 5.44/5.72 = ( suc @ K ) )
% 5.44/5.72 => ! [M2: nat,T6: real] :
% 5.44/5.72 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.44/5.72 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.44/5.72 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [U2: real] :
% 5.44/5.72 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 5.44/5.72 @ ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ U2 @ P4 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M2 ) ) )
% 5.44/5.72 @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) )
% 5.44/5.72 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T6 )
% 5.44/5.72 @ ( plus_plus_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [P4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P4 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P4 ) ) @ ( power_power_real @ T6 @ P4 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) )
% 5.44/5.72 @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ T6 @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) ) ) ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Maclaurin_lemma2
% 5.44/5.72 thf(fact_9882_DERIV__arctan__series,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.72 => ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [X9: real] :
% 5.44/5.72 ( suminf_real
% 5.44/5.72 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_arctan_series
% 5.44/5.72 thf(fact_9883_DERIV__even__real__root,axiom,
% 5.44/5.72 ! [N2: nat,X: real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_even_real_root
% 5.44/5.72 thf(fact_9884_DERIV__power__series_H,axiom,
% 5.44/5.72 ! [R2: real,F: nat > real,X0: real] :
% 5.44/5.72 ( ! [X5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.44/5.72 => ( summable_real
% 5.44/5.72 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X5 @ N ) ) ) )
% 5.44/5.72 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.44/5.72 => ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( suminf_real
% 5.44/5.72 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) )
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X0 @ N ) ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_power_series'
% 5.44/5.72 thf(fact_9885_tanh__real__bounds,axiom,
% 5.44/5.72 ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % tanh_real_bounds
% 5.44/5.72 thf(fact_9886_DERIV__isconst3,axiom,
% 5.44/5.72 ! [A: real,B: real,X: real,Y: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.44/5.72 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.44/5.72 => ( ( F @ X )
% 5.44/5.72 = ( F @ Y ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_isconst3
% 5.44/5.72 thf(fact_9887_DERIV__series_H,axiom,
% 5.44/5.72 ! [F: real > nat > real,F6: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.44/5.72 ( ! [N4: nat] :
% 5.44/5.72 ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [X2: real] : ( F @ X2 @ N4 )
% 5.44/5.72 @ ( F6 @ X0 @ N4 )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.44/5.72 => ( summable_real @ ( F @ X5 ) ) )
% 5.44/5.72 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.44/5.72 => ( ( summable_real @ ( F6 @ X0 ) )
% 5.44/5.72 => ( ( summable_real @ L5 )
% 5.44/5.72 => ( ! [N4: nat,X5: real,Y5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.44/5.72 => ( ( member_real @ Y5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.44/5.72 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X5 @ N4 ) @ ( F @ Y5 @ N4 ) ) ) @ ( times_times_real @ ( L5 @ N4 ) @ ( abs_abs_real @ ( minus_minus_real @ X5 @ Y5 ) ) ) ) ) )
% 5.44/5.72 => ( has_fi5821293074295781190e_real
% 5.44/5.72 @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 5.44/5.72 @ ( suminf_real @ ( F6 @ X0 ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_series'
% 5.44/5.72 thf(fact_9888_upto__aux__rec,axiom,
% 5.44/5.72 ( upto_aux
% 5.44/5.72 = ( ^ [I5: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I5 ) @ Js @ ( upto_aux @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_aux_rec
% 5.44/5.72 thf(fact_9889_card__greaterThanLessThan,axiom,
% 5.44/5.72 ! [L2: nat,U: nat] :
% 5.44/5.72 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 5.44/5.72 = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % card_greaterThanLessThan
% 5.44/5.72 thf(fact_9890_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.44/5.72 ! [L2: nat,U: nat] :
% 5.44/5.72 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 5.44/5.72 = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeastSucLessThan_greaterThanLessThan
% 5.44/5.72 thf(fact_9891_isCont__Lb__Ub,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 & ( ord_less_eq_real @ X5 @ B ) )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.44/5.72 => ? [L6: real,M8: real] :
% 5.44/5.72 ( ! [X3: real] :
% 5.44/5.72 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.44/5.72 & ( ord_less_eq_real @ X3 @ B ) )
% 5.44/5.72 => ( ( ord_less_eq_real @ L6 @ ( F @ X3 ) )
% 5.44/5.72 & ( ord_less_eq_real @ ( F @ X3 ) @ M8 ) ) )
% 5.44/5.72 & ! [Y2: real] :
% 5.44/5.72 ( ( ( ord_less_eq_real @ L6 @ Y2 )
% 5.44/5.72 & ( ord_less_eq_real @ Y2 @ M8 ) )
% 5.44/5.72 => ? [X5: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 & ( ord_less_eq_real @ X5 @ B )
% 5.44/5.72 & ( ( F @ X5 )
% 5.44/5.72 = Y2 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_Lb_Ub
% 5.44/5.72 thf(fact_9892_LIM__fun__gt__zero,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,C: real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.44/5.72 => ? [R3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.44/5.72 & ! [X3: real] :
% 5.44/5.72 ( ( ( X3 != C )
% 5.44/5.72 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X3 ) ) @ R3 ) )
% 5.44/5.72 => ( ord_less_real @ zero_zero_real @ ( F @ X3 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIM_fun_gt_zero
% 5.44/5.72 thf(fact_9893_LIM__fun__not__zero,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,C: real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.44/5.72 => ( ( L2 != zero_zero_real )
% 5.44/5.72 => ? [R3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.44/5.72 & ! [X3: real] :
% 5.44/5.72 ( ( ( X3 != C )
% 5.44/5.72 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X3 ) ) @ R3 ) )
% 5.44/5.72 => ( ( F @ X3 )
% 5.44/5.72 != zero_zero_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIM_fun_not_zero
% 5.44/5.72 thf(fact_9894_LIM__fun__less__zero,axiom,
% 5.44/5.72 ! [F: real > real,L2: real,C: real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.44/5.72 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.44/5.72 => ? [R3: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.44/5.72 & ! [X3: real] :
% 5.44/5.72 ( ( ( X3 != C )
% 5.44/5.72 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X3 ) ) @ R3 ) )
% 5.44/5.72 => ( ord_less_real @ ( F @ X3 ) @ zero_zero_real ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIM_fun_less_zero
% 5.44/5.72 thf(fact_9895_isCont__real__sqrt,axiom,
% 5.44/5.72 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_real_sqrt
% 5.44/5.72 thf(fact_9896_isCont__real__root,axiom,
% 5.44/5.72 ! [X: real,N2: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_real_root
% 5.44/5.72 thf(fact_9897_isCont__inverse__function2,axiom,
% 5.44/5.72 ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ B )
% 5.44/5.72 => ( ! [Z4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ Z4 )
% 5.44/5.72 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.44/5.72 => ( ( G @ ( F @ Z4 ) )
% 5.44/5.72 = Z4 ) ) )
% 5.44/5.72 => ( ! [Z4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ Z4 )
% 5.44/5.72 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) ) )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_inverse_function2
% 5.44/5.72 thf(fact_9898_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.44/5.72 ! [I2: nat,J: nat] :
% 5.44/5.72 ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 5.44/5.72 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 5.44/5.72 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sorted_list_of_set_greaterThanLessThan
% 5.44/5.72 thf(fact_9899_isCont__arcosh,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_arcosh
% 5.44/5.72 thf(fact_9900_LIM__cos__div__sin,axiom,
% 5.44/5.72 ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIM_cos_div_sin
% 5.44/5.72 thf(fact_9901_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.44/5.72 ! [N2: nat,J: nat,I2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 5.44/5.72 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N2 )
% 5.44/5.72 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nth_sorted_list_of_set_greaterThanLessThan
% 5.44/5.72 thf(fact_9902_DERIV__inverse__function,axiom,
% 5.44/5.72 ! [F: real > real,D4: real,G: real > real,X: real,A: real,B: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 5.44/5.72 => ( ( D4 != zero_zero_real )
% 5.44/5.72 => ( ( ord_less_real @ A @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ B )
% 5.44/5.72 => ( ! [Y5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ Y5 )
% 5.44/5.72 => ( ( ord_less_real @ Y5 @ B )
% 5.44/5.72 => ( ( F @ ( G @ Y5 ) )
% 5.44/5.72 = Y5 ) ) )
% 5.44/5.72 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_inverse_function
% 5.44/5.72 thf(fact_9903_isCont__arccos,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_arccos
% 5.44/5.72 thf(fact_9904_isCont__arcsin,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_arcsin
% 5.44/5.72 thf(fact_9905_LIM__less__bound,axiom,
% 5.44/5.72 ! [B: real,X: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ B @ X )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 5.44/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.44/5.72 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 5.44/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIM_less_bound
% 5.44/5.72 thf(fact_9906_isCont__artanh,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_artanh
% 5.44/5.72 thf(fact_9907_isCont__inverse__function,axiom,
% 5.44/5.72 ! [D: real,X: real,G: real > real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ D )
% 5.44/5.72 => ( ! [Z4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z4 @ X ) ) @ D )
% 5.44/5.72 => ( ( G @ ( F @ Z4 ) )
% 5.44/5.72 = Z4 ) )
% 5.44/5.72 => ( ! [Z4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z4 @ X ) ) @ D )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % isCont_inverse_function
% 5.44/5.72 thf(fact_9908_GMVT_H,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F6: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ! [Z4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ Z4 )
% 5.44/5.72 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) ) )
% 5.44/5.72 => ( ! [Z4: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ Z4 )
% 5.44/5.72 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ G ) ) )
% 5.44/5.72 => ( ! [Z4: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ Z4 )
% 5.44/5.72 => ( ( ord_less_real @ Z4 @ B )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z4 ) @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ( ! [Z4: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ Z4 )
% 5.44/5.72 => ( ( ord_less_real @ Z4 @ B )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ Z4 ) @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ? [C3: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ C3 )
% 5.44/5.72 & ( ord_less_real @ C3 @ B )
% 5.44/5.72 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.44/5.72 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F6 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % GMVT'
% 5.44/5.72 thf(fact_9909_summable__Leibniz_I3_J,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ( topolo6980174941875973593q_real @ A )
% 5.44/5.72 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.44/5.72 => ! [N9: nat] :
% 5.44/5.72 ( member_real
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.44/5.72 @ ( set_or1222579329274155063t_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz(3)
% 5.44/5.72 thf(fact_9910_summable__Leibniz_I2_J,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ( topolo6980174941875973593q_real @ A )
% 5.44/5.72 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.44/5.72 => ! [N9: nat] :
% 5.44/5.72 ( member_real
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.44/5.72 @ ( set_or1222579329274155063t_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz(2)
% 5.44/5.72 thf(fact_9911_summable__Leibniz_H_I4_J,axiom,
% 5.44/5.72 ! [A: nat > real,N2: nat] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.44/5.72 => ( ord_less_eq_real
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz'(4)
% 5.44/5.72 thf(fact_9912_filterlim__Suc,axiom,
% 5.44/5.72 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.44/5.72
% 5.44/5.72 % filterlim_Suc
% 5.44/5.72 thf(fact_9913_mult__nat__right__at__top,axiom,
% 5.44/5.72 ! [C: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.44/5.72 => ( filterlim_nat_nat
% 5.44/5.72 @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 5.44/5.72 @ at_top_nat
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % mult_nat_right_at_top
% 5.44/5.72 thf(fact_9914_mult__nat__left__at__top,axiom,
% 5.44/5.72 ! [C: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.44/5.72 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % mult_nat_left_at_top
% 5.44/5.72 thf(fact_9915_monoseq__convergent,axiom,
% 5.44/5.72 ! [X8: nat > real,B2: real] :
% 5.44/5.72 ( ( topolo6980174941875973593q_real @ X8 )
% 5.44/5.72 => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B2 )
% 5.44/5.72 => ~ ! [L6: real] :
% 5.44/5.72 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % monoseq_convergent
% 5.44/5.72 thf(fact_9916_LIMSEQ__root,axiom,
% 5.44/5.72 ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( root @ N @ ( semiri5074537144036343181t_real @ N ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.44/5.72 @ at_top_nat ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_root
% 5.44/5.72 thf(fact_9917_nested__sequence__unique,axiom,
% 5.44/5.72 ! [F: nat > real,G: nat > real] :
% 5.44/5.72 ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N4 ) ) @ ( G @ N4 ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.44/5.72 => ( ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_nat )
% 5.44/5.72 => ? [L4: real] :
% 5.44/5.72 ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L4 )
% 5.44/5.72 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.44/5.72 & ! [N9: nat] : ( ord_less_eq_real @ L4 @ ( G @ N9 ) )
% 5.44/5.72 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nested_sequence_unique
% 5.44/5.72 thf(fact_9918_LIMSEQ__inverse__zero,axiom,
% 5.44/5.72 ! [X8: nat > real] :
% 5.44/5.72 ( ! [R3: real] :
% 5.44/5.72 ? [N7: nat] :
% 5.44/5.72 ! [N4: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ N7 @ N4 )
% 5.44/5.72 => ( ord_less_real @ R3 @ ( X8 @ N4 ) ) )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( inverse_inverse_real @ ( X8 @ N ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_inverse_zero
% 5.44/5.72 thf(fact_9919_lim__inverse__n_H,axiom,
% 5.44/5.72 ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_nat ) ).
% 5.44/5.72
% 5.44/5.72 % lim_inverse_n'
% 5.44/5.72 thf(fact_9920_LIMSEQ__root__const,axiom,
% 5.44/5.72 ! [C: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ C )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( root @ N @ C )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_root_const
% 5.44/5.72 thf(fact_9921_LIMSEQ__inverse__real__of__nat,axiom,
% 5.44/5.72 ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_nat ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_inverse_real_of_nat
% 5.44/5.72 thf(fact_9922_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.44/5.72 ! [R: real] :
% 5.44/5.72 ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ R )
% 5.44/5.72 @ at_top_nat ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_inverse_real_of_nat_add
% 5.44/5.72 thf(fact_9923_increasing__LIMSEQ,axiom,
% 5.44/5.72 ! [F: nat > real,L2: real] :
% 5.44/5.72 ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ L2 )
% 5.44/5.72 => ( ! [E2: real] :
% 5.44/5.72 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.44/5.72 => ? [N9: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N9 ) @ E2 ) ) )
% 5.44/5.72 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % increasing_LIMSEQ
% 5.44/5.72 thf(fact_9924_LIMSEQ__realpow__zero,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( ord_less_real @ X @ one_one_real )
% 5.44/5.72 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_realpow_zero
% 5.44/5.72 thf(fact_9925_LIMSEQ__divide__realpow__zero,axiom,
% 5.44/5.72 ! [X: real,A: real] :
% 5.44/5.72 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_divide_realpow_zero
% 5.44/5.72 thf(fact_9926_LIMSEQ__abs__realpow__zero,axiom,
% 5.44/5.72 ! [C: real] :
% 5.44/5.72 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.44/5.72 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_abs_realpow_zero
% 5.44/5.72 thf(fact_9927_LIMSEQ__abs__realpow__zero2,axiom,
% 5.44/5.72 ! [C: real] :
% 5.44/5.72 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.44/5.72 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_abs_realpow_zero2
% 5.44/5.72 thf(fact_9928_LIMSEQ__inverse__realpow__zero,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_real @ one_one_real @ X )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_inverse_realpow_zero
% 5.44/5.72 thf(fact_9929_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.44/5.72 ! [R: real] :
% 5.44/5.72 ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ R )
% 5.44/5.72 @ at_top_nat ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.44/5.72 thf(fact_9930_tendsto__exp__limit__sequentially,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.44/5.72 @ at_top_nat ) ).
% 5.44/5.72
% 5.44/5.72 % tendsto_exp_limit_sequentially
% 5.44/5.72 thf(fact_9931_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.44/5.72 ! [R: real] :
% 5.44/5.72 ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ R )
% 5.44/5.72 @ at_top_nat ) ).
% 5.44/5.72
% 5.44/5.72 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.44/5.72 thf(fact_9932_summable__Leibniz_I1_J,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ( topolo6980174941875973593q_real @ A )
% 5.44/5.72 => ( summable_real
% 5.44/5.72 @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz(1)
% 5.44/5.72 thf(fact_9933_summable,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.44/5.72 => ( summable_real
% 5.44/5.72 @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable
% 5.44/5.72 thf(fact_9934_cos__diff__limit__1,axiom,
% 5.44/5.72 ! [Theta: nat > real,Theta2: real] :
% 5.44/5.72 ( ( filterlim_nat_real
% 5.44/5.72 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.44/5.72 @ at_top_nat )
% 5.44/5.72 => ~ ! [K2: nat > int] :
% 5.44/5.72 ~ ( filterlim_nat_real
% 5.44/5.72 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % cos_diff_limit_1
% 5.44/5.72 thf(fact_9935_cos__limit__1,axiom,
% 5.44/5.72 ! [Theta: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real
% 5.44/5.72 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.44/5.72 @ at_top_nat )
% 5.44/5.72 => ? [K2: nat > int] :
% 5.44/5.72 ( filterlim_nat_real
% 5.44/5.72 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % cos_limit_1
% 5.44/5.72 thf(fact_9936_summable__Leibniz_I4_J,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ( topolo6980174941875973593q_real @ A )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] :
% 5.44/5.72 ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.44/5.72 @ at_top_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz(4)
% 5.44/5.72 thf(fact_9937_zeroseq__arctan__series,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % zeroseq_arctan_series
% 5.44/5.72 thf(fact_9938_summable__Leibniz_H_I2_J,axiom,
% 5.44/5.72 ! [A: nat > real,N2: nat] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.44/5.72 => ( ord_less_eq_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz'(2)
% 5.44/5.72 thf(fact_9939_summable__Leibniz_H_I3_J,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] :
% 5.44/5.72 ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.44/5.72 @ at_top_nat ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz'(3)
% 5.44/5.72 thf(fact_9940_sums__alternating__upper__lower,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.44/5.72 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ? [L4: real] :
% 5.44/5.72 ( ! [N9: nat] :
% 5.44/5.72 ( ord_less_eq_real
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.44/5.72 @ L4 )
% 5.44/5.72 & ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] :
% 5.44/5.72 ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ L4 )
% 5.44/5.72 @ at_top_nat )
% 5.44/5.72 & ! [N9: nat] :
% 5.44/5.72 ( ord_less_eq_real @ L4
% 5.44/5.72 @ ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 5.44/5.72 & ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] :
% 5.44/5.72 ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ L4 )
% 5.44/5.72 @ at_top_nat ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sums_alternating_upper_lower
% 5.44/5.72 thf(fact_9941_summable__Leibniz_I5_J,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ( topolo6980174941875973593q_real @ A )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] :
% 5.44/5.72 ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.44/5.72 @ at_top_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz(5)
% 5.44/5.72 thf(fact_9942_summable__Leibniz_H_I5_J,axiom,
% 5.44/5.72 ! [A: nat > real] :
% 5.44/5.72 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.44/5.72 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.44/5.72 => ( filterlim_nat_real
% 5.44/5.72 @ ^ [N: nat] :
% 5.44/5.72 ( groups6591440286371151544t_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.44/5.72 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real
% 5.44/5.72 @ ( suminf_real
% 5.44/5.72 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.44/5.72 @ at_top_nat ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % summable_Leibniz'(5)
% 5.44/5.72 thf(fact_9943_real__bounded__linear,axiom,
% 5.44/5.72 ( real_V5970128139526366754l_real
% 5.44/5.72 = ( ^ [F5: real > real] :
% 5.44/5.72 ? [C2: real] :
% 5.44/5.72 ( F5
% 5.44/5.72 = ( ^ [X2: real] : ( times_times_real @ X2 @ C2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % real_bounded_linear
% 5.44/5.72 thf(fact_9944_tendsto__exp__limit__at__right,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( filterlim_real_real
% 5.44/5.72 @ ^ [Y3: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y3 ) ) @ ( divide_divide_real @ one_one_real @ Y3 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % tendsto_exp_limit_at_right
% 5.44/5.72 thf(fact_9945_tendsto__arctan__at__bot,axiom,
% 5.44/5.72 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.44/5.72
% 5.44/5.72 % tendsto_arctan_at_bot
% 5.44/5.72 thf(fact_9946_artanh__real__at__right__1,axiom,
% 5.44/5.72 filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % artanh_real_at_right_1
% 5.44/5.72 thf(fact_9947_filterlim__tan__at__right,axiom,
% 5.44/5.72 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 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % filterlim_tan_at_right
% 5.44/5.72 thf(fact_9948_tanh__real__at__bot,axiom,
% 5.44/5.72 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.44/5.72
% 5.44/5.72 % tanh_real_at_bot
% 5.44/5.72 thf(fact_9949_tendsto__arcosh__at__left__1,axiom,
% 5.44/5.72 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % tendsto_arcosh_at_left_1
% 5.44/5.72 thf(fact_9950_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.44/5.72 ! [B: real,F: real > real,Flim: real] :
% 5.44/5.72 ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ X5 @ B )
% 5.44/5.72 => ? [Y2: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_real @ zero_zero_real @ Y2 ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.44/5.72 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_pos_imp_increasing_at_bot
% 5.44/5.72 thf(fact_9951_filterlim__pow__at__bot__odd,axiom,
% 5.44/5.72 ! [N2: nat,F: real > real,F3: filter_real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 5.44/5.72 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 5.44/5.72 @ at_bot_real
% 5.44/5.72 @ F3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % filterlim_pow_at_bot_odd
% 5.44/5.72 thf(fact_9952_filterlim__pow__at__bot__even,axiom,
% 5.44/5.72 ! [N2: nat,F: real > real,F3: filter_real] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 5.44/5.72 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 5.44/5.72 @ at_top_real
% 5.44/5.72 @ F3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % filterlim_pow_at_bot_even
% 5.44/5.72 thf(fact_9953_sqrt__at__top,axiom,
% 5.44/5.72 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.44/5.72
% 5.44/5.72 % sqrt_at_top
% 5.44/5.72 thf(fact_9954_greaterThan__0,axiom,
% 5.44/5.72 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.44/5.72 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % greaterThan_0
% 5.44/5.72 thf(fact_9955_tanh__real__at__top,axiom,
% 5.44/5.72 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.44/5.72
% 5.44/5.72 % tanh_real_at_top
% 5.44/5.72 thf(fact_9956_artanh__real__at__left__1,axiom,
% 5.44/5.72 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % artanh_real_at_left_1
% 5.44/5.72 thf(fact_9957_greaterThan__Suc,axiom,
% 5.44/5.72 ! [K: nat] :
% 5.44/5.72 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.44/5.72 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % greaterThan_Suc
% 5.44/5.72 thf(fact_9958_ln__x__over__x__tendsto__0,axiom,
% 5.44/5.72 ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_real ) ).
% 5.44/5.72
% 5.44/5.72 % ln_x_over_x_tendsto_0
% 5.44/5.72 thf(fact_9959_tendsto__power__div__exp__0,axiom,
% 5.44/5.72 ! [K: nat] :
% 5.44/5.72 ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.44/5.72 @ at_top_real ) ).
% 5.44/5.72
% 5.44/5.72 % tendsto_power_div_exp_0
% 5.44/5.72 thf(fact_9960_tendsto__exp__limit__at__top,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( filterlim_real_real
% 5.44/5.72 @ ^ [Y3: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y3 ) ) @ Y3 )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.44/5.72 @ at_top_real ) ).
% 5.44/5.72
% 5.44/5.72 % tendsto_exp_limit_at_top
% 5.44/5.72 thf(fact_9961_filterlim__tan__at__left,axiom,
% 5.44/5.72 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 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % filterlim_tan_at_left
% 5.44/5.72 thf(fact_9962_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.44/5.72 ! [B: real,F: real > real,Flim: real] :
% 5.44/5.72 ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ B @ X5 )
% 5.44/5.72 => ? [Y2: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_real @ Y2 @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.44/5.72 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_neg_imp_decreasing_at_top
% 5.44/5.72 thf(fact_9963_tendsto__arctan__at__top,axiom,
% 5.44/5.72 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.44/5.72
% 5.44/5.72 % tendsto_arctan_at_top
% 5.44/5.72 thf(fact_9964_lhopital__right__at__top,axiom,
% 5.44/5.72 ! [G: real > real,X: real,G2: real > real,F: real > real,F6: real > real,Y: real] :
% 5.44/5.72 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ Y )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ Y )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_right_at_top
% 5.44/5.72 thf(fact_9965_eventually__sequentially__Suc,axiom,
% 5.44/5.72 ! [P: nat > $o] :
% 5.44/5.72 ( ( eventually_nat
% 5.44/5.72 @ ^ [I5: nat] : ( P @ ( suc @ I5 ) )
% 5.44/5.72 @ at_top_nat )
% 5.44/5.72 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % eventually_sequentially_Suc
% 5.44/5.72 thf(fact_9966_eventually__sequentially__seg,axiom,
% 5.44/5.72 ! [P: nat > $o,K: nat] :
% 5.44/5.72 ( ( eventually_nat
% 5.44/5.72 @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 5.44/5.72 @ at_top_nat )
% 5.44/5.72 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % eventually_sequentially_seg
% 5.44/5.72 thf(fact_9967_eventually__sequentiallyI,axiom,
% 5.44/5.72 ! [C: nat,P: nat > $o] :
% 5.44/5.72 ( ! [X5: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ C @ X5 )
% 5.44/5.72 => ( P @ X5 ) )
% 5.44/5.72 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % eventually_sequentiallyI
% 5.44/5.72 thf(fact_9968_eventually__sequentially,axiom,
% 5.44/5.72 ! [P: nat > $o] :
% 5.44/5.72 ( ( eventually_nat @ P @ at_top_nat )
% 5.44/5.72 = ( ? [N6: nat] :
% 5.44/5.72 ! [N: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ N6 @ N )
% 5.44/5.72 => ( P @ N ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % eventually_sequentially
% 5.44/5.72 thf(fact_9969_le__sequentially,axiom,
% 5.44/5.72 ! [F3: filter_nat] :
% 5.44/5.72 ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 5.44/5.72 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F3 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % le_sequentially
% 5.44/5.72 thf(fact_9970_sequentially__offset,axiom,
% 5.44/5.72 ! [P: nat > $o,K: nat] :
% 5.44/5.72 ( ( eventually_nat @ P @ at_top_nat )
% 5.44/5.72 => ( eventually_nat
% 5.44/5.72 @ ^ [I5: nat] : ( P @ ( plus_plus_nat @ I5 @ K ) )
% 5.44/5.72 @ at_top_nat ) ) ).
% 5.44/5.72
% 5.44/5.72 % sequentially_offset
% 5.44/5.72 thf(fact_9971_eventually__at__left__real,axiom,
% 5.44/5.72 ! [B: real,A: real] :
% 5.44/5.72 ( ( ord_less_real @ B @ A )
% 5.44/5.72 => ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % eventually_at_left_real
% 5.44/5.72 thf(fact_9972_eventually__at__right__to__0,axiom,
% 5.44/5.72 ! [P: real > $o,A: real] :
% 5.44/5.72 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 = ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % eventually_at_right_to_0
% 5.44/5.72 thf(fact_9973_eventually__at__right__real,axiom,
% 5.44/5.72 ! [A: real,B: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % eventually_at_right_real
% 5.44/5.72 thf(fact_9974_lhopital__at__top__at__top,axiom,
% 5.44/5.72 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ at_top_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ at_top_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_at_top_at_top
% 5.44/5.72 thf(fact_9975_lhopital__left__at__top__at__top,axiom,
% 5.44/5.72 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ at_top_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ at_top_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_left_at_top_at_top
% 5.44/5.72 thf(fact_9976_lhopital,axiom,
% 5.44/5.72 ! [F: real > real,X: real,G: real > real,G2: real > real,F6: real > real,F3: filter_real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ F3
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ F3
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital
% 5.44/5.72 thf(fact_9977_lhopital__left,axiom,
% 5.44/5.72 ! [F: real > real,X: real,G: real > real,G2: real > real,F6: real > real,F3: filter_real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ F3
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ F3
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_left
% 5.44/5.72 thf(fact_9978_lhopital__right__at__top__at__top,axiom,
% 5.44/5.72 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ at_top_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ at_top_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_right_at_top_at_top
% 5.44/5.72 thf(fact_9979_lhopital__at__top__at__bot,axiom,
% 5.44/5.72 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ at_bot_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ at_bot_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_at_top_at_bot
% 5.44/5.72 thf(fact_9980_lhopital__left__at__top__at__bot,axiom,
% 5.44/5.72 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ at_bot_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ at_bot_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_left_at_top_at_bot
% 5.44/5.72 thf(fact_9981_lhospital__at__top__at__top,axiom,
% 5.44/5.72 ! [G: real > real,G2: real > real,F: real > real,F6: real > real,X: real] :
% 5.44/5.72 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ at_top_real )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ at_top_real )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ at_top_real )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ X )
% 5.44/5.72 @ at_top_real )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ X )
% 5.44/5.72 @ at_top_real ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhospital_at_top_at_top
% 5.44/5.72 thf(fact_9982_lhopital__at__top,axiom,
% 5.44/5.72 ! [G: real > real,X: real,G2: real > real,F: real > real,F6: real > real,Y: real] :
% 5.44/5.72 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ Y )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ Y )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_at_top
% 5.44/5.72 thf(fact_9983_lhopital__left__at__top,axiom,
% 5.44/5.72 ! [G: real > real,X: real,G2: real > real,F: real > real,F6: real > real,Y: real] :
% 5.44/5.72 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ Y )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ Y )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_left_at_top
% 5.44/5.72 thf(fact_9984_lhopital__right__0,axiom,
% 5.44/5.72 ! [F0: real > real,G0: real > real,G2: real > real,F6: real > real,F3: filter_real] :
% 5.44/5.72 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G0 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ F3
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F0 @ X2 ) @ ( G0 @ X2 ) )
% 5.44/5.72 @ F3
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_right_0
% 5.44/5.72 thf(fact_9985_lhopital__right,axiom,
% 5.44/5.72 ! [F: real > real,X: real,G: real > real,G2: real > real,F6: real > real,F3: filter_real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ F3
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ F3
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_right
% 5.44/5.72 thf(fact_9986_lhopital__right__at__top__at__bot,axiom,
% 5.44/5.72 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 5.44/5.72 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ at_bot_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ at_bot_real
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_right_at_top_at_bot
% 5.44/5.72 thf(fact_9987_lhopital__right__0__at__top,axiom,
% 5.44/5.72 ! [G: real > real,G2: real > real,F: real > real,F6: real > real,X: real] :
% 5.44/5.72 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] :
% 5.44/5.72 ( ( G2 @ X2 )
% 5.44/5.72 != zero_zero_real )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( eventually_real
% 5.44/5.72 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ X )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.44/5.72 => ( filterlim_real_real
% 5.44/5.72 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.44/5.72 @ ( topolo2815343760600316023s_real @ X )
% 5.44/5.72 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % lhopital_right_0_at_top
% 5.44/5.72 thf(fact_9988_Bseq__realpow,axiom,
% 5.44/5.72 ! [X: real] :
% 5.44/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.72 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.44/5.72 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Bseq_realpow
% 5.44/5.72 thf(fact_9989_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.44/5.72 ! [L2: nat,U: nat] :
% 5.44/5.72 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 5.44/5.72 = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeastSucAtMost_greaterThanAtMost
% 5.44/5.72 thf(fact_9990_GreatestI__ex__nat,axiom,
% 5.44/5.72 ! [P: nat > $o,B: nat] :
% 5.44/5.72 ( ? [X_12: nat] : ( P @ X_12 )
% 5.44/5.72 => ( ! [Y5: nat] :
% 5.44/5.72 ( ( P @ Y5 )
% 5.44/5.72 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.44/5.72 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % GreatestI_ex_nat
% 5.44/5.72 thf(fact_9991_Greatest__le__nat,axiom,
% 5.44/5.72 ! [P: nat > $o,K: nat,B: nat] :
% 5.44/5.72 ( ( P @ K )
% 5.44/5.72 => ( ! [Y5: nat] :
% 5.44/5.72 ( ( P @ Y5 )
% 5.44/5.72 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.44/5.72 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Greatest_le_nat
% 5.44/5.72 thf(fact_9992_GreatestI__nat,axiom,
% 5.44/5.72 ! [P: nat > $o,K: nat,B: nat] :
% 5.44/5.72 ( ( P @ K )
% 5.44/5.72 => ( ! [Y5: nat] :
% 5.44/5.72 ( ( P @ Y5 )
% 5.44/5.72 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.44/5.72 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % GreatestI_nat
% 5.44/5.72 thf(fact_9993_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.44/5.72 ! [I2: nat,J: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 5.44/5.72 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 5.44/5.72 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % sorted_list_of_set_greaterThanAtMost
% 5.44/5.72 thf(fact_9994_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.44/5.72 ! [N2: nat,J: nat,I2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I2 ) )
% 5.44/5.72 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N2 )
% 5.44/5.72 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nth_sorted_list_of_set_greaterThanAtMost
% 5.44/5.72 thf(fact_9995_atLeast__Suc__greaterThan,axiom,
% 5.44/5.72 ! [K: nat] :
% 5.44/5.72 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.44/5.72 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeast_Suc_greaterThan
% 5.44/5.72 thf(fact_9996_decseq__bounded,axiom,
% 5.44/5.72 ! [X8: nat > real,B2: real] :
% 5.44/5.72 ( ( order_9091379641038594480t_real @ X8 )
% 5.44/5.72 => ( ! [I4: nat] : ( ord_less_eq_real @ B2 @ ( X8 @ I4 ) )
% 5.44/5.72 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % decseq_bounded
% 5.44/5.72 thf(fact_9997_decseq__convergent,axiom,
% 5.44/5.72 ! [X8: nat > real,B2: real] :
% 5.44/5.72 ( ( order_9091379641038594480t_real @ X8 )
% 5.44/5.72 => ( ! [I4: nat] : ( ord_less_eq_real @ B2 @ ( X8 @ I4 ) )
% 5.44/5.72 => ~ ! [L6: real] :
% 5.44/5.72 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.44/5.72 => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % decseq_convergent
% 5.44/5.72 thf(fact_9998_atLeast__Suc,axiom,
% 5.44/5.72 ! [K: nat] :
% 5.44/5.72 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.44/5.72 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeast_Suc
% 5.44/5.72 thf(fact_9999_upto_Opsimps,axiom,
% 5.44/5.72 ! [I2: int,J: int] :
% 5.44/5.72 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 5.44/5.72 => ( ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.72 => ( ( upto @ I2 @ J )
% 5.44/5.72 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ I2 @ J )
% 5.44/5.72 => ( ( upto @ I2 @ J )
% 5.44/5.72 = nil_int ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto.psimps
% 5.44/5.72 thf(fact_10000_upto__empty,axiom,
% 5.44/5.72 ! [J: int,I2: int] :
% 5.44/5.72 ( ( ord_less_int @ J @ I2 )
% 5.44/5.72 => ( ( upto @ I2 @ J )
% 5.44/5.72 = nil_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_empty
% 5.44/5.72 thf(fact_10001_upto__Nil2,axiom,
% 5.44/5.72 ! [I2: int,J: int] :
% 5.44/5.72 ( ( nil_int
% 5.44/5.72 = ( upto @ I2 @ J ) )
% 5.44/5.72 = ( ord_less_int @ J @ I2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_Nil2
% 5.44/5.72 thf(fact_10002_upto__Nil,axiom,
% 5.44/5.72 ! [I2: int,J: int] :
% 5.44/5.72 ( ( ( upto @ I2 @ J )
% 5.44/5.72 = nil_int )
% 5.44/5.72 = ( ord_less_int @ J @ I2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_Nil
% 5.44/5.72 thf(fact_10003_upto__single,axiom,
% 5.44/5.72 ! [I2: int] :
% 5.44/5.72 ( ( upto @ I2 @ I2 )
% 5.44/5.72 = ( cons_int @ I2 @ nil_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_single
% 5.44/5.72 thf(fact_10004_nth__upto,axiom,
% 5.44/5.72 ! [I2: int,K: nat,J: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.44/5.72 => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 5.44/5.72 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nth_upto
% 5.44/5.72 thf(fact_10005_length__upto,axiom,
% 5.44/5.72 ! [I2: int,J: int] :
% 5.44/5.72 ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 5.44/5.72 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % length_upto
% 5.44/5.72 thf(fact_10006_upto__rec__numeral_I1_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 = nil_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_rec_numeral(1)
% 5.44/5.72 thf(fact_10007_upto__rec__numeral_I4_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( 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 @ N2 ) ) ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = nil_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_rec_numeral(4)
% 5.44/5.72 thf(fact_10008_upto__rec__numeral_I3_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 = ( 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 @ N2 ) ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 = nil_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_rec_numeral(3)
% 5.44/5.72 thf(fact_10009_upto__rec__numeral_I2_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = nil_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_rec_numeral(2)
% 5.44/5.72 thf(fact_10010_greaterThanAtMost__upto,axiom,
% 5.44/5.72 ( set_or6656581121297822940st_int
% 5.44/5.72 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % greaterThanAtMost_upto
% 5.44/5.72 thf(fact_10011_atLeastLessThan__upto,axiom,
% 5.44/5.72 ( set_or4662586982721622107an_int
% 5.44/5.72 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeastLessThan_upto
% 5.44/5.72 thf(fact_10012_atLeastAtMost__upto,axiom,
% 5.44/5.72 ( set_or1266510415728281911st_int
% 5.44/5.72 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ J3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % atLeastAtMost_upto
% 5.44/5.72 thf(fact_10013_distinct__upto,axiom,
% 5.44/5.72 ! [I2: int,J: int] : ( distinct_int @ ( upto @ I2 @ J ) ) ).
% 5.44/5.72
% 5.44/5.72 % distinct_upto
% 5.44/5.72 thf(fact_10014_upto__code,axiom,
% 5.44/5.72 ( upto
% 5.44/5.72 = ( ^ [I5: int,J3: int] : ( upto_aux @ I5 @ J3 @ nil_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_code
% 5.44/5.72 thf(fact_10015_upto__aux__def,axiom,
% 5.44/5.72 ( upto_aux
% 5.44/5.72 = ( ^ [I5: int,J3: int] : ( append_int @ ( upto @ I5 @ J3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_aux_def
% 5.44/5.72 thf(fact_10016_upto__split2,axiom,
% 5.44/5.72 ! [I2: int,J: int,K: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.72 => ( ( ord_less_eq_int @ J @ K )
% 5.44/5.72 => ( ( upto @ I2 @ K )
% 5.44/5.72 = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_split2
% 5.44/5.72 thf(fact_10017_upto__split1,axiom,
% 5.44/5.72 ! [I2: int,J: int,K: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.72 => ( ( ord_less_eq_int @ J @ K )
% 5.44/5.72 => ( ( upto @ I2 @ K )
% 5.44/5.72 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_split1
% 5.44/5.72 thf(fact_10018_greaterThanLessThan__upto,axiom,
% 5.44/5.72 ( set_or5832277885323065728an_int
% 5.44/5.72 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % greaterThanLessThan_upto
% 5.44/5.72 thf(fact_10019_upto_Osimps,axiom,
% 5.44/5.72 ( upto
% 5.44/5.72 = ( ^ [I5: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I5 @ J3 ) @ ( cons_int @ I5 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto.simps
% 5.44/5.72 thf(fact_10020_upto_Oelims,axiom,
% 5.44/5.72 ! [X: int,Xa2: int,Y: list_int] :
% 5.44/5.72 ( ( ( upto @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.44/5.72 => ( Y = nil_int ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto.elims
% 5.44/5.72 thf(fact_10021_upto__rec1,axiom,
% 5.44/5.72 ! [I2: int,J: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.72 => ( ( upto @ I2 @ J )
% 5.44/5.72 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_rec1
% 5.44/5.72 thf(fact_10022_upto__rec2,axiom,
% 5.44/5.72 ! [I2: int,J: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.72 => ( ( upto @ I2 @ J )
% 5.44/5.72 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_rec2
% 5.44/5.72 thf(fact_10023_upto__split3,axiom,
% 5.44/5.72 ! [I2: int,J: int,K: int] :
% 5.44/5.72 ( ( ord_less_eq_int @ I2 @ J )
% 5.44/5.72 => ( ( ord_less_eq_int @ J @ K )
% 5.44/5.72 => ( ( upto @ I2 @ K )
% 5.44/5.72 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto_split3
% 5.44/5.72 thf(fact_10024_upto_Opelims,axiom,
% 5.44/5.72 ! [X: int,Xa2: int,Y: list_int] :
% 5.44/5.72 ( ( ( upto @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.44/5.72 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.44/5.72 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.44/5.72 => ( Y = nil_int ) ) )
% 5.44/5.72 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % upto.pelims
% 5.44/5.72 thf(fact_10025_GMVT,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 & ( ord_less_eq_real @ X5 @ B ) )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 & ( ord_less_real @ X5 @ B ) )
% 5.44/5.72 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.44/5.72 & ( ord_less_eq_real @ X5 @ B ) )
% 5.44/5.72 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ G ) )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 & ( ord_less_real @ X5 @ B ) )
% 5.44/5.72 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.44/5.72 => ? [G_c: real,F_c: real,C3: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.44/5.72 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_real @ A @ C3 )
% 5.44/5.72 & ( ord_less_real @ C3 @ B )
% 5.44/5.72 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.44/5.72 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % GMVT
% 5.44/5.72 thf(fact_10026_MVT,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_real @ X5 @ B )
% 5.44/5.72 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ? [L4: real,Z4: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ Z4 )
% 5.44/5.72 & ( ord_less_real @ Z4 @ B )
% 5.44/5.72 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) )
% 5.44/5.72 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.44/5.72 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % MVT
% 5.44/5.72 thf(fact_10027_continuous__on__arcosh,axiom,
% 5.44/5.72 ! [A2: set_real] :
% 5.44/5.72 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.44/5.72 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % continuous_on_arcosh
% 5.44/5.72 thf(fact_10028_continuous__on__arcosh_H,axiom,
% 5.44/5.72 ! [A2: set_real,F: real > real] :
% 5.44/5.72 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ A2 )
% 5.44/5.72 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.44/5.72 => ( topolo5044208981011980120l_real @ A2
% 5.44/5.72 @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % continuous_on_arcosh'
% 5.44/5.72 thf(fact_10029_continuous__image__closed__interval,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ? [C3: real,D3: real] :
% 5.44/5.72 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.44/5.72 = ( set_or1222579329274155063t_real @ C3 @ D3 ) )
% 5.44/5.72 & ( ord_less_eq_real @ C3 @ D3 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % continuous_image_closed_interval
% 5.44/5.72 thf(fact_10030_continuous__on__arccos_H,axiom,
% 5.44/5.72 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.44/5.72
% 5.44/5.72 % continuous_on_arccos'
% 5.44/5.72 thf(fact_10031_continuous__on__arcsin_H,axiom,
% 5.44/5.72 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.44/5.72
% 5.44/5.72 % continuous_on_arcsin'
% 5.44/5.72 thf(fact_10032_continuous__on__artanh,axiom,
% 5.44/5.72 ! [A2: set_real] :
% 5.44/5.72 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.44/5.72 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.44/5.72
% 5.44/5.72 % continuous_on_artanh
% 5.44/5.72 thf(fact_10033_continuous__on__artanh_H,axiom,
% 5.44/5.72 ! [A2: set_real,F: real > real] :
% 5.44/5.72 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( member_real @ X5 @ A2 )
% 5.44/5.72 => ( member_real @ ( F @ X5 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.44/5.72 => ( topolo5044208981011980120l_real @ A2
% 5.44/5.72 @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % continuous_on_artanh'
% 5.44/5.72 thf(fact_10034_Rolle__deriv,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real,F6: real > real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ( ( F @ A )
% 5.44/5.72 = ( F @ B ) )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_real @ X5 @ B )
% 5.44/5.72 => ( has_de1759254742604945161l_real @ F @ ( F6 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ? [Z4: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ Z4 )
% 5.44/5.72 & ( ord_less_real @ Z4 @ B )
% 5.44/5.72 & ( ( F6 @ Z4 )
% 5.44/5.72 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Rolle_deriv
% 5.44/5.72 thf(fact_10035_mvt,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real,F6: real > real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_real @ X5 @ B )
% 5.44/5.72 => ( has_de1759254742604945161l_real @ F @ ( F6 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ~ ! [Xi: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ Xi )
% 5.44/5.72 => ( ( ord_less_real @ Xi @ B )
% 5.44/5.72 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.44/5.72 != ( F6 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % mvt
% 5.44/5.72 thf(fact_10036_DERIV__pos__imp__increasing__open,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_real @ X5 @ B )
% 5.44/5.72 => ? [Y2: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_real @ zero_zero_real @ Y2 ) ) ) )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_pos_imp_increasing_open
% 5.44/5.72 thf(fact_10037_DERIV__neg__imp__decreasing__open,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_real @ X5 @ B )
% 5.44/5.72 => ? [Y2: real] :
% 5.44/5.72 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.72 & ( ord_less_real @ Y2 @ zero_zero_real ) ) ) )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_neg_imp_decreasing_open
% 5.44/5.72 thf(fact_10038_DERIV__isconst__end,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_real @ X5 @ B )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ( ( F @ B )
% 5.44/5.72 = ( F @ A ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_isconst_end
% 5.44/5.72 thf(fact_10039_DERIV__isconst2,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real,X: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_real @ X5 @ B )
% 5.44/5.72 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ( ( ord_less_eq_real @ A @ X )
% 5.44/5.72 => ( ( ord_less_eq_real @ X @ B )
% 5.44/5.72 => ( ( F @ X )
% 5.44/5.72 = ( F @ A ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % DERIV_isconst2
% 5.44/5.72 thf(fact_10040_Rolle,axiom,
% 5.44/5.72 ! [A: real,B: real,F: real > real] :
% 5.44/5.72 ( ( ord_less_real @ A @ B )
% 5.44/5.72 => ( ( ( F @ A )
% 5.44/5.72 = ( F @ B ) )
% 5.44/5.72 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.44/5.72 => ( ! [X5: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ X5 )
% 5.44/5.72 => ( ( ord_less_real @ X5 @ B )
% 5.44/5.72 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.44/5.72 => ? [Z4: real] :
% 5.44/5.72 ( ( ord_less_real @ A @ Z4 )
% 5.44/5.72 & ( ord_less_real @ Z4 @ B )
% 5.44/5.72 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Rolle
% 5.44/5.72 thf(fact_10041_take__bit__numeral__minus__numeral__int,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( case_option_int_num @ zero_zero_int
% 5.44/5.72 @ ^ [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 ) ) )
% 5.44/5.72 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_numeral_minus_numeral_int
% 5.44/5.72 thf(fact_10042_and__minus__numerals_I3_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.44/5.72 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_minus_numerals(3)
% 5.44/5.72 thf(fact_10043_take__bit__num__simps_I1_J,axiom,
% 5.44/5.72 ! [M: num] :
% 5.44/5.72 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.44/5.72 = none_num ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_num_simps(1)
% 5.44/5.72 thf(fact_10044_take__bit__num__simps_I2_J,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 5.44/5.72 = ( some_num @ one ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_num_simps(2)
% 5.44/5.72 thf(fact_10045_take__bit__num__simps_I5_J,axiom,
% 5.44/5.72 ! [R: num] :
% 5.44/5.72 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 5.44/5.72 = ( some_num @ one ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_num_simps(5)
% 5.44/5.72 thf(fact_10046_take__bit__num__simps_I3_J,axiom,
% 5.44/5.72 ! [N2: nat,M: num] :
% 5.44/5.72 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 5.44/5.72 = ( case_o6005452278849405969um_num @ none_num
% 5.44/5.72 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.44/5.72 @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_num_simps(3)
% 5.44/5.72 thf(fact_10047_take__bit__num__simps_I4_J,axiom,
% 5.44/5.72 ! [N2: nat,M: num] :
% 5.44/5.72 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 5.44/5.72 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_num_simps(4)
% 5.44/5.72 thf(fact_10048_take__bit__num__simps_I6_J,axiom,
% 5.44/5.72 ! [R: num,M: num] :
% 5.44/5.72 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 5.44/5.72 = ( case_o6005452278849405969um_num @ none_num
% 5.44/5.72 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.44/5.72 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_num_simps(6)
% 5.44/5.72 thf(fact_10049_take__bit__num__simps_I7_J,axiom,
% 5.44/5.72 ! [R: num,M: num] :
% 5.44/5.72 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 5.44/5.72 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_num_simps(7)
% 5.44/5.72 thf(fact_10050_and__minus__numerals_I8_J,axiom,
% 5.44/5.72 ! [N2: num,M: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.44/5.72 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_minus_numerals(8)
% 5.44/5.72 thf(fact_10051_and__minus__numerals_I4_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.44/5.72 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_minus_numerals(4)
% 5.44/5.72 thf(fact_10052_and__minus__numerals_I7_J,axiom,
% 5.44/5.72 ! [N2: num,M: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.44/5.72 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_minus_numerals(7)
% 5.44/5.72 thf(fact_10053_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.44/5.72 ! [N2: nat,M: num] :
% 5.44/5.72 ( ( bit_take_bit_num @ N2 @ ( bit0 @ M ) )
% 5.44/5.72 = ( case_nat_option_num @ none_num
% 5.44/5.72 @ ^ [N: nat] :
% 5.44/5.72 ( case_o6005452278849405969um_num @ none_num
% 5.44/5.72 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.44/5.72 @ ( bit_take_bit_num @ N @ M ) )
% 5.44/5.72 @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.44/5.72 thf(fact_10054_and__not__num_Osimps_I1_J,axiom,
% 5.44/5.72 ( ( bit_and_not_num @ one @ one )
% 5.44/5.72 = none_num ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(1)
% 5.44/5.72 thf(fact_10055_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( bit_take_bit_num @ N2 @ one )
% 5.44/5.72 = ( case_nat_option_num @ none_num
% 5.44/5.72 @ ^ [N: nat] : ( some_num @ one )
% 5.44/5.72 @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.44/5.72 thf(fact_10056_and__not__num_Osimps_I4_J,axiom,
% 5.44/5.72 ! [M: num] :
% 5.44/5.72 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.44/5.72 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(4)
% 5.44/5.72 thf(fact_10057_and__not__num_Osimps_I2_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( bit_and_not_num @ one @ ( bit0 @ N2 ) )
% 5.44/5.72 = ( some_num @ one ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(2)
% 5.44/5.72 thf(fact_10058_and__not__num_Osimps_I3_J,axiom,
% 5.44/5.72 ! [N2: num] :
% 5.44/5.72 ( ( bit_and_not_num @ one @ ( bit1 @ N2 ) )
% 5.44/5.72 = none_num ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(3)
% 5.44/5.72 thf(fact_10059_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.44/5.72 ! [N2: nat,M: num] :
% 5.44/5.72 ( ( bit_take_bit_num @ N2 @ ( bit1 @ M ) )
% 5.44/5.72 = ( case_nat_option_num @ none_num
% 5.44/5.72 @ ^ [N: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) )
% 5.44/5.72 @ N2 ) ) ).
% 5.44/5.72
% 5.44/5.72 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.44/5.72 thf(fact_10060_and__not__num_Osimps_I7_J,axiom,
% 5.44/5.72 ! [M: num] :
% 5.44/5.72 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.44/5.72 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(7)
% 5.44/5.72 thf(fact_10061_and__not__num__eq__Some__iff,axiom,
% 5.44/5.72 ! [M: num,N2: num,Q2: num] :
% 5.44/5.72 ( ( ( bit_and_not_num @ M @ N2 )
% 5.44/5.72 = ( some_num @ Q2 ) )
% 5.44/5.72 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num_eq_Some_iff
% 5.44/5.72 thf(fact_10062_and__not__num_Osimps_I8_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.72 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.44/5.72 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.44/5.72 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(8)
% 5.44/5.72 thf(fact_10063_and__not__num__eq__None__iff,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( ( bit_and_not_num @ M @ N2 )
% 5.44/5.72 = none_num )
% 5.44/5.72 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = zero_zero_int ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num_eq_None_iff
% 5.44/5.72 thf(fact_10064_int__numeral__not__and__num,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.44/5.72 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % int_numeral_not_and_num
% 5.44/5.72 thf(fact_10065_int__numeral__and__not__num,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.44/5.72 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % int_numeral_and_not_num
% 5.44/5.72 thf(fact_10066_take__bit__num__def,axiom,
% 5.44/5.72 ( bit_take_bit_num
% 5.44/5.72 = ( ^ [N: nat,M6: num] :
% 5.44/5.72 ( if_option_num
% 5.44/5.72 @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) )
% 5.44/5.72 = zero_zero_nat )
% 5.44/5.72 @ none_num
% 5.44/5.72 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % take_bit_num_def
% 5.44/5.72 thf(fact_10067_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.44/5.72 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.44/5.72 ( X
% 5.44/5.72 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( Xa2 != one_one_nat ) ) )
% 5.44/5.72 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 = ( ~ ( ( Deg2 = Xa2 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 & ( case_o184042715313410164at_nat
% 5.44/5.72 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 @ ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [Mi3: nat,Ma3: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 & ! [I5: nat] :
% 5.44/5.72 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.44/5.72 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.44/5.72 & ( ( Mi3 = Ma3 )
% 5.44/5.72 => ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 & ( ( Mi3 != Ma3 )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.44/5.72 & ! [X2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.44/5.72 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.72 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.44/5.72 @ Mima ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.valid'.elims(1)
% 5.44/5.72 thf(fact_10068_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.72 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.44/5.72 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.44/5.72 ( X
% 5.44/5.72 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.72 => ( Xa2 != one_one_nat ) )
% 5.44/5.72 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.72 => ~ ( ( Deg2 = Xa2 )
% 5.44/5.72 & ! [X3: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 & ( case_o184042715313410164at_nat
% 5.44/5.72 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 @ ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [Mi3: nat,Ma3: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 & ! [I5: nat] :
% 5.44/5.72 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.44/5.72 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.44/5.72 & ( ( Mi3 = Ma3 )
% 5.44/5.72 => ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 & ( ( Mi3 != Ma3 )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.44/5.72 & ! [X2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.44/5.72 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.72 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.44/5.72 @ Mima ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.valid'.elims(2)
% 5.44/5.72 thf(fact_10069_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.44/5.72 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.44/5.72 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 5.44/5.72 = ( ( Deg = Deg4 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.72 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 & ( case_o184042715313410164at_nat
% 5.44/5.72 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X4 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 @ ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [Mi3: nat,Ma3: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.44/5.72 & ! [I5: nat] :
% 5.44/5.72 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.44/5.72 = ( vEBT_V8194947554948674370ptions @ Summary @ I5 ) ) )
% 5.44/5.72 & ( ( Mi3 = Ma3 )
% 5.44/5.72 => ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 & ( ( Mi3 != Ma3 )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.44/5.72 & ! [X2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.44/5.72 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.72 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.44/5.72 @ Mima2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.valid'.simps(2)
% 5.44/5.72 thf(fact_10070_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.72 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.44/5.72 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.44/5.72 ( X
% 5.44/5.72 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.72 => ( Xa2 = one_one_nat ) )
% 5.44/5.72 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.72 => ( ( Deg2 = Xa2 )
% 5.44/5.72 & ! [X5: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 & ( case_o184042715313410164at_nat
% 5.44/5.72 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 @ ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [Mi3: nat,Ma3: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 & ! [I5: nat] :
% 5.44/5.72 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.44/5.72 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.44/5.72 & ( ( Mi3 = Ma3 )
% 5.44/5.72 => ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 & ( ( Mi3 != Ma3 )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.44/5.72 & ! [X2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.44/5.72 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.72 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.44/5.72 @ Mima ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.valid'.elims(3)
% 5.44/5.72 thf(fact_10071_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.72 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.44/5.72 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.72 => ( ! [Uu2: $o,Uv2: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.72 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.44/5.72 => ( Xa2 = one_one_nat ) ) )
% 5.44/5.72 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.72 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.44/5.72 => ( ( Deg2 = Xa2 )
% 5.44/5.72 & ! [X5: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 & ( case_o184042715313410164at_nat
% 5.44/5.72 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 @ ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [Mi3: nat,Ma3: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 & ! [I5: nat] :
% 5.44/5.72 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.44/5.72 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.44/5.72 & ( ( Mi3 = Ma3 )
% 5.44/5.72 => ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 & ( ( Mi3 != Ma3 )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.44/5.72 & ! [X2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.44/5.72 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.72 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.44/5.72 @ Mima ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.valid'.pelims(3)
% 5.44/5.72 thf(fact_10072_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.44/5.72 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.44/5.72 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.72 => ( ! [Uu2: $o,Uv2: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.72 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.44/5.72 => ( Xa2 != one_one_nat ) ) )
% 5.44/5.72 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.72 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.44/5.72 => ~ ( ( Deg2 = Xa2 )
% 5.44/5.72 & ! [X3: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 & ( case_o184042715313410164at_nat
% 5.44/5.72 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 @ ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [Mi3: nat,Ma3: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 & ! [I5: nat] :
% 5.44/5.72 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.44/5.72 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.44/5.72 & ( ( Mi3 = Ma3 )
% 5.44/5.72 => ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 & ( ( Mi3 != Ma3 )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.44/5.72 & ! [X2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.44/5.72 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.72 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.44/5.72 @ Mima ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.valid'.pelims(2)
% 5.44/5.72 thf(fact_10073_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.44/5.72 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.44/5.72 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.44/5.72 => ( ! [Uu2: $o,Uv2: $o] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.44/5.72 => ( ( Y
% 5.44/5.72 = ( Xa2 = one_one_nat ) )
% 5.44/5.72 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.44/5.72 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.44/5.72 => ( ( Y
% 5.44/5.72 = ( ( Deg2 = Xa2 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.44/5.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.44/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 & ( case_o184042715313410164at_nat
% 5.44/5.72 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.44/5.72 & ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 @ ( produc6081775807080527818_nat_o
% 5.44/5.72 @ ^ [Mi3: nat,Ma3: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.44/5.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 & ! [I5: nat] :
% 5.44/5.72 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.44/5.72 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.44/5.72 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.44/5.72 & ( ( Mi3 = Ma3 )
% 5.44/5.72 => ! [X2: vEBT_VEBT] :
% 5.44/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.44/5.72 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.44/5.72 & ( ( Mi3 != Ma3 )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.44/5.72 & ! [X2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.44/5.72 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.44/5.72 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.44/5.72 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.44/5.72 @ Mima ) ) )
% 5.44/5.72 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % VEBT_internal.valid'.pelims(1)
% 5.44/5.72 thf(fact_10074_Bit__Operations_Otake__bit__num__code,axiom,
% 5.44/5.72 ( bit_take_bit_num
% 5.44/5.72 = ( ^ [N: nat,M6: num] :
% 5.44/5.72 ( produc478579273971653890on_num
% 5.44/5.72 @ ^ [A4: nat,X2: num] :
% 5.44/5.72 ( case_nat_option_num @ none_num
% 5.44/5.72 @ ^ [O: nat] :
% 5.44/5.72 ( case_num_option_num @ ( some_num @ one )
% 5.44/5.72 @ ^ [P4: num] :
% 5.44/5.72 ( case_o6005452278849405969um_num @ none_num
% 5.44/5.72 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.44/5.72 @ ( bit_take_bit_num @ O @ P4 ) )
% 5.44/5.72 @ ^ [P4: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P4 ) ) )
% 5.44/5.72 @ X2 )
% 5.44/5.72 @ A4 )
% 5.44/5.72 @ ( product_Pair_nat_num @ N @ M6 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % Bit_Operations.take_bit_num_code
% 5.44/5.72 thf(fact_10075_mono__Suc,axiom,
% 5.44/5.72 order_mono_nat_nat @ suc ).
% 5.44/5.72
% 5.44/5.72 % mono_Suc
% 5.44/5.72 thf(fact_10076_mono__times__nat,axiom,
% 5.44/5.72 ! [N2: nat] :
% 5.44/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.72 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % mono_times_nat
% 5.44/5.72 thf(fact_10077_incseq__bounded,axiom,
% 5.44/5.72 ! [X8: nat > real,B2: real] :
% 5.44/5.72 ( ( order_mono_nat_real @ X8 )
% 5.44/5.72 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B2 )
% 5.44/5.72 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % incseq_bounded
% 5.44/5.72 thf(fact_10078_incseq__convergent,axiom,
% 5.44/5.72 ! [X8: nat > real,B2: real] :
% 5.44/5.72 ( ( order_mono_nat_real @ X8 )
% 5.44/5.72 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B2 )
% 5.44/5.72 => ~ ! [L6: real] :
% 5.44/5.72 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.44/5.72 => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L6 ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % incseq_convergent
% 5.44/5.72 thf(fact_10079_mono__ge2__power__minus__self,axiom,
% 5.44/5.72 ! [K: nat] :
% 5.44/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.44/5.72 => ( order_mono_nat_nat
% 5.44/5.72 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % mono_ge2_power_minus_self
% 5.44/5.72 thf(fact_10080_and__not__num_Oelims,axiom,
% 5.44/5.72 ! [X: num,Xa2: num,Y: option_num] :
% 5.44/5.72 ( ( ( bit_and_not_num @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y != none_num ) ) )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ( ? [N4: num] :
% 5.44/5.72 ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ one ) ) ) )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ( ? [N4: num] :
% 5.44/5.72 ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y != none_num ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.44/5.72 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.44/5.72 @ ( bit_and_not_num @ M5 @ N4 ) ) ) ) )
% 5.44/5.72 => ~ ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.elims
% 5.44/5.72 thf(fact_10081_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.44/5.72 ! [F: nat > real,G: nat > nat] :
% 5.44/5.72 ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.44/5.72 => ( ( order_mono_nat_real @ F )
% 5.44/5.72 => ( ( order_5726023648592871131at_nat @ G )
% 5.44/5.72 => ( ( bfun_nat_real
% 5.44/5.72 @ ^ [X2: nat] : ( F @ ( G @ X2 ) )
% 5.44/5.72 @ at_top_nat )
% 5.44/5.72 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % nonneg_incseq_Bseq_subseq_iff
% 5.44/5.72 thf(fact_10082_and__not__num_Osimps_I5_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.72 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(5)
% 5.44/5.72 thf(fact_10083_strict__mono__imp__increasing,axiom,
% 5.44/5.72 ! [F: nat > nat,N2: nat] :
% 5.44/5.72 ( ( order_5726023648592871131at_nat @ F )
% 5.44/5.72 => ( ord_less_eq_nat @ N2 @ ( F @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % strict_mono_imp_increasing
% 5.44/5.72 thf(fact_10084_and__not__num_Osimps_I6_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.72 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(6)
% 5.44/5.72 thf(fact_10085_and__not__num_Osimps_I9_J,axiom,
% 5.44/5.72 ! [M: num,N2: num] :
% 5.44/5.72 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.72 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_not_num.simps(9)
% 5.44/5.72 thf(fact_10086_and__num_Oelims,axiom,
% 5.44/5.72 ! [X: num,Xa2: num,Y: option_num] :
% 5.44/5.72 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ one ) ) ) )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ( ? [N4: num] :
% 5.44/5.72 ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y != none_num ) ) )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ( ? [N4: num] :
% 5.44/5.72 ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ one ) ) ) )
% 5.44/5.72 => ( ( ? [M5: num] :
% 5.44/5.72 ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y != none_num ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) ) ) )
% 5.44/5.72 => ( ( ? [M5: num] :
% 5.44/5.72 ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ one ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) ) ) )
% 5.44/5.72 => ~ ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.44/5.72 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.44/5.72 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_num.elims
% 5.44/5.72 thf(fact_10087_xor__num_Oelims,axiom,
% 5.44/5.72 ! [X: num,Xa2: num,Y: option_num] :
% 5.44/5.72 ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 5.44/5.72 = Y )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y != none_num ) ) )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ ( bit1 @ N4 ) ) ) ) )
% 5.44/5.72 => ( ( ( X = one )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ ( bit0 @ N4 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit0 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ( ( Xa2 = one )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.44/5.72 => ( ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit0 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) ) ) )
% 5.44/5.72 => ~ ! [M5: num] :
% 5.44/5.72 ( ( X
% 5.44/5.72 = ( bit1 @ M5 ) )
% 5.44/5.72 => ! [N4: num] :
% 5.44/5.72 ( ( Xa2
% 5.44/5.72 = ( bit1 @ N4 ) )
% 5.44/5.72 => ( Y
% 5.44/5.72 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.72
% 5.44/5.72 % xor_num.elims
% 5.44/5.72 thf(fact_10088_and__num_Osimps_I1_J,axiom,
% 5.44/5.72 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.44/5.72 = ( some_num @ one ) ) ).
% 5.44/5.72
% 5.44/5.72 % and_num.simps(1)
% 5.44/5.72 thf(fact_10089_xor__num_Osimps_I1_J,axiom,
% 5.44/5.72 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.44/5.72 = none_num ) ).
% 5.44/5.72
% 5.44/5.72 % xor_num.simps(1)
% 5.44/5.72 thf(fact_10090_xor__num_Osimps_I5_J,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.73 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % xor_num.simps(5)
% 5.44/5.73 thf(fact_10091_and__num_Osimps_I5_J,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.73 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % and_num.simps(5)
% 5.44/5.73 thf(fact_10092_and__num_Osimps_I3_J,axiom,
% 5.44/5.73 ! [N2: num] :
% 5.44/5.73 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N2 ) )
% 5.44/5.73 = ( some_num @ one ) ) ).
% 5.44/5.73
% 5.44/5.73 % and_num.simps(3)
% 5.44/5.73 thf(fact_10093_and__num_Osimps_I7_J,axiom,
% 5.44/5.73 ! [M: num] :
% 5.44/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.44/5.73 = ( some_num @ one ) ) ).
% 5.44/5.73
% 5.44/5.73 % and_num.simps(7)
% 5.44/5.73 thf(fact_10094_and__num_Osimps_I2_J,axiom,
% 5.44/5.73 ! [N2: num] :
% 5.44/5.73 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N2 ) )
% 5.44/5.73 = none_num ) ).
% 5.44/5.73
% 5.44/5.73 % and_num.simps(2)
% 5.44/5.73 thf(fact_10095_and__num_Osimps_I4_J,axiom,
% 5.44/5.73 ! [M: num] :
% 5.44/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.44/5.73 = none_num ) ).
% 5.44/5.73
% 5.44/5.73 % and_num.simps(4)
% 5.44/5.73 thf(fact_10096_and__num_Osimps_I8_J,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.73 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % and_num.simps(8)
% 5.44/5.73 thf(fact_10097_and__num_Osimps_I6_J,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.73 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % and_num.simps(6)
% 5.44/5.73 thf(fact_10098_xor__num_Osimps_I9_J,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.73 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % xor_num.simps(9)
% 5.44/5.73 thf(fact_10099_xor__num_Osimps_I2_J,axiom,
% 5.44/5.73 ! [N2: num] :
% 5.44/5.73 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N2 ) )
% 5.44/5.73 = ( some_num @ ( bit1 @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % xor_num.simps(2)
% 5.44/5.73 thf(fact_10100_xor__num_Osimps_I3_J,axiom,
% 5.44/5.73 ! [N2: num] :
% 5.44/5.73 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N2 ) )
% 5.44/5.73 = ( some_num @ ( bit0 @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % xor_num.simps(3)
% 5.44/5.73 thf(fact_10101_xor__num_Osimps_I4_J,axiom,
% 5.44/5.73 ! [M: num] :
% 5.44/5.73 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.44/5.73 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % xor_num.simps(4)
% 5.44/5.73 thf(fact_10102_xor__num_Osimps_I7_J,axiom,
% 5.44/5.73 ! [M: num] :
% 5.44/5.73 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.44/5.73 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % xor_num.simps(7)
% 5.44/5.73 thf(fact_10103_and__num_Osimps_I9_J,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.73 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.44/5.73 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.44/5.73 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % and_num.simps(9)
% 5.44/5.73 thf(fact_10104_pos__deriv__imp__strict__mono,axiom,
% 5.44/5.73 ! [F: real > real,F6: real > real] :
% 5.44/5.73 ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.44/5.73 => ( ! [X5: real] : ( ord_less_real @ zero_zero_real @ ( F6 @ X5 ) )
% 5.44/5.73 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % pos_deriv_imp_strict_mono
% 5.44/5.73 thf(fact_10105_xor__num_Osimps_I6_J,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.44/5.73 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % xor_num.simps(6)
% 5.44/5.73 thf(fact_10106_xor__num_Osimps_I8_J,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.44/5.73 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % xor_num.simps(8)
% 5.44/5.73 thf(fact_10107_xor__num__dict,axiom,
% 5.44/5.73 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.44/5.73
% 5.44/5.73 % xor_num_dict
% 5.44/5.73 thf(fact_10108_and__num__dict,axiom,
% 5.44/5.73 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.44/5.73
% 5.44/5.73 % and_num_dict
% 5.44/5.73 thf(fact_10109_inj__sgn__power,axiom,
% 5.44/5.73 ! [N2: nat] :
% 5.44/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.44/5.73 => ( inj_on_real_real
% 5.44/5.73 @ ^ [Y3: real] : ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N2 ) )
% 5.44/5.73 @ top_top_set_real ) ) ).
% 5.44/5.73
% 5.44/5.73 % inj_sgn_power
% 5.44/5.73 thf(fact_10110_log__inj,axiom,
% 5.44/5.73 ! [B: real] :
% 5.44/5.73 ( ( ord_less_real @ one_one_real @ B )
% 5.44/5.73 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % log_inj
% 5.44/5.73 thf(fact_10111_inj__Suc,axiom,
% 5.44/5.73 ! [N3: set_nat] : ( inj_on_nat_nat @ suc @ N3 ) ).
% 5.44/5.73
% 5.44/5.73 % inj_Suc
% 5.44/5.73 thf(fact_10112_inj__on__diff__nat,axiom,
% 5.44/5.73 ! [N3: set_nat,K: nat] :
% 5.44/5.73 ( ! [N4: nat] :
% 5.44/5.73 ( ( member_nat @ N4 @ N3 )
% 5.44/5.73 => ( ord_less_eq_nat @ K @ N4 ) )
% 5.44/5.73 => ( inj_on_nat_nat
% 5.44/5.73 @ ^ [N: nat] : ( minus_minus_nat @ N @ K )
% 5.44/5.73 @ N3 ) ) ).
% 5.44/5.73
% 5.44/5.73 % inj_on_diff_nat
% 5.44/5.73 thf(fact_10113_inj__on__char__of__nat,axiom,
% 5.44/5.73 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % inj_on_char_of_nat
% 5.44/5.73 thf(fact_10114_sup__int__def,axiom,
% 5.44/5.73 sup_sup_int = ord_max_int ).
% 5.44/5.73
% 5.44/5.73 % sup_int_def
% 5.44/5.73 thf(fact_10115_card_Ocomp__fun__commute__on,axiom,
% 5.44/5.73 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.44/5.73 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.44/5.73
% 5.44/5.73 % card.comp_fun_commute_on
% 5.44/5.73 thf(fact_10116_sup__nat__def,axiom,
% 5.44/5.73 sup_sup_nat = ord_max_nat ).
% 5.44/5.73
% 5.44/5.73 % sup_nat_def
% 5.44/5.73 thf(fact_10117_sup__enat__def,axiom,
% 5.44/5.73 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.44/5.73
% 5.44/5.73 % sup_enat_def
% 5.44/5.73 thf(fact_10118_atLeastLessThan__add__Un,axiom,
% 5.44/5.73 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.73 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.44/5.73 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % atLeastLessThan_add_Un
% 5.44/5.73 thf(fact_10119_summable__reindex,axiom,
% 5.44/5.73 ! [F: nat > real,G: nat > nat] :
% 5.44/5.73 ( ( summable_real @ F )
% 5.44/5.73 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.44/5.73 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.44/5.73 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % summable_reindex
% 5.44/5.73 thf(fact_10120_suminf__reindex__mono,axiom,
% 5.44/5.73 ! [F: nat > real,G: nat > nat] :
% 5.44/5.73 ( ( summable_real @ F )
% 5.44/5.73 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.44/5.73 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.44/5.73 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % suminf_reindex_mono
% 5.44/5.73 thf(fact_10121_suminf__reindex,axiom,
% 5.44/5.73 ! [F: nat > real,G: nat > nat] :
% 5.44/5.73 ( ( summable_real @ F )
% 5.44/5.73 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.44/5.73 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.44/5.73 => ( ! [X5: nat] :
% 5.44/5.73 ( ~ ( member_nat @ X5 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 5.44/5.73 => ( ( F @ X5 )
% 5.44/5.73 = zero_zero_real ) )
% 5.44/5.73 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 5.44/5.73 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % suminf_reindex
% 5.44/5.73 thf(fact_10122_remdups__upt,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( remdups_nat @ ( upt @ M @ N2 ) )
% 5.44/5.73 = ( upt @ M @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % remdups_upt
% 5.44/5.73 thf(fact_10123_length__upt,axiom,
% 5.44/5.73 ! [I2: nat,J: nat] :
% 5.44/5.73 ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 5.44/5.73 = ( minus_minus_nat @ J @ I2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % length_upt
% 5.44/5.73 thf(fact_10124_upt__conv__Nil,axiom,
% 5.44/5.73 ! [J: nat,I2: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ J @ I2 )
% 5.44/5.73 => ( ( upt @ I2 @ J )
% 5.44/5.73 = nil_nat ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_conv_Nil
% 5.44/5.73 thf(fact_10125_sorted__list__of__set__range,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.44/5.73 = ( upt @ M @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % sorted_list_of_set_range
% 5.44/5.73 thf(fact_10126_upt__eq__Nil__conv,axiom,
% 5.44/5.73 ! [I2: nat,J: nat] :
% 5.44/5.73 ( ( ( upt @ I2 @ J )
% 5.44/5.73 = nil_nat )
% 5.44/5.73 = ( ( J = zero_zero_nat )
% 5.44/5.73 | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_eq_Nil_conv
% 5.44/5.73 thf(fact_10127_nth__upt,axiom,
% 5.44/5.73 ! [I2: nat,K: nat,J: nat] :
% 5.44/5.73 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 5.44/5.73 => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 5.44/5.73 = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % nth_upt
% 5.44/5.73 thf(fact_10128_upt__rec__numeral,axiom,
% 5.44/5.73 ! [M: num,N2: num] :
% 5.44/5.73 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.73 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.73 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 5.44/5.73 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.73 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.44/5.73 = nil_nat ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_rec_numeral
% 5.44/5.73 thf(fact_10129_upt__0,axiom,
% 5.44/5.73 ! [I2: nat] :
% 5.44/5.73 ( ( upt @ I2 @ zero_zero_nat )
% 5.44/5.73 = nil_nat ) ).
% 5.44/5.73
% 5.44/5.73 % upt_0
% 5.44/5.73 thf(fact_10130_greaterThanLessThan__upt,axiom,
% 5.44/5.73 ( set_or5834768355832116004an_nat
% 5.44/5.73 = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ M6 ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % greaterThanLessThan_upt
% 5.44/5.73 thf(fact_10131_atLeast__upt,axiom,
% 5.44/5.73 ( set_ord_lessThan_nat
% 5.44/5.73 = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % atLeast_upt
% 5.44/5.73 thf(fact_10132_atLeastLessThan__upt,axiom,
% 5.44/5.73 ( set_or4665077453230672383an_nat
% 5.44/5.73 = ( ^ [I5: nat,J3: nat] : ( set_nat2 @ ( upt @ I5 @ J3 ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % atLeastLessThan_upt
% 5.44/5.73 thf(fact_10133_atLeastAtMost__upt,axiom,
% 5.44/5.73 ( set_or1269000886237332187st_nat
% 5.44/5.73 = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ N @ ( suc @ M6 ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % atLeastAtMost_upt
% 5.44/5.73 thf(fact_10134_greaterThanAtMost__upt,axiom,
% 5.44/5.73 ( set_or6659071591806873216st_nat
% 5.44/5.73 = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ ( suc @ M6 ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % greaterThanAtMost_upt
% 5.44/5.73 thf(fact_10135_upt__conv__Cons__Cons,axiom,
% 5.44/5.73 ! [M: nat,N2: nat,Ns: list_nat,Q2: nat] :
% 5.44/5.73 ( ( ( cons_nat @ M @ ( cons_nat @ N2 @ Ns ) )
% 5.44/5.73 = ( upt @ M @ Q2 ) )
% 5.44/5.73 = ( ( cons_nat @ N2 @ Ns )
% 5.44/5.73 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_conv_Cons_Cons
% 5.44/5.73 thf(fact_10136_distinct__upt,axiom,
% 5.44/5.73 ! [I2: nat,J: nat] : ( distinct_nat @ ( upt @ I2 @ J ) ) ).
% 5.44/5.73
% 5.44/5.73 % distinct_upt
% 5.44/5.73 thf(fact_10137_map__add__upt,axiom,
% 5.44/5.73 ! [N2: nat,M: nat] :
% 5.44/5.73 ( ( map_nat_nat
% 5.44/5.73 @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ N2 )
% 5.44/5.73 @ ( upt @ zero_zero_nat @ M ) )
% 5.44/5.73 = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % map_add_upt
% 5.44/5.73 thf(fact_10138_map__Suc__upt,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( map_nat_nat @ suc @ ( upt @ M @ N2 ) )
% 5.44/5.73 = ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % map_Suc_upt
% 5.44/5.73 thf(fact_10139_atMost__upto,axiom,
% 5.44/5.73 ( set_ord_atMost_nat
% 5.44/5.73 = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % atMost_upto
% 5.44/5.73 thf(fact_10140_upt__conv__Cons,axiom,
% 5.44/5.73 ! [I2: nat,J: nat] :
% 5.44/5.73 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.73 => ( ( upt @ I2 @ J )
% 5.44/5.73 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_conv_Cons
% 5.44/5.73 thf(fact_10141_map__decr__upt,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( map_nat_nat
% 5.44/5.73 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.44/5.73 @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.44/5.73 = ( upt @ M @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % map_decr_upt
% 5.44/5.73 thf(fact_10142_upt__add__eq__append,axiom,
% 5.44/5.73 ! [I2: nat,J: nat,K: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.73 => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.44/5.73 = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_add_eq_append
% 5.44/5.73 thf(fact_10143_upt__eq__Cons__conv,axiom,
% 5.44/5.73 ! [I2: nat,J: nat,X: nat,Xs2: list_nat] :
% 5.44/5.73 ( ( ( upt @ I2 @ J )
% 5.44/5.73 = ( cons_nat @ X @ Xs2 ) )
% 5.44/5.73 = ( ( ord_less_nat @ I2 @ J )
% 5.44/5.73 & ( I2 = X )
% 5.44/5.73 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 5.44/5.73 = Xs2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_eq_Cons_conv
% 5.44/5.73 thf(fact_10144_upt__rec,axiom,
% 5.44/5.73 ( upt
% 5.44/5.73 = ( ^ [I5: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I5 @ J3 ) @ ( cons_nat @ I5 @ ( upt @ ( suc @ I5 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_rec
% 5.44/5.73 thf(fact_10145_upt__Suc,axiom,
% 5.44/5.73 ! [I2: nat,J: nat] :
% 5.44/5.73 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.73 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.44/5.73 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.44/5.73 & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.73 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.44/5.73 = nil_nat ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_Suc
% 5.44/5.73 thf(fact_10146_upt__Suc__append,axiom,
% 5.44/5.73 ! [I2: nat,J: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.44/5.73 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.44/5.73 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % upt_Suc_append
% 5.44/5.73 thf(fact_10147_sum__list__upt,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.44/5.73 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 5.44/5.73 = ( groups3542108847815614940at_nat
% 5.44/5.73 @ ^ [X2: nat] : X2
% 5.44/5.73 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % sum_list_upt
% 5.44/5.73 thf(fact_10148_card__length__sum__list__rec,axiom,
% 5.44/5.73 ! [M: nat,N3: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.44/5.73 => ( ( finite_card_list_nat
% 5.44/5.73 @ ( collect_list_nat
% 5.44/5.73 @ ^ [L: list_nat] :
% 5.44/5.73 ( ( ( size_size_list_nat @ L )
% 5.44/5.73 = M )
% 5.44/5.73 & ( ( groups4561878855575611511st_nat @ L )
% 5.44/5.73 = N3 ) ) ) )
% 5.44/5.73 = ( plus_plus_nat
% 5.44/5.73 @ ( finite_card_list_nat
% 5.44/5.73 @ ( collect_list_nat
% 5.44/5.73 @ ^ [L: list_nat] :
% 5.44/5.73 ( ( ( size_size_list_nat @ L )
% 5.44/5.73 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.44/5.73 & ( ( groups4561878855575611511st_nat @ L )
% 5.44/5.73 = N3 ) ) ) )
% 5.44/5.73 @ ( finite_card_list_nat
% 5.44/5.73 @ ( collect_list_nat
% 5.44/5.73 @ ^ [L: list_nat] :
% 5.44/5.73 ( ( ( size_size_list_nat @ L )
% 5.44/5.73 = M )
% 5.44/5.73 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 5.44/5.73 = N3 ) ) ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % card_length_sum_list_rec
% 5.44/5.73 thf(fact_10149_card__length__sum__list,axiom,
% 5.44/5.73 ! [M: nat,N3: nat] :
% 5.44/5.73 ( ( finite_card_list_nat
% 5.44/5.73 @ ( collect_list_nat
% 5.44/5.73 @ ^ [L: list_nat] :
% 5.44/5.73 ( ( ( size_size_list_nat @ L )
% 5.44/5.73 = M )
% 5.44/5.73 & ( ( groups4561878855575611511st_nat @ L )
% 5.44/5.73 = N3 ) ) ) )
% 5.44/5.73 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N3 @ M ) @ one_one_nat ) @ N3 ) ) ).
% 5.44/5.73
% 5.44/5.73 % card_length_sum_list
% 5.44/5.73 thf(fact_10150_sorted__upt,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % sorted_upt
% 5.44/5.73 thf(fact_10151_sorted__wrt__upt,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % sorted_wrt_upt
% 5.44/5.73 thf(fact_10152_sorted__wrt__less__idx,axiom,
% 5.44/5.73 ! [Ns: list_nat,I2: nat] :
% 5.44/5.73 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.44/5.73 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 5.44/5.73 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % sorted_wrt_less_idx
% 5.44/5.73 thf(fact_10153_sorted__wrt__upto,axiom,
% 5.44/5.73 ! [I2: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J ) ) ).
% 5.44/5.73
% 5.44/5.73 % sorted_wrt_upto
% 5.44/5.73 thf(fact_10154_sorted__upto,axiom,
% 5.44/5.73 ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % sorted_upto
% 5.44/5.73 thf(fact_10155_tl__upt,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( tl_nat @ ( upt @ M @ N2 ) )
% 5.44/5.73 = ( upt @ ( suc @ M ) @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % tl_upt
% 5.44/5.73 thf(fact_10156_hd__upt,axiom,
% 5.44/5.73 ! [I2: nat,J: nat] :
% 5.44/5.73 ( ( ord_less_nat @ I2 @ J )
% 5.44/5.73 => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 5.44/5.73 = I2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % hd_upt
% 5.44/5.73 thf(fact_10157_powr__real__of__int_H,axiom,
% 5.44/5.73 ! [X: real,N2: int] :
% 5.44/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.44/5.73 => ( ( ( X != zero_zero_real )
% 5.44/5.73 | ( ord_less_int @ zero_zero_int @ N2 ) )
% 5.44/5.73 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N2 ) )
% 5.44/5.73 = ( power_int_real @ X @ N2 ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % powr_real_of_int'
% 5.44/5.73 thf(fact_10158_uniformity__real__def,axiom,
% 5.44/5.73 ( topolo1511823702728130853y_real
% 5.44/5.73 = ( comple2936214249959783750l_real
% 5.44/5.73 @ ( image_2178119161166701260l_real
% 5.44/5.73 @ ^ [E3: real] :
% 5.44/5.73 ( princi6114159922880469582l_real
% 5.44/5.73 @ ( collec3799799289383736868l_real
% 5.44/5.73 @ ( produc5414030515140494994real_o
% 5.44/5.73 @ ^ [X2: real,Y3: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X2 @ Y3 ) @ E3 ) ) ) )
% 5.44/5.73 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % uniformity_real_def
% 5.44/5.73 thf(fact_10159_uniformity__complex__def,axiom,
% 5.44/5.73 ( topolo896644834953643431omplex
% 5.44/5.73 = ( comple8358262395181532106omplex
% 5.44/5.73 @ ( image_5971271580939081552omplex
% 5.44/5.73 @ ^ [E3: real] :
% 5.44/5.73 ( princi3496590319149328850omplex
% 5.44/5.73 @ ( collec8663557070575231912omplex
% 5.44/5.73 @ ( produc6771430404735790350plex_o
% 5.44/5.73 @ ^ [X2: complex,Y3: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X2 @ Y3 ) @ E3 ) ) ) )
% 5.44/5.73 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % uniformity_complex_def
% 5.44/5.73 thf(fact_10160_pairs__le__eq__Sigma,axiom,
% 5.44/5.73 ! [M: nat] :
% 5.44/5.73 ( ( collec3392354462482085612at_nat
% 5.44/5.73 @ ( produc6081775807080527818_nat_o
% 5.44/5.73 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ M ) ) )
% 5.44/5.73 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.44/5.73 @ ^ [R4: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R4 ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % pairs_le_eq_Sigma
% 5.44/5.73 thf(fact_10161_eventually__prod__sequentially,axiom,
% 5.44/5.73 ! [P: product_prod_nat_nat > $o] :
% 5.44/5.73 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.44/5.73 = ( ? [N6: nat] :
% 5.44/5.73 ! [M6: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ N6 @ M6 )
% 5.44/5.73 => ! [N: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ N6 @ N )
% 5.44/5.73 => ( P @ ( product_Pair_nat_nat @ N @ M6 ) ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % eventually_prod_sequentially
% 5.44/5.73 thf(fact_10162_pred__nat__def,axiom,
% 5.44/5.73 ( pred_nat
% 5.44/5.73 = ( collec3392354462482085612at_nat
% 5.44/5.73 @ ( produc6081775807080527818_nat_o
% 5.44/5.73 @ ^ [M6: nat,N: nat] :
% 5.44/5.73 ( N
% 5.44/5.73 = ( suc @ M6 ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % pred_nat_def
% 5.44/5.73 thf(fact_10163_at__right__to__0,axiom,
% 5.44/5.73 ! [A: real] :
% 5.44/5.73 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.44/5.73 = ( filtermap_real_real
% 5.44/5.73 @ ^ [X2: real] : ( plus_plus_real @ X2 @ A )
% 5.44/5.73 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % at_right_to_0
% 5.44/5.73 thf(fact_10164_less__eq,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.44/5.73 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % less_eq
% 5.44/5.73 thf(fact_10165_pred__nat__trancl__eq__le,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.44/5.73 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % pred_nat_trancl_eq_le
% 5.44/5.73 thf(fact_10166_min__Suc__Suc,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.44/5.73 = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % min_Suc_Suc
% 5.44/5.73 thf(fact_10167_min__0L,axiom,
% 5.44/5.73 ! [N2: nat] :
% 5.44/5.73 ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 5.44/5.73 = zero_zero_nat ) ).
% 5.44/5.73
% 5.44/5.73 % min_0L
% 5.44/5.73 thf(fact_10168_min__0R,axiom,
% 5.44/5.73 ! [N2: nat] :
% 5.44/5.73 ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 5.44/5.73 = zero_zero_nat ) ).
% 5.44/5.73
% 5.44/5.73 % min_0R
% 5.44/5.73 thf(fact_10169_min__Suc__numeral,axiom,
% 5.44/5.73 ! [N2: nat,K: num] :
% 5.44/5.73 ( ( ord_min_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.44/5.73 = ( suc @ ( ord_min_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % min_Suc_numeral
% 5.44/5.73 thf(fact_10170_min__numeral__Suc,axiom,
% 5.44/5.73 ! [K: num,N2: nat] :
% 5.44/5.73 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.44/5.73 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % min_numeral_Suc
% 5.44/5.73 thf(fact_10171_nat__mult__min__left,axiom,
% 5.44/5.73 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.73 ( ( times_times_nat @ ( ord_min_nat @ M @ N2 ) @ Q2 )
% 5.44/5.73 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % nat_mult_min_left
% 5.44/5.73 thf(fact_10172_nat__mult__min__right,axiom,
% 5.44/5.73 ! [M: nat,N2: nat,Q2: nat] :
% 5.44/5.73 ( ( times_times_nat @ M @ ( ord_min_nat @ N2 @ Q2 ) )
% 5.44/5.73 = ( ord_min_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % nat_mult_min_right
% 5.44/5.73 thf(fact_10173_min__diff,axiom,
% 5.44/5.73 ! [M: nat,I2: nat,N2: nat] :
% 5.44/5.73 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N2 @ I2 ) )
% 5.44/5.73 = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % min_diff
% 5.44/5.73 thf(fact_10174_concat__bit__assoc__sym,axiom,
% 5.44/5.73 ! [M: nat,N2: nat,K: int,L2: int,R: int] :
% 5.44/5.73 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N2 @ K @ L2 ) @ R )
% 5.44/5.73 = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N2 ) @ L2 @ R ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % concat_bit_assoc_sym
% 5.44/5.73 thf(fact_10175_inf__nat__def,axiom,
% 5.44/5.73 inf_inf_nat = ord_min_nat ).
% 5.44/5.73
% 5.44/5.73 % inf_nat_def
% 5.44/5.73 thf(fact_10176_take__bit__concat__bit__eq,axiom,
% 5.44/5.73 ! [M: nat,N2: nat,K: int,L2: int] :
% 5.44/5.73 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N2 @ K @ L2 ) )
% 5.44/5.73 = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N2 ) @ L2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % take_bit_concat_bit_eq
% 5.44/5.73 thf(fact_10177_min__Suc1,axiom,
% 5.44/5.73 ! [N2: nat,M: nat] :
% 5.44/5.73 ( ( ord_min_nat @ ( suc @ N2 ) @ M )
% 5.44/5.73 = ( case_nat_nat @ zero_zero_nat
% 5.44/5.73 @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ N2 @ M3 ) )
% 5.44/5.73 @ M ) ) ).
% 5.44/5.73
% 5.44/5.73 % min_Suc1
% 5.44/5.73 thf(fact_10178_min__Suc2,axiom,
% 5.44/5.73 ! [M: nat,N2: nat] :
% 5.44/5.73 ( ( ord_min_nat @ M @ ( suc @ N2 ) )
% 5.44/5.73 = ( case_nat_nat @ zero_zero_nat
% 5.44/5.73 @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ M3 @ N2 ) )
% 5.44/5.73 @ M ) ) ).
% 5.44/5.73
% 5.44/5.73 % min_Suc2
% 5.44/5.73 thf(fact_10179_min__enat__simps_I2_J,axiom,
% 5.44/5.73 ! [Q2: extended_enat] :
% 5.44/5.73 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.44/5.73 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.73
% 5.44/5.73 % min_enat_simps(2)
% 5.44/5.73 thf(fact_10180_min__enat__simps_I3_J,axiom,
% 5.44/5.73 ! [Q2: extended_enat] :
% 5.44/5.73 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.44/5.73 = zero_z5237406670263579293d_enat ) ).
% 5.44/5.73
% 5.44/5.73 % min_enat_simps(3)
% 5.44/5.73 thf(fact_10181_take__upt,axiom,
% 5.44/5.73 ! [I2: nat,M: nat,N2: nat] :
% 5.44/5.73 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N2 )
% 5.44/5.73 => ( ( take_nat @ M @ ( upt @ I2 @ N2 ) )
% 5.44/5.73 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % take_upt
% 5.44/5.73 thf(fact_10182_drop__upt,axiom,
% 5.44/5.73 ! [M: nat,I2: nat,J: nat] :
% 5.44/5.73 ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 5.44/5.73 = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 5.44/5.73
% 5.44/5.73 % drop_upt
% 5.44/5.73 thf(fact_10183_inf__enat__def,axiom,
% 5.44/5.73 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.44/5.73
% 5.44/5.73 % inf_enat_def
% 5.44/5.73 thf(fact_10184_Rats__eq__int__div__nat,axiom,
% 5.44/5.73 ( field_5140801741446780682s_real
% 5.44/5.73 = ( collect_real
% 5.44/5.73 @ ^ [Uu3: real] :
% 5.44/5.73 ? [I5: int,N: nat] :
% 5.44/5.73 ( ( Uu3
% 5.44/5.73 = ( divide_divide_real @ ( ring_1_of_int_real @ I5 ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.44/5.73 & ( N != zero_zero_nat ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % Rats_eq_int_div_nat
% 5.44/5.73 thf(fact_10185_Rats__abs__iff,axiom,
% 5.44/5.73 ! [X: real] :
% 5.44/5.73 ( ( member_real @ ( abs_abs_real @ X ) @ field_5140801741446780682s_real )
% 5.44/5.73 = ( member_real @ X @ field_5140801741446780682s_real ) ) ).
% 5.44/5.73
% 5.44/5.73 % Rats_abs_iff
% 5.44/5.73 thf(fact_10186_Rats__no__top__le,axiom,
% 5.44/5.73 ! [X: real] :
% 5.44/5.73 ? [X5: real] :
% 5.44/5.73 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.44/5.73 & ( ord_less_eq_real @ X @ X5 ) ) ).
% 5.44/5.73
% 5.44/5.73 % Rats_no_top_le
% 5.44/5.73 thf(fact_10187_Rats__no__bot__less,axiom,
% 5.44/5.73 ! [X: real] :
% 5.44/5.73 ? [X5: real] :
% 5.44/5.73 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.44/5.73 & ( ord_less_real @ X5 @ X ) ) ).
% 5.44/5.73
% 5.44/5.73 % Rats_no_bot_less
% 5.44/5.73 thf(fact_10188_Rats__dense__in__real,axiom,
% 5.44/5.73 ! [X: real,Y: real] :
% 5.44/5.73 ( ( ord_less_real @ X @ Y )
% 5.44/5.73 => ? [X5: real] :
% 5.44/5.73 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.44/5.73 & ( ord_less_real @ X @ X5 )
% 5.44/5.73 & ( ord_less_real @ X5 @ Y ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % Rats_dense_in_real
% 5.44/5.73 thf(fact_10189_Rats__eq__int__div__int,axiom,
% 5.44/5.73 ( field_5140801741446780682s_real
% 5.44/5.73 = ( collect_real
% 5.44/5.73 @ ^ [Uu3: real] :
% 5.44/5.73 ? [I5: int,J3: int] :
% 5.44/5.73 ( ( Uu3
% 5.44/5.73 = ( divide_divide_real @ ( ring_1_of_int_real @ I5 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.44/5.73 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % Rats_eq_int_div_int
% 5.44/5.73 thf(fact_10190_vimage__Suc__insert__Suc,axiom,
% 5.44/5.73 ! [N2: nat,A2: set_nat] :
% 5.44/5.73 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N2 ) @ A2 ) )
% 5.44/5.73 = ( insert_nat @ N2 @ ( vimage_nat_nat @ suc @ A2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % vimage_Suc_insert_Suc
% 5.44/5.73 thf(fact_10191_vimage__Suc__insert__0,axiom,
% 5.44/5.73 ! [A2: set_nat] :
% 5.44/5.73 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 5.44/5.73 = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 5.44/5.73
% 5.44/5.73 % vimage_Suc_insert_0
% 5.44/5.73 thf(fact_10192_finite__vimage__Suc__iff,axiom,
% 5.44/5.73 ! [F3: set_nat] :
% 5.44/5.73 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F3 ) )
% 5.44/5.73 = ( finite_finite_nat @ F3 ) ) ).
% 5.44/5.73
% 5.44/5.73 % finite_vimage_Suc_iff
% 5.44/5.73 thf(fact_10193_set__decode__div__2,axiom,
% 5.44/5.73 ! [X: nat] :
% 5.44/5.73 ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.44/5.73 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % set_decode_div_2
% 5.44/5.73 thf(fact_10194_set__encode__vimage__Suc,axiom,
% 5.44/5.73 ! [A2: set_nat] :
% 5.44/5.73 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A2 ) )
% 5.44/5.73 = ( divide_divide_nat @ ( nat_set_encode @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % set_encode_vimage_Suc
% 5.44/5.73 thf(fact_10195_card__le__Suc__Max,axiom,
% 5.44/5.73 ! [S: set_nat] :
% 5.44/5.73 ( ( finite_finite_nat @ S )
% 5.44/5.73 => ( ord_less_eq_nat @ ( finite_card_nat @ S ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % card_le_Suc_Max
% 5.44/5.73 thf(fact_10196_divide__nat__def,axiom,
% 5.44/5.73 ( divide_divide_nat
% 5.44/5.73 = ( ^ [M6: nat,N: nat] :
% 5.44/5.73 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 5.44/5.73 @ ( lattic8265883725875713057ax_nat
% 5.44/5.73 @ ( collect_nat
% 5.44/5.73 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N ) @ M6 ) ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % divide_nat_def
% 5.44/5.73 thf(fact_10197_Field__natLeq__on,axiom,
% 5.44/5.73 ! [N2: nat] :
% 5.44/5.73 ( ( field_nat
% 5.44/5.73 @ ( collec3392354462482085612at_nat
% 5.44/5.73 @ ( produc6081775807080527818_nat_o
% 5.44/5.73 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.73 ( ( ord_less_nat @ X2 @ N2 )
% 5.44/5.73 & ( ord_less_nat @ Y3 @ N2 )
% 5.44/5.73 & ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ) )
% 5.44/5.73 = ( collect_nat
% 5.44/5.73 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % Field_natLeq_on
% 5.44/5.73 thf(fact_10198_natLess__def,axiom,
% 5.44/5.73 ( bNF_Ca8459412986667044542atLess
% 5.44/5.73 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % natLess_def
% 5.44/5.73 thf(fact_10199_Restr__natLeq,axiom,
% 5.44/5.73 ! [N2: nat] :
% 5.44/5.73 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.44/5.73 @ ( produc457027306803732586at_nat
% 5.44/5.73 @ ( collect_nat
% 5.44/5.73 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) )
% 5.44/5.73 @ ^ [Uu3: nat] :
% 5.44/5.73 ( collect_nat
% 5.44/5.73 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) )
% 5.44/5.73 = ( collec3392354462482085612at_nat
% 5.44/5.73 @ ( produc6081775807080527818_nat_o
% 5.44/5.73 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.73 ( ( ord_less_nat @ X2 @ N2 )
% 5.44/5.73 & ( ord_less_nat @ Y3 @ N2 )
% 5.44/5.73 & ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % Restr_natLeq
% 5.44/5.73 thf(fact_10200_natLeq__def,axiom,
% 5.44/5.73 ( bNF_Ca8665028551170535155natLeq
% 5.44/5.73 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % natLeq_def
% 5.44/5.73 thf(fact_10201_wf__less,axiom,
% 5.44/5.73 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.44/5.73
% 5.44/5.73 % wf_less
% 5.44/5.73 thf(fact_10202_Restr__natLeq2,axiom,
% 5.44/5.73 ! [N2: nat] :
% 5.44/5.73 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.44/5.73 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 5.44/5.73 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 ) ) )
% 5.44/5.73 = ( collec3392354462482085612at_nat
% 5.44/5.73 @ ( produc6081775807080527818_nat_o
% 5.44/5.73 @ ^ [X2: nat,Y3: nat] :
% 5.44/5.73 ( ( ord_less_nat @ X2 @ N2 )
% 5.44/5.73 & ( ord_less_nat @ Y3 @ N2 )
% 5.44/5.73 & ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % Restr_natLeq2
% 5.44/5.73 thf(fact_10203_natLeq__underS__less,axiom,
% 5.44/5.73 ! [N2: nat] :
% 5.44/5.73 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 5.44/5.73 = ( collect_nat
% 5.44/5.73 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N2 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % natLeq_underS_less
% 5.44/5.73 thf(fact_10204_prod__encode__prod__decode__aux,axiom,
% 5.44/5.73 ! [K: nat,M: nat] :
% 5.44/5.73 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.44/5.73 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.44/5.73
% 5.44/5.73 % prod_encode_prod_decode_aux
% 5.44/5.73 thf(fact_10205_le__prod__encode__2,axiom,
% 5.44/5.73 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % le_prod_encode_2
% 5.44/5.73 thf(fact_10206_le__prod__encode__1,axiom,
% 5.44/5.73 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % le_prod_encode_1
% 5.44/5.73 thf(fact_10207_prod__encode__def,axiom,
% 5.44/5.73 ( nat_prod_encode
% 5.44/5.73 = ( produc6842872674320459806at_nat
% 5.44/5.73 @ ^ [M6: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N ) ) @ M6 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % prod_encode_def
% 5.44/5.73 thf(fact_10208_list__encode_Oelims,axiom,
% 5.44/5.73 ! [X: list_nat,Y: nat] :
% 5.44/5.73 ( ( ( nat_list_encode @ X )
% 5.44/5.73 = Y )
% 5.44/5.73 => ( ( ( X = nil_nat )
% 5.44/5.73 => ( Y != zero_zero_nat ) )
% 5.44/5.73 => ~ ! [X5: nat,Xs3: list_nat] :
% 5.44/5.73 ( ( X
% 5.44/5.73 = ( cons_nat @ X5 @ Xs3 ) )
% 5.44/5.73 => ( Y
% 5.44/5.73 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % list_encode.elims
% 5.44/5.73 thf(fact_10209_list__encode_Osimps_I2_J,axiom,
% 5.44/5.73 ! [X: nat,Xs2: list_nat] :
% 5.44/5.73 ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 5.44/5.73 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % list_encode.simps(2)
% 5.44/5.73 thf(fact_10210_list__encode_Opelims,axiom,
% 5.44/5.73 ! [X: list_nat,Y: nat] :
% 5.44/5.73 ( ( ( nat_list_encode @ X )
% 5.44/5.73 = Y )
% 5.44/5.73 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 5.44/5.73 => ( ( ( X = nil_nat )
% 5.44/5.73 => ( ( Y = zero_zero_nat )
% 5.44/5.73 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.44/5.73 => ~ ! [X5: nat,Xs3: list_nat] :
% 5.44/5.73 ( ( X
% 5.44/5.73 = ( cons_nat @ X5 @ Xs3 ) )
% 5.44/5.73 => ( ( Y
% 5.44/5.73 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.44/5.73 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs3 ) ) ) ) ) ) ) ).
% 5.44/5.73
% 5.44/5.73 % list_encode.pelims
% 5.44/5.73
% 5.44/5.73 % Helper facts (44)
% 5.44/5.73 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.44/5.73 ! [X: int,Y: int] :
% 5.44/5.73 ( ( if_int @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.44/5.73 ! [X: int,Y: int] :
% 5.44/5.73 ( ( if_int @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.44/5.73 ! [X: nat,Y: nat] :
% 5.44/5.73 ( ( if_nat @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.44/5.73 ! [X: nat,Y: nat] :
% 5.44/5.73 ( ( if_nat @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.44/5.73 ! [X: num,Y: num] :
% 5.44/5.73 ( ( if_num @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.44/5.73 ! [X: num,Y: num] :
% 5.44/5.73 ( ( if_num @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.44/5.73 ! [X: real,Y: real] :
% 5.44/5.73 ( ( if_real @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.44/5.73 ! [X: real,Y: real] :
% 5.44/5.73 ( ( if_real @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.44/5.73 ! [P: real > $o] :
% 5.44/5.73 ( ( P @ ( fChoice_real @ P ) )
% 5.44/5.73 = ( ? [X4: real] : ( P @ X4 ) ) ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.44/5.73 ! [X: complex,Y: complex] :
% 5.44/5.73 ( ( if_complex @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.44/5.73 ! [X: complex,Y: complex] :
% 5.44/5.73 ( ( if_complex @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.44/5.73 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.73 ( ( if_Extended_enat @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.44/5.73 ! [X: extended_enat,Y: extended_enat] :
% 5.44/5.73 ( ( if_Extended_enat @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.44/5.73 ! [X: code_integer,Y: code_integer] :
% 5.44/5.73 ( ( if_Code_integer @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.44/5.73 ! [X: code_integer,Y: code_integer] :
% 5.44/5.73 ( ( if_Code_integer @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.44/5.73 ! [X: set_nat,Y: set_nat] :
% 5.44/5.73 ( ( if_set_nat @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.44/5.73 ! [X: set_nat,Y: set_nat] :
% 5.44/5.73 ( ( if_set_nat @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.44/5.73 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.44/5.73 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.44/5.73 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.44/5.73 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.44/5.73 ! [X: list_int,Y: list_int] :
% 5.44/5.73 ( ( if_list_int @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.44/5.73 ! [X: list_int,Y: list_int] :
% 5.44/5.73 ( ( if_list_int @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.44/5.73 ! [X: list_nat,Y: list_nat] :
% 5.44/5.73 ( ( if_list_nat @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.44/5.73 ! [X: list_nat,Y: list_nat] :
% 5.44/5.73 ( ( if_list_nat @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Set__Oset_It__Real__Oreal_J_T,axiom,
% 5.44/5.73 ! [X: set_real,Y: set_real] :
% 5.44/5.73 ( ( if_set_real @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Set__Oset_It__Real__Oreal_J_T,axiom,
% 5.44/5.73 ! [X: set_real,Y: set_real] :
% 5.44/5.73 ( ( if_set_real @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.44/5.73 ! [X: int > int,Y: int > int] :
% 5.44/5.73 ( ( if_int_int @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.44/5.73 ! [X: int > int,Y: int > int] :
% 5.44/5.73 ( ( if_int_int @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.44/5.73 ! [X: option_nat,Y: option_nat] :
% 5.44/5.73 ( ( if_option_nat @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.44/5.73 ! [X: option_nat,Y: option_nat] :
% 5.44/5.73 ( ( if_option_nat @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.44/5.73 ! [X: option_num,Y: option_num] :
% 5.44/5.73 ( ( if_option_num @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.44/5.73 ! [X: option_num,Y: option_num] :
% 5.44/5.73 ( ( if_option_num @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.44/5.73 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.44/5.73 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.44/5.73 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.44/5.73 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.44/5.73 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.44/5.73 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.44/5.73 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.44/5.73 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 5.44/5.73 = X ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.44/5.73 ! [X: nat > int > int,Y: nat > int > int] :
% 5.44/5.73 ( ( if_nat_int_int @ $false @ X @ Y )
% 5.44/5.73 = Y ) ).
% 5.44/5.73
% 5.44/5.73 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.44/5.73 ! [X: nat > int > int,Y: nat > int > int] :
% 6.84/7.05 ( ( if_nat_int_int @ $true @ X @ Y )
% 6.84/7.05 = X ) ).
% 6.84/7.05
% 6.84/7.05 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.84/7.05 ! [X: nat > nat > nat,Y: nat > nat > nat] :
% 6.84/7.05 ( ( if_nat_nat_nat @ $false @ X @ Y )
% 6.84/7.05 = Y ) ).
% 6.84/7.05
% 6.84/7.05 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.84/7.05 ! [X: nat > nat > nat,Y: nat > nat > nat] :
% 6.84/7.05 ( ( if_nat_nat_nat @ $true @ X @ Y )
% 6.84/7.05 = X ) ).
% 6.84/7.05
% 6.84/7.05 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.84/7.05 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.84/7.05 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 6.84/7.05 = Y ) ).
% 6.84/7.05
% 6.84/7.05 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.84/7.05 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.84/7.05 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 6.84/7.05 = X ) ).
% 6.84/7.05
% 6.84/7.05 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.84/7.05 ! [P: $o] :
% 6.84/7.05 ( ( P = $true )
% 6.84/7.05 | ( P = $false ) ) ).
% 6.84/7.05
% 6.84/7.05 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.84/7.05 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.84/7.05 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 6.84/7.05 = Y ) ).
% 6.84/7.05
% 6.84/7.05 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.84/7.05 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.84/7.05 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 6.84/7.05 = X ) ).
% 6.84/7.05
% 6.84/7.05 % Conjectures (1)
% 6.84/7.05 thf(conj_0,conjecture,
% 6.84/7.05 ( ord_less_nat
% 6.84/7.05 @ ( if_nat
% 6.84/7.05 @ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 6.84/7.05 = ma )
% 6.84/7.05 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 6.84/7.05 @ ma )
% 6.84/7.05 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ).
% 6.84/7.05
% 6.84/7.05 %------------------------------------------------------------------------------
% 6.84/7.05 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.t9y3RYzHfm/cvc5---1.0.5_22629.p...
% 6.84/7.05 (declare-sort $$unsorted 0)
% 6.84/7.05 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.84/7.05 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.84/7.05 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.84/7.05 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.84/7.05 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.84/7.05 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.84/7.05 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.84/7.05 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.84/7.05 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.84/7.05 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.84/7.05 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.84/7.05 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.84/7.05 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.84/7.05 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.84/7.05 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.84/7.05 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.84/7.05 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.84/7.05 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.84/7.05 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.84/7.05 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.84/7.05 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.84/7.05 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.84/7.05 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.84/7.05 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.84/7.05 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.84/7.05 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.84/7.05 (declare-sort tptp.list_P8526636022914148096eger_o 0)
% 6.84/7.05 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.84/7.05 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.84/7.05 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.84/7.05 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.84/7.05 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.84/7.05 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.84/7.05 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.84/7.05 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.84/7.05 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.84/7.05 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.84/7.05 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.84/7.05 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.84/7.05 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.84/7.05 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.84/7.05 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.84/7.05 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.84/7.05 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.84/7.05 (declare-sort tptp.product_prod_num_num 0)
% 6.84/7.05 (declare-sort tptp.product_prod_nat_num 0)
% 6.84/7.05 (declare-sort tptp.product_prod_nat_nat 0)
% 6.84/7.05 (declare-sort tptp.product_prod_int_int 0)
% 6.84/7.05 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.84/7.05 (declare-sort tptp.set_list_complex 0)
% 6.84/7.05 (declare-sort tptp.set_set_complex 0)
% 6.84/7.05 (declare-sort tptp.set_list_real 0)
% 6.84/7.05 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.84/7.05 (declare-sort tptp.set_set_real 0)
% 6.84/7.05 (declare-sort tptp.set_list_nat 0)
% 6.84/7.05 (declare-sort tptp.set_list_int 0)
% 6.84/7.05 (declare-sort tptp.product_prod_o_nat 0)
% 6.84/7.05 (declare-sort tptp.product_prod_o_int 0)
% 6.84/7.05 (declare-sort tptp.list_Code_integer 0)
% 6.84/7.05 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.84/7.05 (declare-sort tptp.set_set_nat 0)
% 6.84/7.05 (declare-sort tptp.set_Code_integer 0)
% 6.84/7.05 (declare-sort tptp.set_Product_unit 0)
% 6.84/7.05 (declare-sort tptp.set_Extended_enat 0)
% 6.84/7.05 (declare-sort tptp.list_complex 0)
% 6.84/7.05 (declare-sort tptp.set_list_o 0)
% 6.84/7.05 (declare-sort tptp.product_prod_o_o 0)
% 6.84/7.05 (declare-sort tptp.set_complex 0)
% 6.84/7.05 (declare-sort tptp.filter_real 0)
% 6.84/7.05 (declare-sort tptp.option_num 0)
% 6.84/7.05 (declare-sort tptp.option_nat 0)
% 6.84/7.05 (declare-sort tptp.filter_nat 0)
% 6.84/7.05 (declare-sort tptp.set_char 0)
% 6.84/7.05 (declare-sort tptp.list_real 0)
% 6.84/7.05 (declare-sort tptp.set_real 0)
% 6.84/7.05 (declare-sort tptp.list_num 0)
% 6.84/7.05 (declare-sort tptp.list_nat 0)
% 6.84/7.05 (declare-sort tptp.list_int 0)
% 6.84/7.05 (declare-sort tptp.vEBT_VEBT 0)
% 6.84/7.05 (declare-sort tptp.set_num 0)
% 6.84/7.05 (declare-sort tptp.set_nat 0)
% 6.84/7.05 (declare-sort tptp.set_int 0)
% 6.84/7.05 (declare-sort tptp.code_integer 0)
% 6.84/7.05 (declare-sort tptp.extended_enat 0)
% 6.84/7.05 (declare-sort tptp.list_o 0)
% 6.84/7.05 (declare-sort tptp.complex 0)
% 6.84/7.05 (declare-sort tptp.set_o 0)
% 6.84/7.05 (declare-sort tptp.char 0)
% 6.84/7.05 (declare-sort tptp.real 0)
% 6.84/7.05 (declare-sort tptp.num 0)
% 6.84/7.05 (declare-sort tptp.nat 0)
% 6.84/7.05 (declare-sort tptp.int 0)
% 6.84/7.05 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.84/7.05 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.84/7.05 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.84/7.05 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.05 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.05 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.gbinom8545251970709558553nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.84/7.05 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.84/7.05 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.84/7.05 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.84/7.05 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.84/7.05 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.84/7.05 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 6.84/7.05 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.84/7.05 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.84/7.05 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.84/7.05 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.84/7.05 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.84/7.05 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.84/7.05 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.84/7.05 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.84/7.05 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.84/7.05 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.84/7.05 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.84/7.05 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.84/7.05 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.84/7.05 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.84/7.05 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.84/7.05 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.84/7.05 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.84/7.05 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.84/7.05 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.84/7.05 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.84/7.05 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.84/7.05 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.84/7.05 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.84/7.05 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.84/7.05 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.84/7.05 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.84/7.05 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.84/7.05 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.84/7.05 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.84/7.05 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.84/7.05 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.84/7.05 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.84/7.05 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.84/7.05 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.84/7.05 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.84/7.05 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.84/7.05 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.84/7.05 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.84/7.05 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.84/7.05 (declare-fun tptp.comm_s3181272606743183617d_enat (tptp.extended_enat tptp.nat) tptp.extended_enat)
% 6.84/7.05 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.84/7.05 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.84/7.05 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.84/7.05 (declare-fun tptp.semiri4449623510593786356d_enat (tptp.nat) tptp.extended_enat)
% 6.84/7.05 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.84/7.05 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.84/7.05 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.84/7.05 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.84/7.05 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.84/7.05 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.84/7.05 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.84/7.05 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.84/7.05 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.84/7.05 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.84/7.05 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.84/7.05 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.84/7.05 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.84/7.05 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.84/7.05 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.84/7.05 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.84/7.05 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.84/7.05 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.84/7.05 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.84/7.05 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.84/7.05 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.84/7.05 (declare-fun tptp.finite4001608067531595151d_enat (tptp.set_Extended_enat) Bool)
% 6.84/7.05 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.84/7.05 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.84/7.05 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.84/7.05 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.84/7.05 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.84/7.05 (declare-fun tptp.finite306553202115118035t_real (tptp.set_list_real) Bool)
% 6.84/7.05 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.84/7.05 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.84/7.05 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.84/7.05 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.84/7.05 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.84/7.05 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 6.84/7.05 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.84/7.05 (declare-fun tptp.finite9007344921179782393t_real (tptp.set_set_real) Bool)
% 6.84/7.05 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.84/7.05 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.84/7.05 (declare-fun tptp.bij_betw_complex_int ((-> tptp.complex tptp.int) tptp.set_complex tptp.set_int) Bool)
% 6.84/7.05 (declare-fun tptp.bij_be1121013576637796946x_real ((-> tptp.complex tptp.real) tptp.set_complex tptp.set_real) Bool)
% 6.84/7.05 (declare-fun tptp.bij_betw_int_complex ((-> tptp.int tptp.complex) tptp.set_int tptp.set_complex) Bool)
% 6.84/7.05 (declare-fun tptp.bij_betw_int_int ((-> tptp.int tptp.int) tptp.set_int tptp.set_int) Bool)
% 6.84/7.05 (declare-fun tptp.bij_betw_int_real ((-> tptp.int tptp.real) tptp.set_int tptp.set_real) Bool)
% 6.84/7.05 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.84/7.05 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.84/7.05 (declare-fun tptp.bij_be1067425076133476306omplex ((-> tptp.real tptp.complex) tptp.set_real tptp.set_complex) Bool)
% 6.84/7.05 (declare-fun tptp.bij_betw_real_int ((-> tptp.real tptp.int) tptp.set_real tptp.set_int) Bool)
% 6.84/7.05 (declare-fun tptp.bij_betw_real_real ((-> tptp.real tptp.real) tptp.set_real tptp.set_real) Bool)
% 6.84/7.05 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 6.84/7.05 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.84/7.05 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.84/7.05 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.84/7.05 (declare-fun tptp.map_fu4960017516451851995nt_int ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.map_fu3667384564859982768at_int ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.84/7.05 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.84/7.05 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.84/7.05 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.05 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.84/7.05 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.84/7.05 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.84/7.05 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.05 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.84/7.05 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.84/7.05 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.84/7.05 (declare-fun tptp.one_one_int () tptp.int)
% 6.84/7.05 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.84/7.05 (declare-fun tptp.one_one_real () tptp.real)
% 6.84/7.05 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.05 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.84/7.05 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.05 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.05 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.84/7.05 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.84/7.05 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.84/7.05 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.84/7.05 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.84/7.05 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.84/7.05 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.84/7.05 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.84/7.05 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.84/7.06 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.84/7.06 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.84/7.06 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.84/7.06 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups1752964319039525884d_enat ((-> tptp.complex tptp.extended_enat) tptp.set_complex) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups4225252721152677374d_enat ((-> tptp.int tptp.extended_enat) tptp.set_int) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups7108830773950497114d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups6381953495645901045omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups975429370522433651at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups2800946370649118462d_enat ((-> tptp.real tptp.extended_enat) tptp.set_real) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups8682486955453173170nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups8780218893797010257d_enat ((-> tptp.complex tptp.extended_enat) tptp.set_complex) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups3827104343326376752nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups5078248829458667347d_enat ((-> tptp.int tptp.extended_enat) tptp.set_int) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups7961826882256487087d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups8110221916422527690omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups4075276357253098568at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups6036352826371341000t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups6225526099057966256nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.84/7.06 (declare-fun tptp.groups7973222482632965587d_enat ((-> tptp.real tptp.extended_enat) tptp.set_real) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.84/7.06 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.84/7.06 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.84/7.06 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.84/7.06 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.84/7.06 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.if_nat_int_int (Bool (-> tptp.nat tptp.int tptp.int) (-> tptp.nat tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.if_nat_nat_nat (Bool (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.84/7.06 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.84/7.06 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.84/7.06 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.84/7.06 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.84/7.06 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.84/7.06 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.84/7.06 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.if_set_real (Bool tptp.set_real tptp.set_real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.84/7.06 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.84/7.06 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.84/7.06 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.84/7.06 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.84/7.06 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.84/7.06 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.84/7.06 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.84/7.06 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.84/7.06 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.count_list_int (tptp.list_int tptp.int) tptp.nat)
% 6.84/7.06 (declare-fun tptp.count_list_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.count_list_real (tptp.list_real tptp.real) tptp.nat)
% 6.84/7.06 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 6.84/7.06 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 6.84/7.06 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.84/7.06 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.nil_int () tptp.list_int)
% 6.84/7.06 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.84/7.06 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.84/7.06 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.84/7.06 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.84/7.06 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.84/7.06 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.84/7.06 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.84/7.06 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.84/7.06 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.84/7.06 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.84/7.06 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.84/7.06 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.84/7.06 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.84/7.06 (declare-fun tptp.nth_Pr8522763379788166057eger_o (tptp.list_P8526636022914148096eger_o tptp.nat) tptp.produc6271795597528267376eger_o)
% 6.84/7.06 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.84/7.06 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.84/7.06 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.84/7.06 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.84/7.06 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.84/7.06 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.84/7.06 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.84/7.06 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.84/7.06 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.84/7.06 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.84/7.06 (declare-fun tptp.produc3607205314601156340eger_o (tptp.list_Code_integer tptp.list_o) tptp.list_P8526636022914148096eger_o)
% 6.84/7.06 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.84/7.06 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.84/7.06 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.84/7.06 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.84/7.06 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.84/7.06 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.84/7.06 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.84/7.06 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.84/7.06 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.84/7.06 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.84/7.06 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.replic4235873036481779905at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.84/7.06 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.84/7.06 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.84/7.06 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.84/7.06 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.84/7.06 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.84/7.06 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.84/7.06 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.84/7.06 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.84/7.06 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.semiri4055485073559036834nteger ((-> tptp.code_integer tptp.code_integer) tptp.nat tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.semiri8563196900006977889d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.nat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.84/7.06 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.84/7.06 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.84/7.06 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.84/7.06 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.84/7.06 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.84/7.06 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.84/7.06 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.84/7.06 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.84/7.06 (declare-fun tptp.one () tptp.num)
% 6.84/7.06 (declare-fun tptp.case_num_option_num (tptp.option_num (-> tptp.num tptp.option_num) (-> tptp.num tptp.option_num) tptp.num) tptp.option_num)
% 6.84/7.06 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.84/7.06 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.84/7.06 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.84/7.06 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.84/7.06 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.84/7.06 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.84/7.06 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.84/7.06 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.84/7.06 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.84/7.06 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.none_num () tptp.option_num)
% 6.84/7.06 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.84/7.06 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.84/7.06 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.84/7.06 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.84/7.06 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.84/7.06 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.84/7.06 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.84/7.06 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.84/7.06 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.84/7.06 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.84/7.06 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.84/7.06 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.84/7.06 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.84/7.06 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 6.84/7.06 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.84/7.06 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.84/7.06 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.84/7.06 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.84/7.06 (declare-fun tptp.bot_bot_set_set_real () tptp.set_set_real)
% 6.84/7.06 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le2529575680413868914d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le7926960851185191020t_real (tptp.set_set_real tptp.set_set_real) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le4573692005234683329plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le7203529160286727270d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le3558479182127378552t_real (tptp.set_set_real tptp.set_set_real) Bool)
% 6.84/7.06 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.84/7.06 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.84/7.06 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.84/7.06 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.84/7.06 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.84/7.06 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.84/7.06 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.84/7.06 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.84/7.06 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.84/7.06 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.power_8040749407984259932d_enat (tptp.extended_enat tptp.nat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.84/7.06 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.84/7.06 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.84/7.06 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.84/7.06 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.84/7.06 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.84/7.06 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.84/7.06 (declare-fun tptp.produc2899441246263362727at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc6121120109295599847at_nat) tptp.produc5542196010084753463at_nat)
% 6.84/7.06 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.84/7.06 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.84/7.06 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.84/7.06 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.84/7.06 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.84/7.06 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.84/7.06 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.84/7.06 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.84/7.06 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.84/7.06 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.84/7.06 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.84/7.06 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.84/7.06 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.84/7.06 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.84/7.06 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.84/7.06 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.84/7.06 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.84/7.06 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.84/7.06 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.84/7.06 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.produc7828578312038201481er_o_o ((-> tptp.code_integer Bool Bool) tptp.produc6271795597528267376eger_o) Bool)
% 6.84/7.06 (declare-fun tptp.produc1043322548047392435omplex ((-> tptp.code_integer Bool tptp.set_complex) tptp.produc6271795597528267376eger_o) tptp.set_complex)
% 6.84/7.06 (declare-fun tptp.produc1253318751659547953et_int ((-> tptp.code_integer Bool tptp.set_int) tptp.produc6271795597528267376eger_o) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.produc5431169771168744661et_nat ((-> tptp.code_integer Bool tptp.set_nat) tptp.produc6271795597528267376eger_o) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.produc242741666403216561t_real ((-> tptp.code_integer Bool tptp.set_real) tptp.produc6271795597528267376eger_o) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.84/7.06 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.84/7.06 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.84/7.06 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.84/7.06 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.84/7.06 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.84/7.06 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.84/7.06 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.84/7.06 (declare-fun tptp.produc8739625826339149834_nat_o ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.84/7.06 (declare-fun tptp.produc27273713700761075at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.84/7.06 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.84/7.06 (declare-fun tptp.produc1830744345554046123nteger ((-> tptp.nat tptp.nat tptp.code_integer) tptp.product_prod_nat_nat) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.produc2676513652042109336d_enat ((-> tptp.nat tptp.nat tptp.extended_enat) tptp.product_prod_nat_nat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.84/7.06 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.produc4927758841916487424_num_o ((-> tptp.nat tptp.num Bool) tptp.product_prod_nat_num) Bool)
% 6.84/7.06 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.84/7.06 (declare-fun tptp.produc4130284055270567454et_nat ((-> tptp.nat tptp.num tptp.set_nat) tptp.product_prod_nat_num) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.produc1435849484188172666t_real ((-> tptp.nat tptp.num tptp.set_real) tptp.product_prod_nat_num) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.produc5703948589228662326_num_o ((-> tptp.num tptp.num Bool) tptp.product_prod_num_num) Bool)
% 6.84/7.06 (declare-fun tptp.produc2866383454006189126omplex ((-> tptp.num tptp.num tptp.set_complex) tptp.product_prod_num_num) tptp.set_complex)
% 6.84/7.06 (declare-fun tptp.produc6406642877701697732et_int ((-> tptp.num tptp.num tptp.set_int) tptp.product_prod_num_num) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.produc1361121860356118632et_nat ((-> tptp.num tptp.num tptp.set_nat) tptp.product_prod_num_num) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.produc8296048397933160132t_real ((-> tptp.num tptp.num tptp.set_real) tptp.product_prod_num_num) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.84/7.06 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.84/7.06 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.84/7.06 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.84/7.06 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.84/7.06 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.84/7.06 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.84/7.06 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.84/7.06 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.84/7.06 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.84/7.06 (declare-fun tptp.dvd_dv3785147216227455552d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.84/7.06 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.84/7.06 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.84/7.06 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.84/7.06 (declare-fun tptp.zero_n1046097342994218471d_enat (Bool) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.84/7.06 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.84/7.06 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.84/7.06 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.84/7.06 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.84/7.06 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.84/7.06 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.84/7.06 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.84/7.06 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.84/7.06 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.84/7.06 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.84/7.06 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.84/7.06 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.84/7.06 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.84/7.06 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.84/7.06 (declare-fun tptp.collec4429806609662206161d_enat ((-> tptp.extended_enat Bool)) tptp.set_Extended_enat)
% 6.84/7.06 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.84/7.06 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.84/7.06 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.84/7.06 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.84/7.06 (declare-fun tptp.collect_list_real ((-> tptp.list_real Bool)) tptp.set_list_real)
% 6.84/7.06 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.84/7.06 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.84/7.06 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.84/7.06 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 6.84/7.06 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.84/7.06 (declare-fun tptp.collect_set_real ((-> tptp.set_real Bool)) tptp.set_set_real)
% 6.84/7.06 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.84/7.06 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.84/7.06 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.84/7.06 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.84/7.06 (declare-fun tptp.insert_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 6.84/7.06 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 6.84/7.06 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_fo1084959871951514735nteger ((-> tptp.nat tptp.code_integer tptp.code_integer) tptp.nat tptp.nat tptp.code_integer) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.set_fo2538466533108834004d_enat ((-> tptp.nat tptp.extended_enat tptp.extended_enat) tptp.nat tptp.nat tptp.extended_enat) tptp.extended_enat)
% 6.84/7.06 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.84/7.06 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.set_or5403411693681687835d_enat (tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat)
% 6.84/7.06 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.84/7.06 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.84/7.06 (declare-fun tptp.set_or7743017856606604397t_real (tptp.set_real tptp.set_real) tptp.set_set_real)
% 6.84/7.06 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.set_or8332593352340944941d_enat (tptp.extended_enat) tptp.set_Extended_enat)
% 6.84/7.06 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.84/7.06 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.84/7.06 (declare-fun tptp.set_or5092868708245317595t_real (tptp.set_real) tptp.set_set_real)
% 6.84/7.06 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.set_or8419480210114673929d_enat (tptp.extended_enat) tptp.set_Extended_enat)
% 6.84/7.06 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.84/7.06 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.84/7.06 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.84/7.06 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.84/7.06 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.84/7.06 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.84/7.06 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.84/7.06 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo7278393974255667507et_nat ((-> tptp.nat tptp.set_nat)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo2489691266198938127t_real ((-> tptp.nat tptp.set_real)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.84/7.06 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.84/7.06 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.84/7.06 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.84/7.06 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.84/7.06 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.cosh_complex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.cot_complex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.diffs_Code_integer ((-> tptp.nat tptp.code_integer) tptp.nat) tptp.code_integer)
% 6.84/7.06 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.84/7.06 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.84/7.06 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.pi () tptp.real)
% 6.84/7.06 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.84/7.06 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.84/7.06 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.84/7.06 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.84/7.06 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_delete (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_delete_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.84/7.06 (declare-fun tptp.vEBT_V1502963449132264192at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.option4927543243414619207at_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.84/7.06 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.84/7.06 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.84/7.06 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.84/7.06 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.84/7.06 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.84/7.06 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.84/7.06 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.84/7.06 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.84/7.06 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.84/7.06 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.84/7.06 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.84/7.06 (declare-fun tptp.member_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) Bool)
% 6.84/7.06 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.84/7.06 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.84/7.06 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.84/7.06 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.84/7.06 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.84/7.06 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.84/7.06 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.84/7.06 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.84/7.06 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.84/7.06 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.84/7.06 (declare-fun tptp.member_set_real (tptp.set_real tptp.set_set_real) Bool)
% 6.84/7.06 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.84/7.06 (declare-fun tptp.deg () tptp.nat)
% 6.84/7.06 (declare-fun tptp.lx () tptp.nat)
% 6.84/7.06 (declare-fun tptp.m () tptp.nat)
% 6.84/7.06 (declare-fun tptp.ma () tptp.nat)
% 6.84/7.06 (declare-fun tptp.mi () tptp.nat)
% 6.84/7.06 (declare-fun tptp.na () tptp.nat)
% 6.84/7.06 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.summin () tptp.nat)
% 6.84/7.06 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.84/7.06 (declare-fun tptp.xa () tptp.nat)
% 6.84/7.06 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.84/7.06 (assert (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (@ _let_1 A)) (@ _let_1 B)))))
% 6.84/7.06 (assert (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.06 (assert (forall ((Ma tptp.nat) (N2 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 N2) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N2)) (@ _let_1 M))))))
% 6.84/7.06 (assert (= (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))
% 6.84/7.06 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) Y)))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) X)))))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.84/7.06 (assert (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)) X_1)))
% 6.84/7.06 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L))))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.84/7.06 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_1 tptp.na))) tptp.lx)) (@ _let_1 tptp.deg))))
% 6.84/7.06 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na))) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na)))
% 6.84/7.06 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (= _let_3 tptp.ma))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (=> (not (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_5) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_5)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))) _let_5)))))) (=> (not _let_4) _let_4))) (forall ((I 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.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))))) (let ((_let_6 (@ (@ (@ tptp.if_nat (= _let_3 tptp.ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_5 _let_4))))) tptp.ma))) (=> (@ (@ tptp.ord_less_nat I) (@ _let_2 tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high _let_6) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ _let_5 I)) (@ (@ tptp.vEBT_VEBT_low _let_6) tptp.na))) (forall ((Y2 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.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))))) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y2) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ _let_5 I)) (@ (@ tptp.vEBT_VEBT_low Y2) tptp.na))) (and (@ (@ tptp.ord_less_nat _let_3) Y2) (@ (@ tptp.ord_less_eq_nat Y2) (@ (@ (@ tptp.if_nat (= _let_3 tptp.ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_5 _let_4))))) tptp.ma))))))))))))))))))))))))))
% 6.84/7.06 (assert (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na)))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) _let_3)) _let_2) _let_3)))))
% 6.84/7.06 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 tptp.na))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) _let_2)) tptp.lx))) (and (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na)) (@ _let_1 tptp.m)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)) _let_2))))))
% 6.84/7.06 (assert (exists ((X_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))) X_1))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (=> (and (not (= I2 _let_4)) (@ (@ tptp.ord_less_nat I2) (@ _let_2 tptp.m))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ _let_1 _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))) I2) (@ _let_1 I2)))))))))
% 6.84/7.06 (assert (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))))))
% 6.84/7.06 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (@ (@ (@ tptp.if_nat (= _let_3 tptp.ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))) _let_4))))) tptp.ma))) (and (@ (@ tptp.ord_less_nat _let_5) (@ _let_2 tptp.deg)) (@ (@ tptp.ord_less_eq_nat _let_3) _let_5))))))))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.84/7.06 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.84/7.06 (assert (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))))))))
% 6.84/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.84/7.06 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (= _let_3 tptp.ma))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (=> (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_5) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_5)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))) _let_5)))))) (=> (not _let_4) _let_4)) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))))))))))))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx)) tptp.na)) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))
% 6.84/7.06 (assert (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))) tptp.na)))
% 6.84/7.06 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.84/7.06 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))))
% 6.84/7.06 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_1 tptp.na))) tptp.lx))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high _let_2) tptp.na))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_3) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low _let_2) tptp.na)))) (@ _let_1 tptp.m))))))
% 6.84/7.06 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y2) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low Y2) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y2) (@ (@ tptp.ord_less_eq_nat Y2) tptp.ma)))))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.84/7.06 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.84/7.06 (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.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete X3) Xa)) tptp.na))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) Y))))))
% 6.84/7.06 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) Xs) (@ (@ tptp.ord_less_eq_nat X2) Y3)))))))
% 6.84/7.06 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) Xs) (@ (@ tptp.ord_less_eq_nat Y3) X2)))))))
% 6.84/7.06 (assert (=> (= tptp.mi tptp.ma) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N2))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ tptp.set_complex2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) N2))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N2))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N2))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N2 tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N2))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N2))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N2))))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat M) (@ tptp.numera1916890842035813515d_enat N2)) (= M N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N2)) (= M N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N2)) (= M N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N2)) (= M N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N2)) (= M N2))))
% 6.84/7.06 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X3) tptp.na))))
% 6.84/7.06 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.84/7.06 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.collec3392354462482085612at_nat P)) (@ P A))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.84/7.06 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.84/7.06 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.84/7.06 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)))
% 6.84/7.06 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A2))) A2)))
% 6.84/7.06 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)))
% 6.84/7.06 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)))
% 6.84/7.06 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A2))) A2)))
% 6.84/7.06 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)))
% 6.84/7.06 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collec3392354462482085612at_nat P) (@ tptp.collec3392354462482085612at_nat Q)))))
% 6.84/7.06 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 6.84/7.06 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 6.84/7.06 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 6.84/7.06 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.84/7.06 (assert (forall ((X tptp.nat)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete tptp.summary) X)) tptp.m)))
% 6.84/7.06 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)) tptp.na))
% 6.84/7.06 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na)))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat W)) Z)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W)) Z)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N2) (@ tptp.bit0 N2))))
% 6.84/7.06 (assert (and (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma) (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.84/7.06 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.84/7.06 (assert (forall ((Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_low Y) tptp.na))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Y) tptp.na))) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_3)) _let_2) (=> (@ (@ tptp.ord_less_nat _let_3) (@ _let_1 tptp.m)) (and (@ (@ tptp.ord_less_nat tptp.mi) Y) (@ (@ tptp.ord_less_eq_nat Y) tptp.ma) (@ (@ tptp.ord_less_nat _let_2) (@ _let_1 tptp.na))))))))))
% 6.84/7.06 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y2) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low Y2) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y2) (@ (@ tptp.ord_less_eq_nat Y2) tptp.ma))))))))
% 6.84/7.06 (assert (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))))) (@ (@ tptp.vEBT_invar_vebt X3) tptp.na))))))
% 6.84/7.06 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na)))) I)) X4)))) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L2)))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L2)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L2)))))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger L2)) (@ _let_1 (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num K) L2)))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N2) K)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2))) M)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2)) M)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N2) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N2)) Q2)))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) (@ tptp.numera1916890842035813515d_enat tptp.one)) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat tptp.one)) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) I2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.84/7.06 (assert (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.84/7.06 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.84/7.06 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) N))) (@ (@ tptp.vEBT_VEBT_low X2) N)))))
% 6.84/7.06 (assert (and (not (= tptp.mi tptp.ma)) (@ (@ tptp.ord_less_nat tptp.xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_VEBT_VEBT2 Xs2))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_o2 Xs2))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_nat2 Xs2))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_int2 Xs2))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) I2) X))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) I2) X))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) I2) X))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) I2) X))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I2) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I2) (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I2) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I2) (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2))))
% 6.84/7.06 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 6.84/7.06 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2)))))
% 6.84/7.06 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) _let_2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.power_8040749407984259932d_enat X) _let_2)) (@ (@ tptp.power_8040749407984259932d_enat Y) _let_2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat _let_1)) X)) Y)))))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.84/7.06 (assert (and (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.xa) (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma)))
% 6.84/7.06 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary)) N2) (= Deg N2))))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.na))
% 6.84/7.06 (assert (= tptp.xa tptp.mi))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X)) I2) Y) (@ _let_1 Y)))))
% 6.84/7.06 (assert (or (not (= tptp.xa tptp.mi)) (not (= tptp.xa tptp.ma))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.one_on7984719198319812577d_enat) N2) tptp.one_on7984719198319812577d_enat)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N2) tptp.one_one_real)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N2) tptp.one_one_complex)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) (@ tptp.size_size_list_o Xs2))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) (@ tptp.size_size_list_nat Xs2))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) (@ tptp.size_size_list_int Xs2))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ (@ tptp.nth_nat Xs2) I2)) Xs2)))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs2) I2) (@ (@ tptp.nth_int Xs2) I2)) Xs2)))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) Xs2)))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J) (@ (@ tptp.nth_nat Xs2) J)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J) (@ (@ tptp.nth_int Xs2) J)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J) (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat N2) tptp.one_on7984719198319812577d_enat) (= N2 tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N2) tptp.one_one_complex) (= N2 tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real N2) tptp.one_one_real) (= N2 tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat N2) tptp.one_one_nat) (= N2 tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int N2) tptp.one_one_int) (= N2 tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.numera1916890842035813515d_enat N2)) (= tptp.one N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N2)) (= tptp.one N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N2)) (= tptp.one N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N2)) (= tptp.one N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N2)) (= tptp.one N2))))
% 6.84/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.84/7.06 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.84/7.06 (assert (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))
% 6.84/7.06 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.84/7.06 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.84/7.06 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.84/7.06 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.84/7.06 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_complex) (B2 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) B2) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 (@ tptp.set_complex2 Xs2)) (@ _let_1 B2)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) B2) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ _let_1 B2)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (B2 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) B2) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs2)) (@ _let_1 B2)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) B2) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs2)) (@ _let_1 B2)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) B2) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 Xs2)) (@ _let_1 B2)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) B2) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs2)) (@ _let_1 B2)))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N2) (@ (@ tptp.plus_plus_num N2) tptp.one))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.84/7.06 (assert (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.84/7.06 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.84/7.06 (assert (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat)))
% 6.84/7.06 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.84/7.06 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.84/7.06 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.84/7.06 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_7803423173614009249d_enat X) Y) tptp.one_on7984719198319812577d_enat) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.power_8040749407984259932d_enat X) N2)) (@ (@ tptp.power_8040749407984259932d_enat Y) N2)) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) tptp.one_one_complex))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) tptp.one_one_real))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_complex A) N2))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_complex) (A2 tptp.set_complex) (X tptp.complex) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (=> (@ (@ tptp.member_complex X) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) I2) X))) A2)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) I2) X))) A2)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I2) X))) A2)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X))) A2)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_real) (A2 tptp.set_real) (X tptp.real) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A2) (=> (@ (@ tptp.member_real X) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I2) X))) A2)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I2) X))) A2)))))
% 6.84/7.06 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) _let_2))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 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) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 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) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 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) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N3)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N3)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N3)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N3)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N3)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N3)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))))
% 6.84/7.06 (assert (= (@ tptp.numera1916890842035813515d_enat tptp.one) tptp.one_on7984719198319812577d_enat))
% 6.84/7.06 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.84/7.06 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.84/7.06 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.84/7.06 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.84/7.06 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.84/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.06 (assert (= (@ (@ tptp.power_8040749407984259932d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_on7984719198319812577d_enat))
% 6.84/7.06 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.84/7.06 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.84/7.06 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.84/7.06 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs2 Ys)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (not (= Xs2 Ys)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (not (= Xs2 Ys)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (not (= Xs2 Ys)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N2))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (I3 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X6 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs2))) (=> (not (= I2 I3)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I2) X)) I3) X6) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I3) X6)) I2) X))))))
% 6.84/7.06 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.84/7.06 (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 ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))))))))
% 6.84/7.06 (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 ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat)))))))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N2))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N2))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N2))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N2))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N2)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_real (@ _let_1 M)) N2)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_int (@ _let_1 M)) N2)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N2)))))
% 6.84/7.06 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.84/7.06 (assert (forall ((P (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.84/7.06 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.84/7.06 (assert (forall ((P (-> tptp.list_int Bool)) (Xs2 tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I4) (@ (@ tptp.nth_VEBT_VEBT Ys) I4)))) (= Xs2 Ys)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I4) (@ (@ tptp.nth_o Ys) I4)))) (= Xs2 Ys)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I4) (@ (@ tptp.nth_nat Ys) I4)))) (= Xs2 Ys)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I4) (@ (@ tptp.nth_int Ys) I4)))) (= Xs2 Ys)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.vEBT_VEBT)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_VEBT_VEBT Xs) I5)))))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 Bool)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_o Xs) I5)))))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.nat)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_nat Xs) I5)))))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.int)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_int Xs) I5)))))))))
% 6.84/7.06 (assert (= (lambda ((Y4 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y4 Z2)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I5) (@ (@ tptp.nth_VEBT_VEBT Ys3) I5))))))))
% 6.84/7.06 (assert (= (lambda ((Y4 tptp.list_o) (Z2 tptp.list_o)) (= Y4 Z2)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I5) (@ (@ tptp.nth_o Ys3) I5))))))))
% 6.84/7.06 (assert (= (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Ys3) I5))))))))
% 6.84/7.06 (assert (= (lambda ((Y4 tptp.list_int) (Z2 tptp.list_int)) (= Y4 Z2)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I5) (@ (@ tptp.nth_int Ys3) I5))))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N2)) (@ tptp.set_real2 Xs2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N2)) (@ tptp.set_complex2 Xs2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N2)) (@ tptp.set_Pr5648618587558075414at_nat Xs2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N2)) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N2)) (@ tptp.set_o2 Xs2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N2)) (@ tptp.set_nat2 Xs2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N2)) (@ tptp.set_int2 Xs2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X5))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs2)) (@ P X5))) (@ P (@ (@ tptp.nth_o Xs2) N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs2)) (@ P X5))) (@ P (@ (@ tptp.nth_nat Xs2) N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs2)) (@ P X5))) (@ P (@ (@ tptp.nth_int Xs2) N2))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I5) X))))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I5) X))))))
% 6.84/7.06 (assert (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s5460976970255530739at_nat Xs2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I5) X))))))
% 6.84/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I5) X))))))
% 6.84/7.06 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I5) X))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I5) X))))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I5) X))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I4)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P X)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I4)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P X)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I4)))) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I4)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I4)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I4)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I4)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X)))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I5)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I5)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I5)))))))
% 6.84/7.06 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I5)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N2) X))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N2) X))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) N2) X))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N2) X))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N2) X))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N2) X))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N2) X))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool) (J tptp.nat)) (let ((_let_1 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) J) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J)))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J)))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) X)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_o Xs2) I2) X)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_nat Xs2) I2) X)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_int Xs2) I2) X)))))
% 6.84/7.06 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X) X)) X)) X))))
% 6.84/7.06 (assert (forall ((X tptp.real)) (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X) X)) X)) X))))
% 6.84/7.06 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.power_power_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X) X)) X)) X))))
% 6.84/7.06 (assert (forall ((X tptp.int)) (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X) X)) X)) X))))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 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) N2)) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 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) N2)) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 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) N2)) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (N2 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) N2)) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat K) M)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 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 N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.06 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (= tptp.xa tptp.mi))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_5)))))) (=> (not _let_4) (= _let_3 tptp.xa)))))))))
% 6.84/7.06 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))))
% 6.84/7.06 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))))
% 6.84/7.06 (assert (@ (@ tptp.vEBT_vebt_member tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na)))
% 6.84/7.06 (assert (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)) tptp.lx))
% 6.84/7.06 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.84/7.06 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na))))) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.xa) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat _let_3) (@ (@ (@ tptp.if_nat (= _let_3 tptp.ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT _let_5) _let_4))))) tptp.ma)))) tptp.deg) _let_5) tptp.summary))))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N2)) (= M N2))))
% 6.84/7.06 (assert (forall ((R tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R)) (@ (@ tptp.divide_divide_real A) R)))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit0 N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.84/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.06 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N2) N2)))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N2) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 6.84/7.06 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.deg))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Newlist 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.product_Pair_nat_nat Mi))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_4 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_2) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) (@ (@ tptp.power_power_nat _let_1) _let_2))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_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.power_power_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xn) _let_2))) (let ((_let_6 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_5 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_6))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_2) L2) (=> (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))
% 6.84/7.06 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx)))
% 6.84/7.06 (assert (= (@ tptp.some_nat tptp.summin) (@ tptp.vEBT_vebt_mint tptp.summary)))
% 6.84/7.06 (assert (= (@ tptp.some_nat tptp.lx) (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin))))
% 6.84/7.06 (assert (forall ((S tptp.set_real)) (=> (exists ((X3 tptp.real)) (@ (@ tptp.member_real X3) S)) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real X5) Z3)))) (exists ((Y5 tptp.real)) (and (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S) (@ (@ tptp.ord_less_eq_real X3) Y5))) (forall ((Z3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real X5) Z3))) (@ (@ tptp.ord_less_eq_real Y5) Z3)))))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X) N4))))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y3) (= X2 Y3)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J)) U)) K))))
% 6.84/7.06 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))))
% 6.84/7.06 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N2) (=> (= N2 (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))))
% 6.84/7.06 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))))
% 6.84/7.06 (assert (forall ((X tptp.nat)) (=> (forall ((N4 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N4) N4)))) (not (forall ((N4 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N4) (@ tptp.suc N4)))))))))
% 6.84/7.06 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N2))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N2))) TreeList3) S2))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.84/7.06 (assert (not (forall ((Summin tptp.nat)) (not (= (@ tptp.some_nat Summin) (@ tptp.vEBT_vebt_mint tptp.summary))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.84/7.06 (assert (= (@ tptp.suc tptp.na) tptp.m))
% 6.84/7.06 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.84/7.06 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22))))
% 6.84/7.06 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat X) Maxi))))))
% 6.84/7.06 (assert (not (forall ((Lx tptp.nat)) (not (= (@ tptp.some_nat Lx) (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ 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))) N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N2)))))
% 6.84/7.06 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.06 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.06 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.06 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.06 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.one_one_Code_integer) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M) _let_1))))))
% 6.84/7.06 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 6.84/7.06 (assert (forall ((P (-> tptp.extended_enat Bool)) (N2 tptp.extended_enat)) (=> (forall ((N4 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N4) (@ P M2))) (@ P N4))) (@ P N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N2)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N2) Q2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N2)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N2) Q2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q2))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M N2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (or (@ P N2) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N2) (@ P I5)))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M N2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (and (@ P N2) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N2) (@ P I5)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M) (exists ((M3 tptp.nat)) (and (= M (@ tptp.suc M3)) (@ (@ tptp.ord_less_nat N2) M3))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I2) J))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (=> (= J (@ tptp.suc I4)) (@ P I4))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J) (=> (@ P (@ tptp.suc I4)) (@ P I4)))) (@ P I2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N2 M))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (forall ((X5 tptp.nat)) (@ (@ R2 X5) X5)) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ R2 X5))) (=> (@ _let_1 Y5) (=> (@ (@ R2 Y5) Z4) (@ _let_1 Z4))))) (=> (forall ((N4 tptp.nat)) (@ (@ R2 N4) (@ tptp.suc N4))) (@ (@ R2 M) N2)))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P M) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N4) (=> (@ P N4) (@ P (@ tptp.suc N4))))) (@ P N2))))))
% 6.84/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N4) (@ P M2))) (@ P N4))) (@ P N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M _let_1)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M _let_1)))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.06 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_num (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_real (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_num (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.set_real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_real (@ F N5)) (@ F N2))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N5)) (@ F N2))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N2))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N2))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N2))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.set_real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_real (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N5))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P I2) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N4) (=> (@ (@ tptp.ord_less_nat N4) J) (=> (@ P N4) (@ P (@ tptp.suc N4)))))) (@ P J))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P J) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N4) (=> (@ (@ tptp.ord_less_nat N4) J) (=> (@ P (@ tptp.suc N4)) (@ P N4))))) (@ P I2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)) (= N2 M)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.06 (assert (= tptp.ord_less_nat (lambda ((N tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) __flatten_var_0))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (forall ((Q3 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 6.84/7.06 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M) N2)))))
% 6.84/7.06 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.84/7.06 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.84/7.06 (assert (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) A)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) A)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) A)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) A)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N2))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 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 N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 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 N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 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 N2)))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))))
% 6.84/7.06 (assert (forall ((S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S3) T) (not (= S3 T)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.84/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N4) (@ P M2))) (@ P N4))) (@ P N2))))
% 6.84/7.06 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (not (@ P N4)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N4) (not (@ P M2)))))) (@ P N2))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.84/7.06 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y2 tptp.nat)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_nat Y2) X5)))))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)))
% 6.84/7.06 (assert (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))))
% 6.84/7.06 (assert (forall ((X tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y))) (not (= X Y)))))
% 6.84/7.06 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))))
% 6.84/7.06 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))))
% 6.84/7.06 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N2) Q2))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (N2 tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N2))))
% 6.84/7.06 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (N2 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) N2))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1)))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (N2 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) N2))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1)))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (N2 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) N2))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1)))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (N2 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) N2))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1)))))))
% 6.84/7.06 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (not (= M6 N))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N) (= M6 N)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J2) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) K) (@ (@ tptp.ord_less_nat I2) K))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))))
% 6.84/7.06 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N4 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N4))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M6) K3))))))
% 6.84/7.06 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.84/7.06 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) L2))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 6.84/7.06 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N4) (@ (@ tptp.ord_less_nat (@ F M5)) (@ F N4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.84/7.06 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Ma))))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Mi))))))
% 6.84/7.06 (assert (= tptp.ord_less_nat (lambda ((Y3 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)))))
% 6.84/7.06 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z5 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z5) (@ (@ tptp.ord_less_nat X) Z5)) (@ (@ tptp.ord_less_eq_nat Y) Z5)))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z5 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z5) (@ (@ tptp.ord_less_nat Z5) X)) (@ (@ tptp.ord_less_eq_nat Z5) Y)))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Px)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Sx)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 6.84/7.06 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N2) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M5) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))))
% 6.84/7.06 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.84/7.06 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.84/7.06 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.84/7.06 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList2) Summary)))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Ma))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Mi))))
% 6.84/7.06 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y3 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y3))))))
% 6.84/7.06 (assert (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y3 tptp.nat)) (= X (@ tptp.some_nat Y3))))))
% 6.84/7.06 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y3 tptp.num)) (= X (@ tptp.some_num Y3))))))
% 6.84/7.06 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y3 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y3)))) (= X tptp.none_P5556105721700978146at_nat))))
% 6.84/7.06 (assert (forall ((X tptp.option_nat)) (= (forall ((Y3 tptp.nat)) (not (= X (@ tptp.some_nat Y3)))) (= X tptp.none_nat))))
% 6.84/7.06 (assert (forall ((X tptp.option_num)) (= (forall ((Y3 tptp.num)) (not (= X (@ tptp.some_num Y3)))) (= X tptp.none_num))))
% 6.84/7.06 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (and (@ (@ tptp.ord_le6747313008572928689nteger X) Z) (@ (@ tptp.ord_le6747313008572928689nteger Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y)) Z) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y)) Z) (and (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (and (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z) (and (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.84/7.06 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X22 Y22))))
% 6.84/7.06 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y22)) (= X22 Y22))))
% 6.84/7.06 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y22)) (= X22 Y22))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_max_nat A) B))) (= (@ (@ tptp.ord_max_nat _let_1) B) _let_1))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) B) _let_1))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.ord_max_int A) B))) (= (@ (@ tptp.ord_max_int _let_1) B) _let_1))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.ord_max_Code_integer A) B))) (= (@ (@ tptp.ord_max_Code_integer _let_1) B) _let_1))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_max_int A) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A) A) A)))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_eq_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X) tptp.none_nat))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N2)) K))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (and (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (and (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ (@ tptp.ord_le3102999989581377725nteger C) A)))))
% 6.84/7.06 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C) A)))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 6.84/7.06 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ _let_1 (@ _let_1 I2)) I2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) D)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex C) D)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D)))))
% 6.84/7.06 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I2 tptp.nat)) (=> (@ P K) (=> (forall ((N4 tptp.nat)) (=> (@ P (@ tptp.suc N4)) (@ P N4))) (@ P (@ (@ tptp.minus_minus_nat K) I2))))))
% 6.84/7.06 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A) B)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F A) B)))))
% 6.84/7.06 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F A) B)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N2) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M))))))))
% 6.84/7.06 (assert (forall ((J tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N2)) K))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N2) L2)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M N2)))))))
% 6.84/7.06 (assert (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv tptp.option4927543243414619207at_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uu) tptp.none_P5556105721700978146at_nat) Uv) tptp.none_P5556105721700978146at_nat)))
% 6.84/7.06 (assert (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu) tptp.none_num) Uv) tptp.none_num)))
% 6.84/7.06 (assert (forall ((Uu (-> tptp.nat tptp.nat tptp.nat)) (Uv tptp.option_nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M) N2)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y) B))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) A)) B))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N2) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M) N2)) M))))
% 6.84/7.06 (assert (forall ((J tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I2) K)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.minus_minus_nat J) I2) K) (= J (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M)) M) (@ (@ tptp.ord_max_nat N2) M))))
% 6.84/7.06 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.84/7.06 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.84/7.06 (assert (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw) (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)))
% 6.84/7.06 (assert (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)))
% 6.84/7.06 (assert (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw) (@ tptp.some_nat V)) tptp.none_nat) tptp.none_nat)))
% 6.84/7.06 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb) Y) (=> (=> (= 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 ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B3 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B3)) (not (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B3)))))))))))))))
% 6.84/7.06 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B3 tptp.num)) (=> (= Xb (@ tptp.some_num B3)) (not (= Y (@ tptp.some_num (@ (@ X A3) B3)))))))))))))))
% 6.84/7.06 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B3 tptp.nat)) (=> (= Xb (@ tptp.some_nat B3)) (not (= Y (@ tptp.some_nat (@ (@ X A3) B3)))))))))))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I2) K))))))
% 6.84/7.06 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M) N2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.84/7.06 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.84/7.06 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat B))) (let ((_let_2 (@ tptp.ord_max_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat B))) (let ((_let_2 (@ tptp.ord_ma741700101516333627d_enat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int B))) (let ((_let_2 (@ tptp.ord_max_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer B))) (let ((_let_2 (@ tptp.ord_max_Code_integer A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_max_nat B4) A4))))
% 6.84/7.06 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ tptp.ord_ma741700101516333627d_enat B4) A4))))
% 6.84/7.06 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_max_int B4) A4))))
% 6.84/7.06 (assert (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.ord_max_Code_integer B4) A4))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A))) (= (@ (@ tptp.ord_max_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_nat B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat A))) (= (@ (@ tptp.ord_ma741700101516333627d_enat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (= (@ (@ tptp.ord_max_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_int B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer A))) (= (@ (@ tptp.ord_max_Code_integer (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_Code_integer B) C))))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X)) _let_1)))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X)) _let_1)))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X)) _let_1)))))
% 6.84/7.06 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)))))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.84/7.06 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.84/7.06 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4) B4))))
% 6.84/7.06 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A4) B4) B4))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) B4))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) B4))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) B4))))
% 6.84/7.06 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4) A4))))
% 6.84/7.06 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A4) B4) A4))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) A4))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) A4))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) A4))))
% 6.84/7.06 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.ord_max_Code_integer A) B))))
% 6.84/7.06 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.ord_max_Code_integer A) B))))
% 6.84/7.06 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.84/7.06 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4)))))
% 6.84/7.06 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (= A4 (@ (@ tptp.ord_max_Code_integer A4) B4)))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= A4 (@ (@ tptp.ord_max_num A4) B4)))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.ord_max_nat A4) B4)))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.ord_max_int A4) B4)))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A)))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A)))))
% 6.84/7.06 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A)))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (not (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (not (@ (@ tptp.ord_le3102999989581377725nteger C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A (@ (@ tptp.ord_max_Code_integer A) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))
% 6.84/7.06 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= A (@ (@ tptp.ord_max_Code_integer A) B)))))
% 6.84/7.06 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C) D)) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger D) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer C) D)) (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D)) (@ (@ tptp.ord_max_num A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B))))))
% 6.84/7.06 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (not (@ (@ tptp.ord_le6747313008572928689nteger C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 6.84/7.06 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (and (= A4 (@ (@ tptp.ord_max_Code_integer A4) B4)) (not (= A4 B4))))))
% 6.84/7.06 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (and (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4)) (not (= A4 B4))))))
% 6.84/7.06 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B4)) (not (= A4 B4))))))
% 6.84/7.06 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B4)) (not (= A4 B4))))))
% 6.84/7.06 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.ord_max_nat A4) B4)) (not (= A4 B4))))))
% 6.84/7.06 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.ord_max_int A4) B4)) (not (= A4 B4))))))
% 6.84/7.06 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.84/7.06 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.84/7.06 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X7 tptp.option4927543243414619207at_nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P3 tptp.none_P5556105721700978146at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.84/7.06 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (forall ((X7 tptp.option_nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.option_nat Bool))) (and (@ P3 tptp.none_nat) (forall ((X2 tptp.nat)) (@ P3 (@ tptp.some_nat X2)))))))
% 6.84/7.06 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (forall ((X7 tptp.option_num)) (@ P2 X7))) (lambda ((P3 (-> tptp.option_num Bool))) (and (@ P3 tptp.none_num) (forall ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))))
% 6.84/7.06 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X7 tptp.option4927543243414619207at_nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P3 tptp.none_P5556105721700978146at_nat) (exists ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.84/7.06 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (exists ((X7 tptp.option_nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.option_nat Bool))) (or (@ P3 tptp.none_nat) (exists ((X2 tptp.nat)) (@ P3 (@ tptp.some_nat X2)))))))
% 6.84/7.06 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (exists ((X7 tptp.option_num)) (@ P2 X7))) (lambda ((P3 (-> tptp.option_num Bool))) (or (@ P3 tptp.none_num) (exists ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))))
% 6.84/7.06 (assert (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 6.84/7.06 (assert (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (@ tptp.some_nat X23))))))))
% 6.84/7.06 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))))
% 6.84/7.06 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.84/7.06 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 6.84/7.06 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 6.84/7.06 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 6.84/7.06 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 6.84/7.06 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 6.84/7.06 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 6.84/7.06 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 6.84/7.06 (assert (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)))
% 6.84/7.06 (assert (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_Pr8591224930841456533at_nat Option) (@ tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))))
% 6.84/7.06 (assert (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_nat Option) (@ tptp.the_nat Option2)))) (= Option Option2)))))))
% 6.84/7.06 (assert (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))))
% 6.84/7.06 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.84/7.06 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.84/7.06 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A))))
% 6.84/7.06 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.84/7.06 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 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 N2))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 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 N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.84/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex C))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_complex A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) A) B)))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.one_on7984719198319812577d_enat) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex A) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real A) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A) B))))
% 6.84/7.06 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (= tptp.times_times_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.times_times_complex B4) A4))))
% 6.84/7.06 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real B4) A4))))
% 6.84/7.06 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.times_times_nat B4) A4))))
% 6.84/7.06 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int B4) A4))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex B))) (let ((_let_2 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.06 (assert (= tptp.plus_plus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex B4) A4))))
% 6.84/7.06 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real B4) A4))))
% 6.84/7.06 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A4))))
% 6.84/7.06 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A4))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.84/7.06 (assert (forall ((B2 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (let ((_let_2 (@ tptp.plus_plus_complex K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 6.84/7.06 (assert (forall ((B2 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))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 6.84/7.06 (assert (forall ((B2 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))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 6.84/7.06 (assert (forall ((B2 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))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 6.84/7.06 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_complex A2) B) (@ _let_1 (@ (@ tptp.plus_plus_complex A) B)))))))
% 6.84/7.06 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.84/7.06 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.84/7.06 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_real I2) K) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.84/7.06 (assert (forall ((X tptp.extended_enat)) (= (= tptp.one_on7984719198319812577d_enat X) (= X tptp.one_on7984719198319812577d_enat))))
% 6.84/7.06 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.84/7.06 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.84/7.06 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.84/7.06 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.84/7.06 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (exists ((C2 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A4) C2))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat C) D) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) (@ (@ tptp.plus_p3455044024723400733d_enat B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (E tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) E)) C))))
% 6.84/7.06 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 6.84/7.06 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.one_on7984719198319812577d_enat) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B) A)) (@ (@ tptp.times_times_complex C) A)))))
% 6.84/7.06 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C) A)))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 6.84/7.06 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex C) B) A) (= C (@ (@ tptp.minus_minus_complex A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 C)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.minus_minus_complex C) B)) (= (@ (@ tptp.plus_plus_complex A) B) C))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.minus_minus_complex A) B) C) (= A (@ (@ tptp.plus_plus_complex C) B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))))
% 6.84/7.06 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_complex A2) B) (@ _let_1 (@ (@ tptp.minus_minus_complex A) B)))))))
% 6.84/7.06 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 6.84/7.06 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.84/7.06 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger X))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer Y) Z)) (@ (@ tptp.ord_max_Code_integer (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z)) (@ (@ tptp.plus_plus_real Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Z)) (@ (@ tptp.plus_p5714425477246183910nteger Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Z)) (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z)) (@ (@ tptp.minus_minus_real Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.84/7.06 (assert (forall ((M tptp.real) (N2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_real M) N2)))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.84/7.06 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M) N2)))))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat B) tptp.one_on7984719198319812577d_enat)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B) tptp.one_one_real)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.84/7.06 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N2) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N2) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))))
% 6.84/7.06 (assert (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N2) K)))))
% 6.84/7.06 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N2) K)))))
% 6.84/7.06 (assert (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N2) K)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B)) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B)) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) (@ (@ tptp.times_times_complex Y) Y)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex X) Y)))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) A)) E)) D)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) E)) C) D))))
% 6.84/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D))))
% 6.84/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D))))
% 6.84/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.84/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.84/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.84/7.06 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.84/7.06 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))
% 6.84/7.06 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.84/7.06 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real B) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.84/7.06 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C))))
% 6.84/7.06 (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)))
% 6.84/7.06 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.none_nat)))
% 6.84/7.06 (assert (forall ((L2 tptp.num) (R tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L2) (@ (@ tptp.product_Pair_nat_nat Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R))))))))))
% 6.84/7.06 (assert (forall ((L2 tptp.num) (R tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L2) (@ (@ tptp.product_Pair_int_int Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_int L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R))))))))))
% 6.84/7.06 (assert (forall ((L2 tptp.num) (R tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L2) (@ (@ tptp.produc1086072967326762835nteger Q2) R)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R))))))))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _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) X) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.84/7.06 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.84/7.06 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= X Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 Ma))) Deg) TreeList2) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_3) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT) (Summary tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high X) _let_4))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_6 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_4) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_3) _let_4)) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn))))))))))))))))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) _let_1))) (let ((_let_3 (@ tptp.nth_VEBT_VEBT _let_2))) (let ((_let_4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_5 (@ (@ tptp.divide_divide_nat Deg) _let_4))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_4) _let_5))) (let ((_let_7 (@ tptp.if_nat (= X Ma)))) (let ((_let_8 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_5))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_4) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_5) L2) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_1)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 _let_11)))))) Ma)))) Deg) _let_2) _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 H2))))) Ma)))) Deg) _let_2) Summary)))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (= X Mi))) (let ((_let_9 (@ tptp.if_nat _let_8))) (let ((_let_10 (@ (@ _let_9 _let_7) X))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_high _let_10) _let_3))) (let ((_let_12 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_11)) (@ (@ tptp.vEBT_VEBT_low _let_10) _let_3)))) (let ((_let_13 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_11) _let_12))) (let ((_let_14 (@ tptp.nth_VEBT_VEBT _let_13))) (let ((_let_15 (@ tptp.if_nat (and (=> _let_8 (= _let_7 Ma)) (=> (not _let_8) (= X Ma)))))) (let ((_let_16 (@ (@ _let_9 _let_10) Mi))) (let ((_let_17 (@ tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (@ (@ tptp.vEBT_vebt_delete Summary) _let_11))) (let ((_let_19 (@ tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (@ tptp.the_nat _let_19))) (=> (and (@ (@ tptp.ord_less_eq_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_11) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_12)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ (@ tptp.if_nat (= _let_19 tptp.none_nat)) _let_16) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_20)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_20)))))) Ma)))) Deg) _let_13) _let_18)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_11) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_11))))) Ma)))) Deg) _let_13) Summary))) _let_1)))))))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H2)) L2))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT _let_3))) (let ((_let_5 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_6 (@ (@ tptp.divide_divide_nat Deg) _let_5))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_5) _let_6))) (let ((_let_8 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_9 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_10 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ tptp.the_nat _let_11))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_6))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_5) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_1 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_6) L2) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ (@ tptp.if_nat (= _let_11 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_12)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 _let_12)))))) Ma)))) Deg) _let_3) _let_10)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 H2))))) Ma)))) Deg) _let_3) Summary))))))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_3))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_12 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_3) L2) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_high Xn) _let_4))) (let ((_let_8 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_7 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_5)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_8))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_4) L2) (=> (@ (@ tptp.ord_less_nat _let_7) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn)))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_8)) (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3)))) (let ((_let_10 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_8) _let_9))) (let ((_let_11 (@ tptp.nth_VEBT_VEBT _let_10))) (let ((_let_12 (@ tptp.if_nat (= _let_7 Ma)))) (let ((_let_13 (@ tptp.product_Pair_nat_nat _let_7))) (let ((_let_14 (@ (@ tptp.vEBT_vebt_delete Summary) _let_8))) (let ((_let_15 (@ tptp.vEBT_vebt_maxt _let_14))) (let ((_let_16 (@ tptp.the_nat _let_15))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ (@ tptp.if_nat (= _let_15 tptp.none_nat)) _let_7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_16)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_16)))))) Ma)))) Deg) _let_10) _let_14)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_8))))) Ma)))) Deg) _let_10) Summary))) _let_1)))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.84/7.06 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _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) X) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.84/7.06 (assert (forall ((C tptp.complex)) (= (lambda ((X2 tptp.complex)) (@ (@ tptp.times_times_complex X2) C)) (@ tptp.times_times_complex C))))
% 6.84/7.06 (assert (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))))
% 6.84/7.06 (assert (forall ((C tptp.nat)) (= (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C)) (@ tptp.times_times_nat C))))
% 6.84/7.06 (assert (forall ((C tptp.int)) (= (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int X2) C)) (@ tptp.times_times_int C))))
% 6.84/7.06 (assert (= (lambda ((X2 tptp.extended_enat)) X2) (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat)))
% 6.84/7.06 (assert (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.84/7.06 (assert (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)))
% 6.84/7.06 (assert (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.84/7.06 (assert (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)))
% 6.84/7.06 (assert (forall ((X tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) (@ tptp.some_P7363390416028606310at_nat B3)))))))))))
% 6.84/7.06 (assert (forall ((X tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) (@ tptp.some_nat B3)))))))))))
% 6.84/7.06 (assert (forall ((X tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A3 tptp.num) (B3 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) (@ tptp.some_num B3)))))))))))
% 6.84/7.06 (assert (forall ((X tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X5 tptp.product_prod_nat_nat) (Y5 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X5)) (@ tptp.some_P7363390416028606310at_nat Y5)))))))))))
% 6.84/7.06 (assert (forall ((X tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X5 tptp.nat) (Y5 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X5)) (@ tptp.some_nat Y5)))))))))))
% 6.84/7.06 (assert (forall ((X tptp.produc7036089656553540234on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num Bool)) (X5 tptp.num) (Y5 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X5)) (@ tptp.some_num Y5)))))))))))
% 6.84/7.06 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.84/7.06 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.84/7.06 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.84/7.06 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.84/7.06 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.84/7.06 (assert (forall ((X3 tptp.real)) (exists ((Y5 tptp.real)) (@ (@ tptp.ord_less_real Y5) X3))))
% 6.84/7.06 (assert (forall ((X3 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X3) X_1))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) W)))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex Y) W)))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W)) (@ (@ tptp.times_times_real Y) Z)))))
% 6.84/7.06 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W)) (@ (@ tptp.times_times_complex Y) Z)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B))))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 6.84/7.06 (assert (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat X) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.84/7.06 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.member_nat Y3) Xs) (@ (@ tptp.ord_less_nat Y3) X2) (forall ((Z5 tptp.nat)) (=> (@ (@ tptp.member_nat Z5) Xs) (=> (@ (@ tptp.ord_less_nat Z5) X2) (@ (@ tptp.ord_less_eq_nat Z5) Y3))))))))
% 6.84/7.06 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.member_nat Y3) Xs) (@ (@ tptp.ord_less_nat X2) Y3) (forall ((Z5 tptp.nat)) (=> (@ (@ tptp.member_nat Z5) Xs) (=> (@ (@ tptp.ord_less_nat X2) Z5) (@ (@ tptp.ord_less_eq_nat Y3) Z5))))))))
% 6.84/7.06 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) __flatten_var_0))))
% 6.84/7.06 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (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.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= X Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= X Ma))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (@ (@ tptp.vEBT_vebt_delete _let_2) X))) (let ((_let_24 (and _let_9 _let_16))) (let ((_let_25 (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)))) (and (=> _let_25 (= _let_23 _let_2)) (=> (not _let_25) (and (=> _let_24 (= _let_23 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary))) (=> (not _let_24) (= _let_23 (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma)))) _let_1) _let_14) Summary))) _let_2)))))))))))))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y3 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat X) Y3)))) tptp.bot_bot_set_nat)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y3 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat Y3) X)))) tptp.bot_bot_set_nat)))))
% 6.84/7.06 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 6.84/7.06 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S3)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.84/7.06 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.84/7.06 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 Bool)) (=> (exists ((Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (exists ((Va2 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va2)))) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc 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 TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.06 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A4 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B4))))))
% 6.84/7.06 (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))))))
% 6.84/7.06 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= N2 tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3)))))))
% 6.84/7.06 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))
% 6.84/7.06 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 6.84/7.06 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y222 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 6.84/7.06 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((N2 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2)) (= N2 tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.zero_z5237406670263579293d_enat) (or (= A tptp.zero_z5237406670263579293d_enat) (= B tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.zero_z5237406670263579293d_enat) A) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.zero_z5237406670263579293d_enat) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.84/7.06 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (= tptp.zero_z5237406670263579293d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.84/7.06 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.06 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.zero_z5237406670263579293d_enat) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.84/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.84/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.84/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.84/7.06 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.84/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))))
% 6.84/7.06 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))))
% 6.84/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.06 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 6.84/7.06 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 6.84/7.06 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_real B) A))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))))
% 6.84/7.06 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.84/7.06 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.84/7.06 (assert (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C) A) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C) A) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.84/7.06 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.84/7.06 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) A))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) A) B))))
% 6.84/7.06 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) A) B))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 6.84/7.06 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.84/7.06 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))))
% 6.84/7.06 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))))
% 6.84/7.06 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.84/7.06 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.84/7.06 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.84/7.06 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.84/7.06 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger A) A) tptp.one_one_Code_integer))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 6.84/7.06 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))))
% 6.84/7.06 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 6.84/7.06 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 6.84/7.06 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.suc N2)) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)))
% 6.84/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numeral_numeral_nat K)) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.84/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.84/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.84/7.06 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.84/7.06 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.84/7.06 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.84/7.06 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.84/7.06 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))))
% 6.84/7.06 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.zero_z3403309356797280102nteger) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (= M _let_1) (= N2 _let_1))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))))
% 6.84/7.06 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (@ _let_1 M) (@ _let_1 N2))))))
% 6.84/7.06 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.84/7.06 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.84/7.06 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.06 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.84/7.06 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.84/7.06 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.07 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.84/7.07 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.07 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.84/7.07 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M) _let_1) (or (= M tptp.zero_zero_nat) (= X _let_1))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (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) N2)))))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.84/7.07 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 6.84/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M)) N2) M))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N2)) N2) M))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.84/7.07 (assert (forall ((B tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))))
% 6.84/7.07 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.84/7.07 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.84/7.07 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.84/7.07 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.84/7.07 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.84/7.07 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((B tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.84/7.07 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 6.84/7.07 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B))))
% 6.84/7.07 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux))))
% 6.84/7.07 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.84/7.07 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.84/7.07 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.84/7.07 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))))
% 6.84/7.07 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.84/7.07 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X5)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2)) X5)))))))))
% 6.84/7.07 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on7984719198319812577d_enat)) (=> (not _let_2) (= _let_1 tptp.zero_z5237406670263579293d_enat)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N2) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N2) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2) tptp.zero_zero_complex))))
% 6.84/7.07 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))))
% 6.84/7.07 (assert (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.84/7.07 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) Deg3))))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.07 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) X)))
% 6.84/7.07 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.84/7.07 (assert (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (=> (not (= N2 tptp.zero_z5237406670263579293d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.07 (assert (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N2)))))
% 6.84/7.07 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (= A B)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 6.84/7.07 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (not (= A tptp.zero_z5237406670263579293d_enat)) (=> (not (= B tptp.zero_z5237406670263579293d_enat)) (not (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.zero_z5237406670263579293d_enat))))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.zero_z5237406670263579293d_enat) (or (= A tptp.zero_z5237406670263579293d_enat) (= B tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (not (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.zero_z5237406670263579293d_enat)) (and (not (= A tptp.zero_z5237406670263579293d_enat)) (not (= B tptp.zero_z5237406670263579293d_enat))))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.zero_z5237406670263579293d_enat) A)))
% 6.84/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.zero_z5237406670263579293d_enat) A) A)))
% 6.84/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.84/7.07 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.84/7.07 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.84/7.07 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.84/7.07 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.84/7.07 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.84/7.07 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex)))))
% 6.84/7.07 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.84/7.07 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.84/7.07 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.84/7.07 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.84/7.07 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va2 tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va2))))))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ tptp.suc N4)))) (@ P N2)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (@ (@ P X5) tptp.zero_zero_nat)) (=> (forall ((Y5 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y5))) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ P X5) Y5) (@ (@ P (@ tptp.suc X5)) (@ tptp.suc Y5)))) (@ (@ P M) N2))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N4 tptp.nat)) (=> (@ P (@ tptp.suc N4)) (@ P N4))) (@ P tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (not (@ P N4)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N4) (not (@ P M2))))))) (@ P N2)))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (= M N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.84/7.07 (assert (forall ((A Bool) (B Bool) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) (@ tptp.suc (@ tptp.suc N2))) _let_1))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.84/7.07 (assert (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (= A B))))))))
% 6.84/7.07 (assert (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (= A B))))))))
% 6.84/7.07 (assert (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (= A B))))))))
% 6.84/7.07 (assert (= (lambda ((H tptp.extended_enat)) tptp.zero_z5237406670263579293d_enat) (@ tptp.times_7803423173614009249d_enat tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.07 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.84/7.07 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.84/7.07 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.84/7.07 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X) (or (= X Mi) (= X Ma)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (N2 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) N2) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (N2 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) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))))
% 6.84/7.07 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc N4)))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5)))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5)))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))))
% 6.84/7.07 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))
% 6.84/7.07 (assert (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.84/7.07 (assert (forall ((A Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 6.84/7.07 (assert (forall ((B Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) tptp.zero_z5237406670263579293d_enat) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat))))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.84/7.07 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat B))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.84/7.07 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) B)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat B))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (C tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.84/7.07 (assert (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.84/7.07 (assert (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat B))) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (not (forall ((C3 tptp.extended_enat)) (=> (= B (@ (@ tptp.plus_p3455044024723400733d_enat A) C3)) (= C3 tptp.zero_z5237406670263579293d_enat)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.84/7.07 (assert (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.84/7.07 (assert (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.84/7.07 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A4) B4)) tptp.zero_zero_real))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A4) B4)) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.84/7.07 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A4) B4)) tptp.zero_zero_real))))
% 6.84/7.07 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A4) B4)) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (N2 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) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (N2 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) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C)) (= (@ (@ tptp.times_times_real A) C) B)))))
% 6.84/7.07 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (= (@ (@ tptp.times_times_complex A) C) B)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C) A) (= B (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.07 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (= B (@ (@ tptp.times_times_complex A) C))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B) (= A (@ (@ tptp.divide_divide_real B) C))))))
% 6.84/7.07 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B) C) A)))))
% 6.84/7.07 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B) C) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X) Z) (@ (@ tptp.times_times_real W) Y)))))))
% 6.84/7.07 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X) Z) (@ (@ tptp.times_times_complex W) Y)))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.power_8040749407984259932d_enat A) tptp.zero_zero_nat) tptp.one_on7984719198319812577d_enat)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.84/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (or (@ P tptp.zero_zero_nat) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N2) (@ P (@ tptp.suc I5))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M6 tptp.nat)) (= N2 (@ tptp.suc M6))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (and (@ P tptp.zero_zero_nat) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N2) (@ P (@ tptp.suc I5))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N2)))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.84/7.07 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))))
% 6.84/7.07 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J))))))
% 6.84/7.07 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.84/7.07 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.84/7.07 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.84/7.07 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.84/7.07 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) M))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))))
% 6.84/7.07 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2)) X5)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2)) X5)))))))))))
% 6.84/7.07 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S2)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5)))))))))))
% 6.84/7.07 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (Uw2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (Va2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc Va2)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ 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 (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve)) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5)))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B3)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N4))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X (@ (@ 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 (= X (@ (@ 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 (= X (@ (@ 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) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5))))))))))))
% 6.84/7.07 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S3))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.84/7.07 (assert (forall ((B Bool) (A Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))))
% 6.84/7.07 (assert (forall ((Uv Bool) (Uw Bool) (N2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N2)) tptp.none_nat)))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) B) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.one_on7984719198319812577d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) B)) tptp.one_on7984719198319812577d_enat))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.one_one_real))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))))
% 6.84/7.07 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) tptp.one_on7984719198319812577d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) A)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) A)))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.84/7.07 (assert (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat)))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 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) N2)) tptp.one_one_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 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) N2)) tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 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) N2)) tptp.one_one_int)))))
% 6.84/7.07 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.84/7.07 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.84/7.07 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B)) (= A tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.84/7.07 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 6.84/7.07 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.84/7.07 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.84/7.07 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.84/7.07 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.84/7.07 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 6.84/7.07 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.84/7.07 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.84/7.07 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.84/7.07 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 6.84/7.07 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TrLst2) Smry2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 6.84/7.07 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M) N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I2))) N2))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N2) K)))))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ P N4) (@ P (@ tptp.suc N4))))) (@ P N2))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 6.84/7.07 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 6.84/7.07 (assert (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs2)))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.84/7.07 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 6.84/7.07 (assert (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N2))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D2)) (not (@ P D2)))))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D2)) (@ P D2)))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 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) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M)))))))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.divide_divide_nat M) N2))))))
% 6.84/7.07 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N2) Q2))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))))
% 6.84/7.07 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A3) B3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 6.84/7.07 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Mi2)))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z4) (=> (@ (@ tptp.ord_less_real Z4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z4) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)) (= A tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.84/7.07 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 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 N2))) A)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 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 N2))) A)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 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 N2))) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 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 N2))) tptp.one_one_real)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 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 N2))) tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 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 N2))) tptp.one_one_int)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N3)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N3)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N3)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_z5237406670263579293d_enat))
% 6.84/7.07 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.84/7.07 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.84/7.07 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.84/7.07 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N3)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N3)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_nat A) N2)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_int A) N2)))))))
% 6.84/7.07 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.07 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.84/7.07 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= N2 (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.84/7.07 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N2) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I5)) J3)) (@ P I5))))))))))
% 6.84/7.07 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.84/7.07 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))))
% 6.84/7.07 (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)))
% 6.84/7.07 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve2)) Vf2) tptp.none_nat)))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.84/7.07 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.84/7.07 (assert (forall ((U tptp.real) (V tptp.real) (R tptp.real) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_eq_real R) S3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R) (@ (@ tptp.minus_minus_real V) U))) S3))) V))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_nat))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 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 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 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 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ (@ tptp.plus_plus_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N2))))))
% 6.84/7.07 (assert (= tptp.power_8040749407984259932d_enat (lambda ((P4 tptp.extended_enat) (M6 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M6 tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat P4) (@ (@ tptp.power_8040749407984259932d_enat P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.07 (assert (= tptp.power_power_complex (lambda ((P4 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P4) (@ (@ tptp.power_power_complex P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.07 (assert (= tptp.power_power_real (lambda ((P4 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P4) (@ (@ tptp.power_power_real P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.07 (assert (= tptp.power_power_nat (lambda ((P4 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P4) (@ (@ tptp.power_power_nat P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.07 (assert (= tptp.power_power_int (lambda ((P4 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P4) (@ (@ tptp.power_power_int P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.84/7.07 (assert (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.none_nat)))
% 6.84/7.07 (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)))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 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))) N2)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 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))) N2)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ P N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (= Y (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 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))) N2)))) (@ _let_1 A)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 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))) N2)))) (@ _let_1 A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 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))) N2)))) tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 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))) N2)))) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N2)) (@ _let_1 M)))))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N2)) (@ _let_1 N2)))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.84/7.07 (assert (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.84/7.07 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A4 Bool) (B4 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B4))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N) _let_1)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N 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 N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N) _let_3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))
% 6.84/7.07 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 N4) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 (@ tptp.suc N4)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 N4) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 (@ tptp.suc N4)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2)))))))))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.vEBT_Leaf false) B3)))))) (=> (forall ((A3 Bool)) (=> (exists ((B3 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.vEBT_Leaf A3) false)))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (exists ((N4 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc N4)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (not (= Y _let_1))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa2 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi2))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (not (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))))))))))))))))))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) Uu) _let_1))))
% 6.84/7.07 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)))))
% 6.84/7.07 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))))
% 6.84/7.07 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (forall ((Uu2 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uu2) B3)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N4 tptp.nat)) (= Xa2 (@ tptp.suc N4))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ 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) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc 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 TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))))
% 6.84/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ 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))) N2)) tptp.one_one_nat))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N2)) tptp.bot_bot_set_nat)))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)))
% 6.84/7.07 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)))
% 6.84/7.07 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)))
% 6.84/7.07 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.bot_bo4199563552545308370d_enat) X) X)))
% 6.84/7.07 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)))
% 6.84/7.07 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)))
% 6.84/7.07 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)))
% 6.84/7.07 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) tptp.bot_bo4199563552545308370d_enat) X)))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.suc N4))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low 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))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B2) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B2) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B2) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X))))
% 6.84/7.07 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real A) A)))
% 6.84/7.07 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.84/7.07 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.84/7.07 (assert (forall ((X tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real X) X)))
% 6.84/7.07 (assert (forall ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) X)))
% 6.84/7.07 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 6.84/7.07 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 6.84/7.07 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= A2 B2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= A2 B2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_real A2) B2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_nat A2) B2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_int A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex)) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le211207098394363844omplex A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_real A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_nat A2) B2))))
% 6.84/7.07 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N2) tptp.zero_z5237406670263579293d_enat) N2)))
% 6.84/7.07 (assert (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K)))))
% 6.84/7.07 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.84/7.07 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.84/7.07 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.07 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N2)))
% 6.84/7.07 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.84/7.07 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.84/7.07 (assert (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real Y) X) (= (@ (@ tptp.ord_less_eq_set_real X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (F (-> tptp.set_real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.set_real) (Y5 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B tptp.int) (C tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (F (-> tptp.set_real tptp.num)) (B tptp.set_real) (C tptp.set_real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((X5 tptp.set_real) (Y5 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (F (-> tptp.set_real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.set_real) (Y5 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (F (-> tptp.num tptp.set_real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_set_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.set_real) (Z2 tptp.set_real)) (= Y4 Z2)) (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A4) B4) (@ (@ tptp.ord_less_eq_set_real B4) A4)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A4)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (@ (@ tptp.ord_less_eq_num B4) A4)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ tptp.ord_less_eq_nat B4) A4)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ tptp.ord_less_eq_int B4) A4)))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ (@ tptp.ord_less_eq_set_real B) A) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.set_real) (A tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real C))) (=> (@ (@ tptp.ord_less_eq_set_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.set_real) (A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real B) A) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.set_real) (Z2 tptp.set_real)) (= Y4 Z2)) (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real B4) A4) (@ (@ tptp.ord_less_eq_set_real A4) B4)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A4) (@ (@ tptp.ord_less_eq_set_nat A4) B4)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (@ (@ tptp.ord_less_eq_num A4) B4)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (@ (@ tptp.ord_less_eq_nat A4) B4)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (@ (@ tptp.ord_less_eq_int A4) B4)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real) (Z tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_real Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (=> (@ (@ tptp.ord_less_eq_set_real Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (@ (@ tptp.ord_less_eq_set_real A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ (@ tptp.ord_less_eq_set_nat A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.set_real) (Z2 tptp.set_real)) (= Y4 Z2)) (lambda ((X2 tptp.set_real) (Y3 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real X2) Y3) (@ (@ tptp.ord_less_eq_set_real Y3) X2)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (@ (@ tptp.ord_less_eq_set_nat Y3) X2)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((X2 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y3) (@ (@ tptp.ord_less_eq_num Y3) X2)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (@ (@ tptp.ord_less_eq_int Y3) X2)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num B) A) (not (= B A))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= B A))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (not (= B A))))))
% 6.84/7.07 (assert (forall ((X tptp.real)) (exists ((Y5 tptp.real)) (@ (@ tptp.ord_less_real Y5) X))))
% 6.84/7.07 (assert (forall ((X tptp.int)) (exists ((Y5 tptp.int)) (@ (@ tptp.ord_less_int Y5) X))))
% 6.84/7.07 (assert (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))))
% 6.84/7.07 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 6.84/7.07 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real X) Z4) (@ (@ tptp.ord_less_real Z4) Y))))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (not (@ (@ tptp.ord_le72135733267957522d_enat B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (= A B) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (@ (@ tptp.ord_le72135733267957522d_enat A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.extended_enat Bool)) (A tptp.extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (forall ((Y2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y2) X5) (@ P Y2))) (@ P X5))) (@ P A))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y2) X5) (@ P Y2))) (@ P X5))) (@ P A))))
% 6.84/7.07 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.84/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat A) B)))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) A))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.84/7.07 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.84/7.07 (assert (= (lambda ((P2 (-> tptp.extended_enat Bool))) (exists ((X7 tptp.extended_enat)) (@ P2 X7))) (lambda ((P3 (-> tptp.extended_enat Bool))) (exists ((N tptp.extended_enat)) (and (@ P3 N) (forall ((M6 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M6) N) (not (@ P3 M6)))))))))
% 6.84/7.07 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N tptp.nat)) (and (@ P3 N) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (not (@ P3 M6)))))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.extended_enat tptp.extended_enat Bool)) (A tptp.extended_enat) (B tptp.extended_enat)) (=> (forall ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.extended_enat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.real)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.num)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.int)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (or (@ (@ tptp.ord_le72135733267957522d_enat Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (or (@ (@ tptp.ord_less_real Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 6.84/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (not (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (= X Y)) (or (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (not (@ (@ tptp.ord_le72135733267957522d_enat B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (F (-> tptp.extended_enat tptp.real)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (F (-> tptp.extended_enat tptp.num)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (F (-> tptp.extended_enat tptp.nat)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (F (-> tptp.extended_enat tptp.int)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat X) X))))
% 6.84/7.07 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 6.84/7.07 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.84/7.07 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.84/7.07 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.num tptp.extended_enat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (F (-> tptp.extended_enat tptp.real)) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B)) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (P Bool)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) X) P))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (= X Y) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= Y X)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (or (@ (@ tptp.ord_less_set_real A5) B5) (= A5 B5)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B5) (= A5 B5)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C4 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.ord_less_set_real B2) C4) (@ (@ tptp.ord_less_set_real A2) C4)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_set_nat B2) C4) (@ (@ tptp.ord_less_set_nat A2) C4)))))
% 6.84/7.07 (assert (= tptp.ord_less_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A5) B5) (not (@ (@ tptp.ord_less_eq_set_real B5) A5))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (@ (@ tptp.ord_less_eq_set_nat B5) A5))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_set_real A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (@ _let_1 C4))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C4) (@ _let_1 C4))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B2) (@ (@ tptp.ord_less_eq_set_real A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2))))
% 6.84/7.07 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ P X2) (@ Q X2))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X2 tptp.complex)) (=> (@ P X2) (@ Q X2))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)) (forall ((X2 tptp.list_nat)) (=> (@ P X2) (@ Q X2))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X2 tptp.real)) (=> (@ P X2) (@ Q X2))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X2 tptp.nat)) (=> (@ P X2) (@ Q X2))))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.set_real) (Z2 tptp.set_real)) (= Y4 Z2)) (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A5) B5) (@ (@ tptp.ord_less_eq_set_real B5) A5)))))
% 6.84/7.07 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (@ (@ tptp.ord_less_eq_set_nat B5) A5)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (@ _let_1 C4))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C4) (@ _let_1 C4))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real A2) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) A2)))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (forall ((T2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A5) B5) (not (= A5 B5))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (= A5 B5))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_real B2) A2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat B2) A2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_real A2) B2))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (not (@ (@ tptp.ord_less_eq_set_real B2) A2)))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (not (@ (@ tptp.ord_less_eq_set_nat B2) A2)))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B2) (not (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ (@ tptp.ord_less_eq_set_real B2) A2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.ord_less_eq_set_nat B2) A2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C4 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (= (@ (@ tptp.minus_minus_set_real B2) (@ (@ tptp.minus_minus_set_real C4) A2)) A2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C4) (= (@ (@ tptp.minus_minus_set_nat B2) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) B2)) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B2)) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (C4 tptp.set_real) (D4 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real D4) B2) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_set_real C4) D4))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D4 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_set_nat C4) D4))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 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 N2)) A))))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N4)) Y))))))
% 6.84/7.07 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ 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) N2) A)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N2) A) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.power_power_real Y2) N2) A)) (= Y2 X5)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A5))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B5))))))
% 6.84/7.07 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A5))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B5))))))
% 6.84/7.07 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A5))) (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) B5))))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A5))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B5))))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A5))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B5))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X2) A2) (@ P X2))))) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X2) A2) (@ P X2))))) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) A2)))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) A2)))
% 6.84/7.07 (assert (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.07 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X) (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real Y) X) (not (@ (@ tptp.ord_less_set_real X) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 6.84/7.07 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le2932123472753598470d_enat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat A) B)) (or (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B)) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (= (not (@ (@ tptp.ord_less_set_real A) B)) (or (not (@ (@ tptp.ord_less_eq_set_real A) B)) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (= A B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (= A B)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (not (@ (@ tptp.ord_less_set_real X) Y)) (= (@ (@ tptp.ord_less_eq_set_real X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (= (not (@ (@ tptp.ord_less_set_real X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (@ (@ tptp.ord_less_eq_real Y) X5))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y) (@ (@ tptp.ord_less_eq_real X5) Z))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 6.84/7.07 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat X2) Y3) (not (@ (@ tptp.ord_le2932123472753598470d_enat Y3) X2))))))
% 6.84/7.07 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y3) (not (@ (@ tptp.ord_less_eq_real Y3) X2))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_real (lambda ((X2 tptp.set_real) (Y3 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real X2) Y3) (not (@ (@ tptp.ord_less_eq_set_real Y3) X2))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (not (@ (@ tptp.ord_less_eq_set_nat Y3) X2))))))
% 6.84/7.07 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y3) (not (@ (@ tptp.ord_less_eq_num Y3) X2))))))
% 6.84/7.07 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (not (@ (@ tptp.ord_less_eq_nat Y3) X2))))))
% 6.84/7.07 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (not (@ (@ tptp.ord_less_eq_int Y3) X2))))))
% 6.84/7.07 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le2932123472753598470d_enat Y) X)) (@ (@ tptp.ord_le72135733267957522d_enat X) Y))))
% 6.84/7.07 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.07 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 6.84/7.07 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 6.84/7.07 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 6.84/7.07 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat A4) B4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (or (@ (@ tptp.ord_less_set_real A4) B4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A4) B4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A4) B4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (= A4 B4))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (@ (@ tptp.ord_le72135733267957522d_enat A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ (@ tptp.ord_less_set_real B) C) (@ (@ tptp.ord_less_set_real A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_set_nat B) C) (@ (@ tptp.ord_less_set_nat A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_set_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.84/7.07 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4) (not (@ (@ tptp.ord_le2932123472753598470d_enat B4) A4))))))
% 6.84/7.07 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (@ (@ tptp.ord_less_eq_real B4) A4))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A4) B4) (not (@ (@ tptp.ord_less_eq_set_real B4) A4))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B4) (not (@ (@ tptp.ord_less_eq_set_nat B4) A4))))))
% 6.84/7.07 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (@ (@ tptp.ord_less_eq_num B4) A4))))))
% 6.84/7.07 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (@ (@ tptp.ord_less_eq_nat B4) A4))))))
% 6.84/7.07 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (@ (@ tptp.ord_less_eq_int B4) A4))))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.84/7.07 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat B4) A4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_real (lambda ((B4 tptp.set_real) (A4 tptp.set_real)) (or (@ (@ tptp.ord_less_set_real B4) A4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B4) A4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B4) A4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B4) A4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A4) (= A4 B4)))))
% 6.84/7.07 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat B4) A4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_real (lambda ((B4 tptp.set_real) (A4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real B4) A4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (= A4 B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (= A4 B4))))))
% 6.84/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.set_real) (A tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_set_real C))) (=> (@ (@ tptp.ord_less_eq_set_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) B) (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_real C) A)))))
% 6.84/7.07 (assert (forall ((B tptp.set_real) (A tptp.set_real) (C tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real B) A) (=> (@ (@ tptp.ord_less_eq_set_real C) B) (@ (@ tptp.ord_less_set_real C) A)))))
% 6.84/7.07 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) B) (@ (@ tptp.ord_less_set_nat C) A)))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) B) (@ (@ tptp.ord_less_num C) A)))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A)))))
% 6.84/7.07 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat B4) A4) (not (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (@ (@ tptp.ord_less_eq_real A4) B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_real (lambda ((B4 tptp.set_real) (A4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real B4) A4) (not (@ (@ tptp.ord_less_eq_set_real A4) B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A4) (not (@ (@ tptp.ord_less_eq_set_nat A4) B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (@ (@ tptp.ord_less_eq_num A4) B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (@ (@ tptp.ord_less_eq_nat A4) B4))))))
% 6.84/7.07 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (@ (@ tptp.ord_less_eq_int A4) B4))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (@ (@ tptp.ord_le2932123472753598470d_enat A) B))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A) B) (@ (@ tptp.ord_less_eq_set_real A) B))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.84/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.84/7.07 (assert (forall ((B tptp.set_real) (A tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real B) A) (@ (@ tptp.ord_less_eq_set_real B) A))))
% 6.84/7.07 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.84/7.07 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat X2) Y3) (= X2 Y3)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y3) (= X2 Y3)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_real (lambda ((X2 tptp.set_real) (Y3 tptp.set_real)) (or (@ (@ tptp.ord_less_set_real X2) Y3) (= X2 Y3)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X2) Y3) (= X2 Y3)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y3) (= X2 Y3)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y3) (= X2 Y3)))))
% 6.84/7.07 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y3) (= X2 Y3)))))
% 6.84/7.07 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat X2) Y3) (not (= X2 Y3))))))
% 6.84/7.07 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y3) (not (= X2 Y3))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_real (lambda ((X2 tptp.set_real) (Y3 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real X2) Y3) (not (= X2 Y3))))))
% 6.84/7.07 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (not (= X2 Y3))))))
% 6.84/7.07 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y3) (not (= X2 Y3))))))
% 6.84/7.07 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (not (= X2 Y3))))))
% 6.84/7.07 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (not (= X2 Y3))))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le2932123472753598470d_enat X) Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le2932123472753598470d_enat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (@ (@ tptp.ord_le2932123472753598470d_enat X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real X) Y) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (not (= A B)) (@ (@ tptp.ord_le72135733267957522d_enat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (@ (@ tptp.ord_le72135733267957522d_enat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (@ (@ tptp.ord_less_set_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.ord_less_set_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) Z) (@ (@ tptp.ord_le72135733267957522d_enat X) Z)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X) Z)))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real) (Z tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (=> (@ (@ tptp.ord_less_set_real Y) Z) (@ (@ tptp.ord_less_set_real X) Z)))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z) (@ (@ tptp.ord_less_set_nat X) Z)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X) Z)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real) (Z tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_set_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_real Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (F (-> tptp.extended_enat tptp.real)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.num tptp.extended_enat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.num tptp.extended_enat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (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_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (or (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (or (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (or (@ (@ tptp.ord_less_set_real X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.84/7.07 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.84/7.07 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.84/7.07 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.84/7.07 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A)))
% 6.84/7.07 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.84/7.07 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.84/7.07 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.84/7.07 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.84/7.07 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.84/7.07 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.84/7.07 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.84/7.07 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.84/7.07 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y) Y))))
% 6.84/7.07 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= (@ (@ tptp.ord_max_Code_integer X) Y) Y))))
% 6.84/7.07 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (= (@ (@ tptp.ord_max_set_real X) Y) Y))))
% 6.84/7.07 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_max_set_nat X) Y) Y))))
% 6.84/7.07 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (@ (@ tptp.ord_max_num X) Y) Y))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))))
% 6.84/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))))
% 6.84/7.07 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y) X))))
% 6.84/7.07 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) X) (= (@ (@ tptp.ord_max_Code_integer X) Y) X))))
% 6.84/7.07 (assert (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real Y) X) (= (@ (@ tptp.ord_max_set_real X) Y) X))))
% 6.84/7.07 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_max_set_nat X) Y) X))))
% 6.84/7.07 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_max_num X) Y) X))))
% 6.84/7.07 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))))
% 6.84/7.07 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))))
% 6.84/7.07 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le3102999989581377725nteger A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (@ (@ (@ tptp.if_set_real (@ (@ tptp.ord_less_eq_set_real A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (=> (= Xa2 _let_1) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) _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))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X _let_1) (=> (= Y 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) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.vEBT_Leaf false) B3)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A3))) (let ((_let_3 (@ _let_2 B3))) (=> (= X _let_3) (=> (= Xa2 _let_1) (=> (= Y (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N4)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa2 _let_1) (=> (= Y _let_2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa2 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi2))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (=> (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _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) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S2))) (=> (= X _let_1) (=> (= Y _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) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (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) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 6.84/7.07 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.84/7.07 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) (@ _let_1 K)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.84/7.07 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.84/7.07 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.84/7.07 (assert (forall ((K tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N2) K))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (=> (not Y) (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))) (=> (= X _let_1) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.84/7.07 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.84/7.07 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.set_or5403411693681687835d_enat A) B) tptp.bot_bo7653980558646680370d_enat))))
% 6.84/7.07 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))))
% 6.84/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real) (D tptp.set_real)) (= (@ (@ tptp.ord_le3558479182127378552t_real (@ (@ tptp.set_or7743017856606604397t_real A) B)) (@ (@ tptp.set_or7743017856606604397t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_set_real A) B)) (and (@ (@ tptp.ord_less_eq_set_real C) A) (@ (@ tptp.ord_less_eq_set_real B) D))))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B) D))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D))))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (= (= (@ (@ tptp.set_or7743017856606604397t_real A) B) tptp.bot_bot_set_set_real) (not (@ (@ tptp.ord_less_eq_set_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real)) (= (= tptp.bot_bot_set_set_real (@ (@ tptp.set_or7743017856606604397t_real A) B)) (not (@ (@ tptp.ord_less_eq_set_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.84/7.07 (assert (forall ((L2 tptp.set_real) (H2 tptp.set_real) (L3 tptp.set_real) (H3 tptp.set_real)) (= (= (@ (@ tptp.set_or7743017856606604397t_real L2) H2) (@ (@ tptp.set_or7743017856606604397t_real L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_real L2) H2)) (not (@ (@ tptp.ord_less_eq_set_real L3) H3)))))))
% 6.84/7.07 (assert (forall ((L2 tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L2) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))))
% 6.84/7.07 (assert (forall ((L2 tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L2) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L2) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 6.84/7.07 (assert (forall ((L2 tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L2) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 6.84/7.07 (assert (forall ((L2 tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L2) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L2) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 6.84/7.07 (assert (forall ((L2 tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L2) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L2) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 6.84/7.07 (assert (forall ((I2 tptp.set_real) (L2 tptp.set_real) (U tptp.set_real)) (= (@ (@ tptp.member_set_real I2) (@ (@ tptp.set_or7743017856606604397t_real L2) U)) (and (@ (@ tptp.ord_less_eq_set_real L2) I2) (@ (@ tptp.ord_less_eq_set_real I2) U)))))
% 6.84/7.07 (assert (forall ((I2 tptp.set_nat) (L2 tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ (@ tptp.set_or4548717258645045905et_nat L2) U)) (and (@ (@ tptp.ord_less_eq_set_nat L2) I2) (@ (@ tptp.ord_less_eq_set_nat I2) U)))))
% 6.84/7.07 (assert (forall ((I2 tptp.num) (L2 tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L2) U)) (and (@ (@ tptp.ord_less_eq_num L2) I2) (@ (@ tptp.ord_less_eq_num I2) U)))))
% 6.84/7.07 (assert (forall ((I2 tptp.nat) (L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (and (@ (@ tptp.ord_less_eq_nat L2) I2) (@ (@ tptp.ord_less_eq_nat I2) U)))))
% 6.84/7.07 (assert (forall ((I2 tptp.int) (L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (and (@ (@ tptp.ord_less_eq_int L2) I2) (@ (@ tptp.ord_less_eq_int I2) U)))))
% 6.84/7.07 (assert (forall ((I2 tptp.real) (L2 tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L2) U)) (and (@ (@ tptp.ord_less_eq_real L2) I2) (@ (@ tptp.ord_less_eq_real I2) U)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M7 tptp.nat)) (=> (@ P X) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M5)))))))))))
% 6.84/7.07 (assert (forall ((X tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A3 tptp.nat) (B3 tptp.nat) (Acc tptp.num)) (not (= X (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A3) (@ (@ tptp.product_Pair_nat_num B3) Acc)))))))))
% 6.84/7.07 (assert (forall ((X tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat) (Acc tptp.nat)) (not (= X (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A3) (@ (@ tptp.product_Pair_nat_nat B3) Acc)))))))))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (= (@ (@ tptp.ord_le2529575680413868914d_enat (@ (@ tptp.set_or5403411693681687835d_enat A) B)) (@ (@ tptp.set_or5403411693681687835d_enat C) D)) (and (or (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_le2932123472753598470d_enat B) D) (or (@ (@ tptp.ord_le72135733267957522d_enat C) A) (@ (@ tptp.ord_le72135733267957522d_enat B) D)))) (@ _let_1 D))))))
% 6.84/7.07 (assert (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real) (D tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real C))) (= (@ (@ tptp.ord_le7926960851185191020t_real (@ (@ tptp.set_or7743017856606604397t_real A) B)) (@ (@ tptp.set_or7743017856606604397t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_real B) D) (or (@ (@ tptp.ord_less_set_real C) A) (@ (@ tptp.ord_less_set_real B) D)))) (@ _let_1 D))))))
% 6.84/7.07 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B) D)))) (@ _let_1 D))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A3 tptp.real) (B3 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (=> (@ (@ P B3) C3) (=> (@ (@ tptp.ord_less_eq_real A3) B3) (=> (@ (@ tptp.ord_less_eq_real B3) C3) (@ _let_1 C3))))))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A3 tptp.real) (B3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A3) X5) (@ (@ tptp.ord_less_eq_real X5) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B3) A3)) D5)) (@ (@ P A3) B3)))))))) (@ (@ P A) B))))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 6.84/7.07 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.84/7.07 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.84/7.07 (assert (forall ((Q2 tptp.nat) (R tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R)) (= R tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R)) (= R tptp.zero_zero_int))))
% 6.84/7.07 (assert (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B) _let_1))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (= (@ (@ tptp.modulo_modulo_int _let_1) B) _let_1))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) (@ _let_1 K)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.84/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.84/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.84/7.07 (assert (forall ((K tptp.nat) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N2)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N2) K)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.84/7.07 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.84/7.07 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.84/7.07 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.84/7.07 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ (@ tptp.modulo_modulo_nat M) _let_1)))))
% 6.84/7.07 (assert (forall ((K tptp.num) (N2 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) N2))) _let_1) tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (A6 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A6) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A6) B6)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A6) B6)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (A6 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A6) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A6) B6)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A6) B6)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A6) B6)) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N2)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N2)) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N2)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N2)) B))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N2))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) K)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B)) A))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B)) A))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))))
% 6.84/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))))
% 6.84/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((M tptp.num) (N2 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 N2)) _let_1)))))
% 6.84/7.07 (assert (forall ((M tptp.num) (N2 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 N2)) _let_1)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D3 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C)))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (let ((_let_3 (= _let_1 N2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (P5 tptp.nat) (M tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) P5) (=> (@ (@ tptp.ord_less_nat M) P5) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) P5) (=> (@ P N4) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N4)) P5))))) (@ P M)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)))
% 6.84/7.07 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q3))))))
% 6.84/7.07 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N)) N)))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.modulo_modulo_nat A) B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.modulo_modulo_int A) B) A)))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.84/7.07 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))))
% 6.84/7.07 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.84/7.07 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.84/7.07 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))))
% 6.84/7.07 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))))
% 6.84/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))))
% 6.84/7.07 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q3 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q3))))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (forall ((S2 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S2))))))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (forall ((S2 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q2) S2))))))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N2)) Q2))) (@ _let_1 N2)))))))
% 6.84/7.07 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N)) N)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N2)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I5)) J3)) (@ P J3))))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.84/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N2))) M) tptp.one_one_nat))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 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 N2))) (= (@ (@ 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 N2) M)))) _let_2))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 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 N2))) (= (@ (@ 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 N2) M)))) _let_2))))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.84/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.84/7.07 (assert (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))))
% 6.84/7.07 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X) Y)))))
% 6.84/7.07 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 6.84/7.07 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B2) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B2) N2))))))
% 6.84/7.07 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A2) N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B2) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ tptp.divide_divide_nat B2) N2))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs2) Ys)) N2) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs2) Ys)) N2) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) N2) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) N2) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs2) Ys)) N2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) N2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs2) Ys)) N2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.84/7.07 (assert (forall ((X tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A2) Z) (=> (@ tptp.finite_finite_nat B2) (=> (= A2 B2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A2) X) X_1))))))))
% 6.84/7.07 (assert (forall ((Z tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X) X_1)))))))
% 6.84/7.07 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (@ (@ tptp.ord_less_nat X3) A))))))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (@ (@ tptp.ord_less_nat A) X3))))))))
% 6.84/7.07 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y22)) (= X22 Y22))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B Bool) (A6 tptp.code_integer) (B6 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A6) B6)) (and (= A A6) (= B B6)))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (A6 tptp.num) (B6 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A6) B6)) (and (= A A6) (= B B6)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.num) (A6 tptp.nat) (B6 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A6) B6)) (and (= A A6) (= B B6)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (A6 tptp.nat) (B6 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A6) B6)) (and (= A A6) (= B B6)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (A6 tptp.int) (B6 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A6) B6)) (and (= A A6) (= B B6)))))
% 6.84/7.07 (assert (forall ((X1 tptp.code_integer) (X22 Bool) (Y1 tptp.code_integer) (Y22 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o X1) X22) (@ (@ tptp.produc6677183202524767010eger_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.84/7.07 (assert (forall ((X1 tptp.num) (X22 tptp.num) (Y1 tptp.num) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X22) (@ (@ tptp.product_Pair_num_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.84/7.07 (assert (forall ((X1 tptp.nat) (X22 tptp.num) (Y1 tptp.nat) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num X1) X22) (@ (@ tptp.product_Pair_nat_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.84/7.07 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.84/7.07 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) (@ _let_1 K)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 6.84/7.07 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))))
% 6.84/7.07 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.84/7.07 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.84/7.07 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 6.84/7.07 (assert (forall ((N3 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N3) (@ (@ tptp.ord_less_nat X5) N2))) (@ tptp.finite_finite_nat N3))))
% 6.84/7.07 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_nat X2) M6)))))))
% 6.84/7.07 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_eq_nat X2) M6)))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I2)))))))
% 6.84/7.07 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) (@ F N4))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) U)))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_o) (N2 tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (= (@ tptp.size_size_list_o Xs) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (= (@ tptp.size_size_list_int Xs) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (N2 tptp.nat)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite306553202115118035t_real (@ tptp.collect_list_real (lambda ((Xs tptp.list_real)) (and (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (= (@ tptp.size_size_list_real Xs) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (= (@ tptp.size_size_list_nat Xs) N2))))))))
% 6.84/7.07 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2))))))
% 6.84/7.07 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L2)) L2))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_o) (N2 tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (N2 tptp.nat)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite306553202115118035t_real (@ tptp.collect_list_real (lambda ((Xs tptp.list_real)) (and (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_real Xs)) N2))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N2))))))))
% 6.84/7.07 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L2)))))
% 6.84/7.07 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L2)) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (@ (@ tptp.ord_less_eq_num A) B)) (not (@ (@ tptp.ord_less_eq_num B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real A) A)))
% 6.84/7.07 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.84/7.07 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.84/7.07 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) A))))
% 6.84/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.84/7.07 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B Bool) (A6 tptp.code_integer) (B6 Bool)) (=> (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A6) B6)) (not (=> (= A A6) (= B (not B6)))))))
% 6.84/7.07 (assert (forall ((A tptp.num) (B tptp.num) (A6 tptp.num) (B6 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.num) (A6 tptp.nat) (B6 tptp.num)) (=> (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (A6 tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (A6 tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.produc6271795597528267376eger_o Bool)) (P5 tptp.produc6271795597528267376eger_o)) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (@ P (@ (@ tptp.produc6677183202524767010eger_o A3) B3))) (@ P P5))))
% 6.84/7.07 (assert (forall ((P (-> tptp.product_prod_num_num Bool)) (P5 tptp.product_prod_num_num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A3) B3))) (@ P P5))))
% 6.84/7.07 (assert (forall ((P (-> tptp.product_prod_nat_num Bool)) (P5 tptp.product_prod_nat_num)) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (@ P (@ (@ tptp.product_Pair_nat_num A3) B3))) (@ P P5))))
% 6.84/7.07 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P5 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P P5))))
% 6.84/7.07 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P5 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A3) B3))) (@ P P5))))
% 6.84/7.07 (assert (forall ((P5 tptp.produc6271795597528267376eger_o)) (exists ((X5 tptp.code_integer) (Y5 Bool)) (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)))))
% 6.84/7.07 (assert (forall ((P5 tptp.product_prod_num_num)) (exists ((X5 tptp.num) (Y5 tptp.num)) (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)))))
% 6.84/7.07 (assert (forall ((P5 tptp.product_prod_nat_num)) (exists ((X5 tptp.nat) (Y5 tptp.num)) (= P5 (@ (@ tptp.product_Pair_nat_num X5) Y5)))))
% 6.84/7.07 (assert (forall ((P5 tptp.product_prod_nat_nat)) (exists ((X5 tptp.nat) (Y5 tptp.nat)) (= P5 (@ (@ tptp.product_Pair_nat_nat X5) Y5)))))
% 6.84/7.07 (assert (forall ((P5 tptp.product_prod_int_int)) (exists ((X5 tptp.int) (Y5 tptp.int)) (= P5 (@ (@ tptp.product_Pair_int_int X5) Y5)))))
% 6.84/7.07 (assert (forall ((Y tptp.produc6271795597528267376eger_o)) (not (forall ((A3 tptp.code_integer) (B3 Bool)) (not (= Y (@ (@ tptp.produc6677183202524767010eger_o A3) B3)))))))
% 6.84/7.07 (assert (forall ((Y tptp.product_prod_num_num)) (not (forall ((A3 tptp.num) (B3 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_num_num A3) B3)))))))
% 6.84/7.07 (assert (forall ((Y tptp.product_prod_nat_num)) (not (forall ((A3 tptp.nat) (B3 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_nat_num A3) B3)))))))
% 6.84/7.07 (assert (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B3 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A3) B3)))))))
% 6.84/7.07 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A3) B3)))))))
% 6.84/7.07 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L2) _let_1))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((B6 tptp.extended_enat) (A6 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le2932123472753598470d_enat B6) A6)) (@ (@ tptp.ord_le72135733267957522d_enat A6) B6))))
% 6.84/7.07 (assert (forall ((B6 tptp.real) (A6 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B6) A6)) (@ (@ tptp.ord_less_real A6) B6))))
% 6.84/7.07 (assert (forall ((B6 tptp.num) (A6 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B6) A6)) (@ (@ tptp.ord_less_num A6) B6))))
% 6.84/7.07 (assert (forall ((B6 tptp.nat) (A6 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B6) A6)) (@ (@ tptp.ord_less_nat A6) B6))))
% 6.84/7.07 (assert (forall ((B6 tptp.int) (A6 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B6) A6)) (@ (@ tptp.ord_less_int A6) B6))))
% 6.84/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.84/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.84/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.84/7.07 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 6.84/7.07 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le3102999989581377725nteger A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (@ (@ (@ tptp.if_set_real (@ (@ tptp.ord_less_eq_set_real A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))))
% 6.84/7.07 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))))
% 6.84/7.07 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))))
% 6.84/7.07 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B5 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B5) A2)))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite9007344921179782393t_real (@ tptp.collect_set_real (lambda ((B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real B5) A2)))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B5) A2)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z5 tptp.real)) (= (@ (@ tptp.power_power_real Z5) N2) tptp.one_one_real)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.extended_enat)) (Y (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_on7984719198319812577d_enat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_on7984719198319812577d_enat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_7803423173614009249d_enat (@ X I5)) (@ Y I5)) tptp.one_on7984719198319812577d_enat))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.extended_enat)) (Y (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_on7984719198319812577d_enat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_on7984719198319812577d_enat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_7803423173614009249d_enat (@ X I5)) (@ Y I5)) tptp.one_on7984719198319812577d_enat))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.extended_enat)) (Y (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_on7984719198319812577d_enat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_on7984719198319812577d_enat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_7803423173614009249d_enat (@ X I5)) (@ Y I5)) tptp.one_on7984719198319812577d_enat))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.extended_enat)) (Y (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.one_on7984719198319812577d_enat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.one_on7984719198319812577d_enat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.times_7803423173614009249d_enat (@ X I5)) (@ Y I5)) tptp.one_on7984719198319812577d_enat))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.extended_enat)) (Y (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_z5237406670263579293d_enat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_z5237406670263579293d_enat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ X I5)) (@ Y I5)) tptp.zero_z5237406670263579293d_enat))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.extended_enat)) (Y (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_z5237406670263579293d_enat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_z5237406670263579293d_enat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ X I5)) (@ Y I5)) tptp.zero_z5237406670263579293d_enat))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.extended_enat)) (Y (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_z5237406670263579293d_enat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_z5237406670263579293d_enat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ X I5)) (@ Y I5)) tptp.zero_z5237406670263579293d_enat))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.extended_enat)) (Y (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.zero_z5237406670263579293d_enat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.zero_z5237406670263579293d_enat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ X I5)) (@ Y I5)) tptp.zero_z5237406670263579293d_enat))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.84/7.07 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R)) (@ (@ (@ 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 R)) tptp.one_one_int)))))))))
% 6.84/7.07 (assert (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N4 tptp.nat)) (forall ((X3 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X3)) N4)))))))
% 6.84/7.07 (assert (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N4 tptp.nat)) (forall ((X3 tptp.list_o)) (=> (@ (@ tptp.member_list_o X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X3)) N4)))))))
% 6.84/7.07 (assert (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N4 tptp.nat)) (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X3)) N4)))))))
% 6.84/7.07 (assert (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N4 tptp.nat)) (forall ((X3 tptp.list_int)) (=> (@ (@ tptp.member_list_int X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X3)) N4)))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real A) X5) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_set_real) (A tptp.set_real)) (=> (@ tptp.finite9007344921179782393t_real A2) (=> (@ (@ tptp.member_set_real A) A2) (exists ((X5 tptp.set_real)) (and (@ (@ tptp.member_set_real X5) A2) (@ (@ tptp.ord_less_eq_set_real A) X5) (forall ((Xa tptp.set_real)) (=> (@ (@ tptp.member_set_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_real X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat A) X5) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A2) (@ (@ tptp.ord_less_eq_num A) X5) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat A) X5) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int A) X5) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real X5) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_set_real) (A tptp.set_real)) (=> (@ tptp.finite9007344921179782393t_real A2) (=> (@ (@ tptp.member_set_real A) A2) (exists ((X5 tptp.set_real)) (and (@ (@ tptp.member_set_real X5) A2) (@ (@ tptp.ord_less_eq_set_real X5) A) (forall ((Xa tptp.set_real)) (=> (@ (@ tptp.member_set_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_real Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat X5) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A2) (@ (@ tptp.ord_less_eq_num X5) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat X5) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int X5) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ tptp.finite3207457112153483333omplex B2) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ tptp.finite_finite_real B2) (@ tptp.finite_finite_real A2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ tptp.finite_finite_nat B2) (@ tptp.finite_finite_nat A2)))))
% 6.84/7.07 (assert (forall ((S tptp.set_complex) (T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex T3))))))
% 6.84/7.07 (assert (forall ((S tptp.set_real) (T3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (not (@ tptp.finite_finite_real S)) (not (@ tptp.finite_finite_real T3))))))
% 6.84/7.07 (assert (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T3) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T3))))))
% 6.84/7.07 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.84/7.07 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real)) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ tptp.finite_finite_real A2)))))
% 6.84/7.07 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ tptp.finite_finite_nat A2)))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_set_real)) (=> (@ tptp.finite9007344921179782393t_real A2) (=> (not (= A2 tptp.bot_bot_set_set_real)) (exists ((X5 tptp.set_real)) (and (@ (@ tptp.member_set_real X5) A2) (forall ((Xa tptp.set_real)) (=> (@ (@ tptp.member_set_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_real X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_set_real)) (=> (@ tptp.finite9007344921179782393t_real A2) (=> (not (= A2 tptp.bot_bot_set_set_real)) (exists ((X5 tptp.set_real)) (and (@ (@ tptp.member_set_real X5) A2) (forall ((Xa tptp.set_real)) (=> (@ (@ tptp.member_set_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_real Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))))
% 6.84/7.07 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R)))))))))))
% 6.84/7.07 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))))))
% 6.84/7.07 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ (@ P N4) (@ (@ tptp.modulo_modulo_nat M5) N4)) (@ (@ P M5) N4)))) (@ (@ P M) N2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N2)) K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N2) (@ (@ tptp.divide_divide_int K) _let_1)) L2)))))))
% 6.84/7.07 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.84/7.07 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.84/7.07 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex A) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) A)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) A)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.84/7.07 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))))
% 6.84/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.84/7.07 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)))
% 6.84/7.07 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.84/7.07 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.84/7.07 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.84/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 6.84/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 6.84/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) tptp.one_one_Code_integer))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.84/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 6.84/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N2) K) L2)) (@ _let_1 L2)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N2) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))
% 6.84/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.84/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.84/7.07 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N2)) (not (@ _let_1 N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N2))) (@ _let_1 N2)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (= (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ _let_2 A))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ _let_2 A))))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ _let_2 A))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N2) _let_1)))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (not (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.84/7.07 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)))))))
% 6.84/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) tptp.one_one_Code_integer))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.84/7.07 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.84/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))))
% 6.84/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))))
% 6.84/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_2 (= A tptp.zero_zero_int)))))))))
% 6.84/7.07 (assert (forall ((N2 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) N2)) tptp.one_one_Code_integer)) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((N2 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) N2)) tptp.one_one_nat)) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((N2 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) N2)) tptp.one_one_int)) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.84/7.07 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.84/7.07 (assert (forall ((P5 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P5) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= P5 (@ (@ tptp.times_times_nat X5) Y5)) (=> (@ (@ tptp.dvd_dvd_nat X5) A) (not (@ (@ tptp.dvd_dvd_nat Y5) B)))))))))
% 6.84/7.07 (assert (forall ((P5 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P5) (@ (@ tptp.times_times_int A) B)) (not (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.times_times_int X5) Y5)) (=> (@ (@ tptp.dvd_dvd_int X5) A) (not (@ (@ tptp.dvd_dvd_int Y5) B)))))))))
% 6.84/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B7 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B7) C5)) (@ (@ tptp.dvd_dvd_nat B7) B) (@ (@ tptp.dvd_dvd_nat C5) C))))))
% 6.84/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B7 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B7) C5)) (@ (@ tptp.dvd_dvd_int B7) B) (@ (@ tptp.dvd_dvd_int C5) C))))))
% 6.84/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))))
% 6.84/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (not (forall ((K2 tptp.complex)) (not (= A (@ (@ tptp.times_times_complex B) K2))))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K2 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K2))))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (K tptp.complex)) (=> (= A (@ (@ tptp.times_times_complex B) K)) (@ (@ tptp.dvd_dvd_complex B) A))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.84/7.08 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A4 (@ (@ tptp.times_3573771949741848930nteger B4) K3))))))
% 6.84/7.08 (assert (= tptp.dvd_dvd_complex (lambda ((B4 tptp.complex) (A4 tptp.complex)) (exists ((K3 tptp.complex)) (= A4 (@ (@ tptp.times_times_complex B4) K3))))))
% 6.84/7.08 (assert (= tptp.dvd_dvd_real (lambda ((B4 tptp.real) (A4 tptp.real)) (exists ((K3 tptp.real)) (= A4 (@ (@ tptp.times_times_real B4) K3))))))
% 6.84/7.08 (assert (= tptp.dvd_dvd_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (exists ((K3 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B4) K3))))))
% 6.84/7.08 (assert (= tptp.dvd_dvd_int (lambda ((B4 tptp.int) (A4 tptp.int)) (exists ((K3 tptp.int)) (= A4 (@ (@ tptp.times_times_int B4) K3))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex A) C))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex A) B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex A) B) (=> (@ (@ tptp.dvd_dvd_complex C) D) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) D))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex B) C))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real B) C))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex B) A))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C)))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.84/7.08 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat tptp.one_on7984719198319812577d_enat) A)))
% 6.84/7.08 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.84/7.08 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int C) B)) (@ _let_1 (@ (@ tptp.minus_minus_int B) C))))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (= A B)))))))
% 6.84/7.08 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (= A B)))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (= A B)))))))
% 6.84/7.08 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (= A B)))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (= A B)))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.84/7.08 (assert (forall ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B) D)) (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B) D)) (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D)) (@ (@ tptp.divide6298287555418463151nteger B) D)) (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)))))
% 6.84/7.08 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N2)))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N2)))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N2)))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (@ _let_1 M))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y5 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 X5) (@ (@ tptp.plus_plus_nat (@ _let_2 Y5)) D3)) (= (@ _let_2 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y5)) D3))))))))))
% 6.84/7.08 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X5 tptp.nat) (Y5 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 X5) (@ (@ tptp.plus_plus_nat (@ _let_3 Y5)) D)) (= (@ _let_3 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y5)) D)))))))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y5 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 X5)) (@ _let_2 Y5)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X5)) (@ _let_1 Y5)) D3)))))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B)))) (@ (@ tptp.dvd_dvd_complex A) B))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) A)))) (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) B)))) (@ (@ tptp.dvd_dvd_real A) B))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 L2)) R)))))
% 6.84/7.08 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.84/7.08 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.84/7.08 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 6.84/7.08 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D)))))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C) A)) (= B C)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C) A)) (= B C)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B C)))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B)) (@ _let_1 C))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N2) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N2) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) M))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) M))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) M))))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) M))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (N2 tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N2))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer C) (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (@ (@ tptp.dvd_dvd_int C) (@ (@ tptp.minus_minus_int A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y5)) D3))))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (or (@ (@ tptp.ord_less_nat N2) M) (@ _let_1 N2))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 M)))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2)))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.84/7.08 (assert (= tptp.neg_nu7009210354673126013omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex X2) X2))))
% 6.84/7.08 (assert (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))
% 6.84/7.08 (assert (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))
% 6.84/7.08 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M)))))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y)) (= X Y)))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D)))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D)))))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D)))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))))
% 6.84/7.08 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.84/7.08 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.84/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat K) N2)))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.84/7.08 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M5 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M5)))))))
% 6.84/7.08 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.84/7.08 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.84/7.08 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3))))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B3) tptp.one_one_nat) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_nat A) B3) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B3)))))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B3) tptp.one_one_int) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_int A) B3) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B3)))))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B3 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B3 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B3) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B3) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B3)))))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.84/7.08 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.84/7.08 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.84/7.08 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.84/7.08 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide_divide_nat A4) _let_1) (@ (@ tptp.divide_divide_nat B4) _let_1))))))))
% 6.84/7.08 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A4 tptp.int) (B4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide_divide_int A4) _let_1) (@ (@ tptp.divide_divide_int B4) _let_1))))))))
% 6.84/7.08 (assert (= (lambda ((Y4 tptp.code_integer) (Z2 tptp.code_integer)) (= Y4 Z2)) (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide6298287555418463151nteger A4) _let_1) (@ (@ tptp.divide6298287555418463151nteger B4) _let_1))))))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.extended_enat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat X) (@ (@ tptp.power_8040749407984259932d_enat X) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N2)) M) (= N2 tptp.one_one_nat)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M)) M) (= N2 tptp.one_one_nat)))))
% 6.84/7.08 (assert (forall ((Q2 tptp.nat) (N2 tptp.nat) (R tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 6.84/7.08 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.08 (assert (forall ((R tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R) N2) (=> (@ (@ tptp.ord_less_eq_nat R) M) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M) R)) (= (@ (@ tptp.modulo_modulo_nat M) N2) R))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.one_one_Code_integer)))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se8260200283734997820nteger M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2793503036327961859nteger M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1345352211410354436nteger M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_integer))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.84/7.08 (assert (forall ((N2 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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (@ _let_1 A))))))
% 6.84/7.08 (assert (forall ((N2 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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (@ _let_1 A))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N2)))))
% 6.84/7.08 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N4 tptp.nat)) (not (= X (@ tptp.suc N4))))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P A3) B3) (@ (@ P B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P A) B))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2))) (= (@ (@ 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) N2))))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2))) (= (@ (@ 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) N2))))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ 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) N2))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.84/7.08 (assert (forall ((X8 tptp.set_Extended_enat)) (=> (not (= X8 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) X8) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) X8) (@ (@ tptp.ord_le72135733267957522d_enat X5) Xa))))) (not (@ tptp.finite4001608067531595151d_enat X8))))))
% 6.84/7.08 (assert (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X5) Xa))))) (not (@ tptp.finite_finite_real X8))))))
% 6.84/7.08 (assert (forall ((X8 tptp.set_num)) (=> (not (= X8 tptp.bot_bot_set_num)) (=> (forall ((X5 tptp.num)) (=> (@ (@ tptp.member_num X5) X8) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X8) (@ (@ tptp.ord_less_num X5) Xa))))) (not (@ tptp.finite_finite_num X8))))))
% 6.84/7.08 (assert (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X5) Xa))))) (not (@ tptp.finite_finite_nat X8))))))
% 6.84/7.08 (assert (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X5) Xa))))) (not (@ tptp.finite_finite_int X8))))))
% 6.84/7.08 (assert (forall ((S tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (not (= S tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) S) (not (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) S) (@ (@ tptp.ord_le72135733267957522d_enat Xa) X5))))))))))
% 6.84/7.08 (assert (forall ((S tptp.set_real)) (=> (@ tptp.finite_finite_real S) (=> (not (= S tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) S) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S) (@ (@ tptp.ord_less_real Xa) X5))))))))))
% 6.84/7.08 (assert (forall ((S tptp.set_num)) (=> (@ tptp.finite_finite_num S) (=> (not (= S tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) S) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S) (@ (@ tptp.ord_less_num Xa) X5))))))))))
% 6.84/7.08 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) S) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S) (@ (@ tptp.ord_less_nat Xa) X5))))))))))
% 6.84/7.08 (assert (forall ((S tptp.set_int)) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) S) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S) (@ (@ tptp.ord_less_int Xa) X5))))))))))
% 6.84/7.08 (assert (forall ((N2 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 N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) _let_3)) _let_2))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N2) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 6.84/7.08 (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)))))))))
% 6.84/7.08 (assert (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X3 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X3) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K4) D4))) T)))))))))
% 6.84/7.08 (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)))))))))
% 6.84/7.08 (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)))))))))
% 6.84/7.08 (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))))))))
% 6.84/7.08 (assert (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X3 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X3) T)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K4) D4))) T))))))))
% 6.84/7.08 (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))))))))
% 6.84/7.08 (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))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.code_integer Bool)) (L2 tptp.code_integer)) (= (exists ((X2 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L2) X2))) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L2) (@ (@ tptp.plus_p5714425477246183910nteger X2) tptp.zero_z3403309356797280102nteger)) (@ P X2))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.extended_enat Bool)) (L2 tptp.extended_enat)) (= (exists ((X2 tptp.extended_enat)) (@ P (@ (@ tptp.times_7803423173614009249d_enat L2) X2))) (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.dvd_dv3785147216227455552d_enat L2) (@ (@ tptp.plus_p3455044024723400733d_enat X2) tptp.zero_z5237406670263579293d_enat)) (@ P X2))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.complex Bool)) (L2 tptp.complex)) (= (exists ((X2 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L2) X2))) (exists ((X2 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L2) (@ (@ tptp.plus_plus_complex X2) tptp.zero_zero_complex)) (@ P X2))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (L2 tptp.real)) (= (exists ((X2 tptp.real)) (@ P (@ (@ tptp.times_times_real L2) X2))) (exists ((X2 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L2) (@ (@ tptp.plus_plus_real X2) tptp.zero_zero_real)) (@ P X2))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool)) (L2 tptp.nat)) (= (exists ((X2 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L2) X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L2) (@ (@ tptp.plus_plus_nat X2) tptp.zero_zero_nat)) (@ P X2))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (L2 tptp.int)) (= (exists ((X2 tptp.int)) (@ P (@ (@ tptp.times_times_int L2) X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L2) (@ (@ tptp.plus_plus_int X2) tptp.zero_zero_int)) (@ P X2))))))
% 6.84/7.08 (assert (= tptp.nat_triangle (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ 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))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 6.84/7.08 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I2))))))
% 6.84/7.08 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I2))))))
% 6.84/7.08 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I2))))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.zero_n1046097342994218471d_enat P)) (@ tptp.zero_n1046097342994218471d_enat Q)) (and (not P) Q))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.84/7.08 (assert (= (@ tptp.zero_n1046097342994218471d_enat true) tptp.one_on7984719198319812577d_enat))
% 6.84/7.08 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.84/7.08 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.84/7.08 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.84/7.08 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.84/7.08 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.84/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1046097342994218471d_enat P) tptp.one_on7984719198319812577d_enat) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.84/7.08 (assert (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M N2) (=> (not (= M tptp.zero_zero_nat)) (= X Y))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) N2)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N2) X)) N2)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N2) X)) N2)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X)) N2)))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.84/7.08 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N2) (@ tptp.zero_n2687167440665602831ol_nat (not (= N2 _let_1)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((X tptp.product_prod_nat_nat) (N2 tptp.nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I2) X))))
% 6.84/7.08 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I2) X))))
% 6.84/7.08 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I2) X))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N2)) _let_1)))))
% 6.84/7.08 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P5))) P5)))
% 6.84/7.08 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P5))) P5)))
% 6.84/7.08 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P5))) P5)))
% 6.84/7.08 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1201886186963655149omplex (and P Q)) (@ (@ tptp.times_times_complex (@ tptp.zero_n1201886186963655149omplex P)) (@ tptp.zero_n1201886186963655149omplex Q)))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n3304061248610475627l_real (and P Q)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.84/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.84/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.84/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.84/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.84/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.84/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.84/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.84/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.84/7.08 (assert (= tptp.zero_n1046097342994218471d_enat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_Extended_enat P4) tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.08 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P4 Bool)) (@ (@ (@ tptp.if_complex P4) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.84/7.08 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P4 Bool)) (@ (@ (@ tptp.if_real P4) tptp.one_one_real) tptp.zero_zero_real))))
% 6.84/7.08 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_nat P4) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.84/7.08 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P4 Bool)) (@ (@ (@ tptp.if_int P4) tptp.one_one_int) tptp.zero_zero_int))))
% 6.84/7.08 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P4 Bool)) (@ (@ (@ tptp.if_Code_integer P4) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.08 (assert (forall ((P (-> tptp.extended_enat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1046097342994218471d_enat P5)) (and (=> P5 (@ P tptp.one_on7984719198319812577d_enat)) (=> (not P5) (@ P tptp.zero_z5237406670263579293d_enat))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (and (=> P5 (@ P tptp.one_one_complex)) (=> (not P5) (@ P tptp.zero_zero_complex))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (and (=> P5 (@ P tptp.one_one_real)) (=> (not P5) (@ P tptp.zero_zero_real))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (and (=> P5 (@ P tptp.one_one_nat)) (=> (not P5) (@ P tptp.zero_zero_nat))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (and (=> P5 (@ P tptp.one_one_int)) (=> (not P5) (@ P tptp.zero_zero_int))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P5)) (and (=> P5 (@ P tptp.one_one_Code_integer)) (=> (not P5) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.extended_enat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1046097342994218471d_enat P5)) (not (or (and P5 (not (@ P tptp.one_on7984719198319812577d_enat))) (and (not P5) (not (@ P tptp.zero_z5237406670263579293d_enat))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (not (or (and P5 (not (@ P tptp.one_one_complex))) (and (not P5) (not (@ P tptp.zero_zero_complex))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (not (or (and P5 (not (@ P tptp.one_one_real))) (and (not P5) (not (@ P tptp.zero_zero_real))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (not (or (and P5 (not (@ P tptp.one_one_nat))) (and (not P5) (not (@ P tptp.zero_zero_nat))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (not (or (and P5 (not (@ P tptp.one_one_int))) (and (not P5) (not (@ P tptp.zero_zero_int))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P5)) (not (or (and P5 (not (@ P tptp.one_one_Code_integer))) (and (not P5) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_real) (N2 tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N2) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) (@ tptp.set_real2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_real N2) X))))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_complex) (N2 tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N2) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) (@ tptp.set_complex2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_complex N2) X))))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (N2 tptp.nat) (X tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs2) N2) (=> (forall ((Y5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y5) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replic4235873036481779905at_nat N2) X))))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2) (=> (forall ((Y5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y5) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N2) X))))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_o) (N2 tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N2) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) (@ tptp.set_o2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_o N2) X))))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_nat) (N2 tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N2) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) (@ tptp.set_nat2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_nat N2) X))))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_int) (N2 tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N2) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) (@ tptp.set_int2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_int N2) X))))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X5 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X) Xs2))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_o) (X Bool)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs2)) (= X5 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X) Xs2))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs2)) (= X5 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X) Xs2))))
% 6.84/7.08 (assert (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs2)) (= X5 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X) Xs2))))
% 6.84/7.08 (assert (forall ((P (-> tptp.extended_enat Bool)) (P6 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q5 (-> tptp.extended_enat Bool))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q5 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q5 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q5 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q5 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.extended_enat Bool)) (P6 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q5 (-> tptp.extended_enat Bool))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q5 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q5 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q5 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q5 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (not (@ (@ tptp.ord_le72135733267957522d_enat X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (not (@ (@ tptp.ord_less_real X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (not (@ (@ tptp.ord_less_num X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (not (@ (@ tptp.ord_less_nat X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (not (@ (@ tptp.ord_less_int X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (@ (@ tptp.ord_le72135733267957522d_enat T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (@ (@ tptp.ord_less_real T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (@ (@ tptp.ord_less_num T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (@ (@ tptp.ord_less_nat T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (@ (@ tptp.ord_less_int T) X3))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.extended_enat Bool)) (P6 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q5 (-> tptp.extended_enat Bool))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q5 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q5 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q5 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q5 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.extended_enat Bool)) (P6 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q5 (-> tptp.extended_enat Bool))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q5 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q5 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q5 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q5 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (not (= X3 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X3))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X3))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X3))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (not (@ (@ tptp.ord_le72135733267957522d_enat T) X3)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (not (@ (@ tptp.ord_less_real T) X3)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (not (@ (@ tptp.ord_less_num T) X3)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (not (@ (@ tptp.ord_less_nat T) X3)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (not (@ (@ tptp.ord_less_int T) X3)))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.modulo_modulo_nat A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.modulo_modulo_int A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n356916108424825756nteger (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.nat) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B3)) (@ (@ tptp.times_times_nat _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.int) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B3)) (@ (@ tptp.times_times_int _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.84/7.08 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B3)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (not (@ (@ tptp.ord_le2932123472753598470d_enat X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (not (@ (@ tptp.ord_less_eq_real X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (not (@ (@ tptp.ord_less_eq_num X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (not (@ (@ tptp.ord_less_eq_nat X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (not (@ (@ tptp.ord_less_eq_int X3) T)))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (@ (@ tptp.ord_le2932123472753598470d_enat T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (@ (@ tptp.ord_less_eq_real T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (@ (@ tptp.ord_less_eq_num T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (@ (@ tptp.ord_less_eq_nat T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (@ (@ tptp.ord_less_eq_int T) X3))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (@ (@ tptp.ord_le2932123472753598470d_enat X3) T))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (@ (@ tptp.ord_less_eq_real X3) T))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (@ (@ tptp.ord_less_eq_num X3) T))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (@ (@ tptp.ord_less_eq_nat X3) T))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (@ (@ tptp.ord_less_eq_int X3) T))))))
% 6.84/7.08 (assert (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (not (@ (@ tptp.ord_le2932123472753598470d_enat T) X3)))))))
% 6.84/7.08 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (not (@ (@ tptp.ord_less_eq_real T) X3)))))))
% 6.84/7.08 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (not (@ (@ tptp.ord_less_eq_num T) X3)))))))
% 6.84/7.08 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (not (@ (@ tptp.ord_less_eq_nat T) X3)))))))
% 6.84/7.08 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (not (@ (@ tptp.ord_less_eq_int T) X3)))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex) (K2 tptp.complex)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K2) D4))))) (=> (forall ((X5 tptp.complex) (K2 tptp.complex)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K2) D4))))) (forall ((X3 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K4) D4)))) (= (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) 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)))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) 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)))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex) (K2 tptp.complex)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K2) D4))))) (=> (forall ((X5 tptp.complex) (K2 tptp.complex)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K2) D4))))) (forall ((X3 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K4) D4)))) (= (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) 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)))))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) 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)))))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.84/7.08 (assert (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.84/7.08 (assert (forall ((D tptp.code_integer) (S3 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S3)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.extended_enat) (S3 tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X3) S3)))) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.real) (S3 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S3)))) (=> (@ (@ tptp.ord_less_real Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.nat) (S3 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S3)))) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.int) (S3 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S3)))) (=> (@ (@ tptp.ord_less_int Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.code_integer) (S3 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S3))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.extended_enat) (S3 tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (not (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X3) S3))))) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.real) (S3 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S3))))) (=> (@ (@ tptp.ord_less_real Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.nat) (S3 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S3))))) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.int) (S3 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S3))))) (=> (@ (@ tptp.ord_less_int Z4) X3) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.code_integer) (S3 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S3)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.extended_enat) (S3 tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X3) S3)))) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.real) (S3 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S3)))) (=> (@ (@ tptp.ord_less_real X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.nat) (S3 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S3)))) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.int) (S3 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S3)))) (=> (@ (@ tptp.ord_less_int X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.code_integer) (S3 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S3))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.extended_enat) (S3 tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (not (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X3) S3))))) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.real) (S3 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S3))))) (=> (@ (@ tptp.ord_less_real X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.nat) (S3 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S3))))) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((D tptp.int) (S3 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S3))))) (=> (@ (@ tptp.ord_less_int X3) Z4) (= _let_1 _let_1)))))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (Y 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 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((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))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 6.84/7.08 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((X (-> tptp.nat tptp.nat)) (X22 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((X (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.84/7.08 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.08 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.84/7.08 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 6.84/7.08 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.84/7.08 (assert (forall ((R tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R))) (=> (not (= R tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))))
% 6.84/7.08 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (=> (not (= R tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 6.84/7.08 (assert (forall ((R tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R))) (=> (not (= R tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 6.84/7.08 (assert (forall ((R tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R))) (=> (not (= R tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri6519982836138164636nteger M) A)) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int M) A)) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((W tptp.complex) (Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.times_times_complex W))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.84/7.08 (assert (forall ((W tptp.real) (Y tptp.real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.84/7.08 (assert (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_complex (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.84/7.08 (assert (forall ((N2 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 N2)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N2))))))))
% 6.84/7.08 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.08 (assert (= tptp.nat_set_decode (lambda ((X2 tptp.nat)) (@ tptp.collect_nat (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat _let_1) N))))))))))
% 6.84/7.08 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A4) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N 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 N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))))))))))
% 6.84/7.08 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A4) _let_1))) (@ (@ (@ tptp.if_int (= N 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 N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))))))))))
% 6.84/7.08 (assert (= tptp.artanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 6.84/7.08 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))
% 6.84/7.08 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))))
% 6.84/7.08 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A4) _let_1)))))))
% 6.84/7.08 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A4) _let_1)))))))
% 6.84/7.08 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A4) _let_1)))))))
% 6.84/7.08 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.pow K) L2)))))
% 6.84/7.08 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L2)))))
% 6.84/7.08 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L2)))))
% 6.84/7.08 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L2)))))
% 6.84/7.08 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L2)))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real B2)) (@ tptp.uminus612125837232591019t_real A2)))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat B2)) (@ tptp.uminus5710092332889474511et_nat A2)))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real A2)) (@ tptp.uminus612125837232591019t_real B2)) (@ (@ tptp.ord_less_eq_set_real B2) A2))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ tptp.uminus5710092332889474511et_nat B2)) (@ (@ tptp.ord_less_eq_set_nat B2) A2))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.84/7.08 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real X)) (@ tptp.uminus612125837232591019t_real Y)) (@ (@ tptp.ord_less_eq_set_real Y) X))))
% 6.84/7.08 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= M N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= M N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= M N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= M N2))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ tptp.ln_ln_real X) (@ tptp.ln_ln_real Y)) (= X Y)))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.84/7.08 (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))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc6842872674320459806at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.84/7.08 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.84/7.08 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.84/7.08 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.84/7.08 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.84/7.08 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.84/7.08 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.84/7.08 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 6.84/7.08 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int B) A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (= (@ _let_1 (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (= (@ tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.84/7.08 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) tptp.one_one_int) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.84/7.08 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N2) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))))
% 6.84/7.08 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.84/7.08 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.84/7.08 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.84/7.08 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.84/7.08 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.84/7.08 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.84/7.08 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.84/7.08 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N2 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N2 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N2 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N2 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= N2 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= N2 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= N2 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= N2 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2))))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)))) (not (= M tptp.one)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (not (= M tptp.one)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M tptp.one)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.plus_plus_int _let_1) _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.plus_plus_complex _let_1) _let_1) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.08 (assert (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.84/7.08 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.84/7.08 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.84/7.08 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.84/7.08 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.84/7.08 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.84/7.08 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.84/7.08 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.84/7.08 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.84/7.08 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.84/7.08 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.power_power_real A) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.power_power_int A) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.power_power_complex A) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N2))))))
% 6.84/7.08 (assert (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.84/7.08 (assert (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.84/7.08 (assert (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.08 (assert (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.84/7.08 (assert (forall ((N2 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))) N2)) tptp.one_one_real)))
% 6.84/7.08 (assert (forall ((N2 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))) N2)) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_complex)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_Code_integer)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2) tptp.one_one_real))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2) tptp.one_one_complex))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2) tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_real _let_1) N2) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_int _let_1) N2) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex _let_1) N2) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 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))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N2) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N2))) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 6.84/7.08 (assert (forall ((N2 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 N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.84/7.08 (assert (forall ((N2 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 N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real Y)) (@ tptp.uminus612125837232591019t_real X)))))
% 6.84/7.08 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X)))))
% 6.84/7.08 (assert (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real Y) (@ tptp.uminus612125837232591019t_real X)) (@ (@ tptp.ord_less_eq_set_real X) (@ tptp.uminus612125837232591019t_real Y)))))
% 6.84/7.08 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 6.84/7.08 (assert (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real Y)) X) (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real X)) Y))))
% 6.84/7.08 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 6.84/7.08 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 6.84/7.08 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.84/7.08 (assert (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.84/7.08 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.84/7.08 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.84/7.08 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc6842872674320459806at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.84/7.08 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (A6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A6) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A6)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A6) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A6)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B))) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B))) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N2))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) B)) (@ _let_1 B)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int) (R tptp.int) (S3 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ tptp.bit_concat_bit N2))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R) S3)) (and (= (@ _let_1 K) (@ _let_1 R)) (= L2 S3)))))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (G (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (= (@ tptp.produc6081775807080527818_nat_o F) G))))
% 6.84/7.08 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (G (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (= (@ tptp.produc6842872674320459806at_nat F) G))))
% 6.84/7.08 (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 ((X5 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.84/7.08 (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 ((X5 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.84/7.08 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_int_int X5) Y5)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.84/7.08 (assert (forall ((F (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y3)))) F)))
% 6.84/7.08 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ tptp.produc6842872674320459806at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y3)))) F)))
% 6.84/7.08 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y3)) __flatten_var_0))) F)))
% 6.84/7.08 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y3)) __flatten_var_0))) F)))
% 6.84/7.08 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y3)))) F)))
% 6.84/7.08 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.nat tptp.nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc6081775807080527818_nat_o P) Z)) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Q (-> tptp.nat Bool)) (P (-> tptp.nat tptp.nat tptp.nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc6842872674320459806at_nat P) Z)) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))))
% 6.84/7.08 (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 ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))))
% 6.84/7.08 (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 ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))))
% 6.84/7.08 (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 ((X5 tptp.int) (Y5 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) X))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N2))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N2) M)) _let_2) _let_1) A))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.84/7.08 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.84/7.08 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.84/7.08 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.84/7.08 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.84/7.08 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))))
% 6.84/7.08 (assert (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 6.84/7.08 (assert (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.84/7.08 (assert (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.84/7.08 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real N2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.84/7.08 (assert (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.84/7.08 (assert (forall ((B2 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B2 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((B2 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B2 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((B2 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B2 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((B2 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B2 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.84/7.08 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))))
% 6.84/7.08 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))))
% 6.84/7.08 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))))
% 6.84/7.08 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B4)))))
% 6.84/7.08 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))))
% 6.84/7.08 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))))
% 6.84/7.08 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))))
% 6.84/7.08 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B4)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B)))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B))))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 6.84/7.08 (assert (forall ((U tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X) X))))
% 6.84/7.08 (assert (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y3)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X))) (@ tptp.uminus_uminus_real X))))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) X))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X)) (=> (@ _let_1 X) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N2)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) A)) (@ _let_1 A))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.84/7.08 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.84/7.08 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.84/7.08 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.84/7.08 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C) B) (@ tptp.uminus_uminus_real A))))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B))))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.84/7.08 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))))
% 6.84/7.08 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))))
% 6.84/7.08 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.84/7.08 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))))
% 6.84/7.08 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))))
% 6.84/7.08 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.84/7.08 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.84/7.08 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.84/7.08 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.84/7.08 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.84/7.08 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.power_power_real A) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int A) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ (@ tptp.power_power_complex A) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ (@ tptp.power_power_int X) _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ (@ tptp.power_power_complex X) _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (= (@ tptp.ln_ln_real X) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.84/7.08 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.08 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.84/7.08 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.84/7.08 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.84/7.08 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.84/7.08 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.84/7.08 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.84/7.08 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.84/7.08 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.84/7.08 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1482373934393186551omplex Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A4 tptp.int)) (@ (@ tptp.modulo_modulo_int A4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.08 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.84/7.08 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y)) Y)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.08 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.08 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.84/7.08 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.84/7.08 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.84/7.08 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.84/7.08 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (or (= A tptp.one_one_real) (= A (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.84/7.08 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.08 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.08 (assert (forall ((U tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.84/7.08 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))
% 6.84/7.08 (assert (forall ((N2 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))) N2))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) K))))
% 6.84/7.08 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N2) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.84/7.08 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.84/7.08 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (= (@ (@ 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))) N2))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (= (@ (@ 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))) N2))))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (= (@ (@ 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))) N2))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K))))))
% 6.84/7.08 (assert (forall ((N2 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))) N2)) _let_1))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L2)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L2) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) 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))) N2))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (N2 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))) N2)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K)))))
% 6.84/7.08 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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))) N2)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 6.84/7.08 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.84/7.08 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.84/7.08 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.84/7.08 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (N2 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))) N2))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N2) 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) N2)) tptp.one_one_Code_integer))))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N2) 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) N2)) tptp.one_one_int))))))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N2) 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) N2)) tptp.one_one_nat))))))))))
% 6.84/7.08 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (N2 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 N2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))))
% 6.84/7.08 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R4)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R4 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R4)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 6.84/7.08 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N2)) (= M N2))))
% 6.84/7.08 (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)))))
% 6.84/7.08 (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)))))
% 6.84/7.08 (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)))))
% 6.84/7.08 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ F A) B) (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.84/7.08 (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)))))
% 6.84/7.08 (assert (forall ((P5 tptp.produc6271795597528267376eger_o) (C (-> tptp.code_integer Bool Bool))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc7828578312038201481er_o_o C) P5))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_num_num) (C (-> tptp.num tptp.num Bool))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc5703948589228662326_num_o C) P5))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_nat_num) (C (-> tptp.nat tptp.num Bool))) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc4927758841916487424_num_o C) P5))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc4947309494688390418_int_o C) P5))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat Bool))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= P5 (@ (@ tptp.product_Pair_nat_nat A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc6081775807080527818_nat_o C) P5))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (assert (forall ((Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc4130284055270567454et_nat C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 6.84/7.08 (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)))))))
% 6.84/7.08 (assert (forall ((P5 tptp.produc6271795597528267376eger_o) (Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.produc6271795597528267376eger_o) (Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ tptp.member_real Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.produc6271795597528267376eger_o) (Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ tptp.member_int Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.produc6271795597528267376eger_o) (Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_num_num) (Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_num_num) (Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ tptp.member_real Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_num_num) (Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ tptp.member_int Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_num_num) (Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_nat_num) (Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat))) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num A3) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4130284055270567454et_nat C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_nat_num) (Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real))) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num A3) B3)) (@ (@ tptp.member_real Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P5)))))
% 6.84/7.08 (assert (forall ((P5 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A3) B3) P5) (@ (@ (@ C A3) B3) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P5) X))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit1 N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.84/7.08 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.84/7.08 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.84/7.08 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.84/7.08 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.84/7.08 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.84/7.08 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N2)) (@ tptp.bit0 (@ _let_1 N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) tptp.one)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.bit1 N2))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) (or (not (= A tptp.zero_zero_real)) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2)) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N2) M)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N2) M)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N2) M)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1))))))
% 6.84/7.08 (assert (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.84/7.08 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R4 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.84/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.84/7.08 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.84/7.08 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.84/7.08 (assert (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P5)) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P5)) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P5)) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ tptp.member_int Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P5)) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P5)) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P5)) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P5)) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ tptp.member_int Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P5)) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat)) (P5 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4130284055270567454et_nat C) P5)) (not (forall ((X5 tptp.nat) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num X5) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (P5 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P5)) (not (forall ((X5 tptp.nat) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num X5) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y5)))))))))
% 6.84/7.08 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 6.84/7.08 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.84/7.08 (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))))
% 6.84/7.08 (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))))
% 6.84/7.08 (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))))
% 6.84/7.08 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.84/7.08 (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))))
% 6.84/7.08 (assert (forall ((C (-> tptp.code_integer Bool Bool)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.produc7828578312038201481er_o_o C) P5) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ C X5) Y5))))))))
% 6.84/7.08 (assert (forall ((C (-> tptp.num tptp.num Bool)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.produc5703948589228662326_num_o C) P5) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ C X5) Y5))))))))
% 6.84/7.08 (assert (forall ((C (-> tptp.nat tptp.num Bool)) (P5 tptp.product_prod_nat_num)) (=> (@ (@ tptp.produc4927758841916487424_num_o C) P5) (not (forall ((X5 tptp.nat) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num X5) Y5)) (not (@ (@ C X5) Y5))))))))
% 6.84/7.08 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P5 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P5) (not (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int X5) Y5)) (not (@ (@ C X5) Y5))))))))
% 6.84/7.08 (assert (forall ((C (-> tptp.nat tptp.nat Bool)) (P5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o C) P5) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= P5 (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ (@ C X5) Y5))))))))
% 6.84/7.08 (assert (forall ((R2 (-> 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 R2) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R2 A) B) C))))
% 6.84/7.08 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P5 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P5) Z) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= P5 (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ (@ (@ C X5) Y5) Z))))))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.84/7.08 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.84/7.08 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N4))))) (=> (forall ((N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N4))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N4))))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N4))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N4))))) (not (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N4))))))))))))))))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y (@ tptp.bit1 X33)))))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) U)) Y))) V)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.one_one_real)))
% 6.84/7.08 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E2))) (= X tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.abs_abs_real A) B) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (or (= A B) (= A (@ tptp.uminus_uminus_real B)))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) B) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B)))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.abs_abs_int A) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (or (= A B) (= A (@ tptp.uminus_uminus_int B)))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.abs_abs_real B)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B A) (= B (@ tptp.uminus_uminus_real A)))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.abs_abs_Code_integer B)) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (or (= B A) (= B (@ tptp.uminus1351360451143612070nteger A)))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.abs_abs_int B)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B A) (= B (@ tptp.uminus_uminus_int A)))))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))))
% 6.84/7.08 (assert (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.84/7.08 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))))
% 6.84/7.08 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.84/7.08 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 6.84/7.08 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.84/7.08 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.84/7.08 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 6.84/7.08 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X) _let_1))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X) _let_1))))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X) _let_1))))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y2))) D3) (and (@ (@ tptp.ord_less_real A) Y2) (@ (@ tptp.ord_less_real Y2) B))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))))
% 6.84/7.08 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))))
% 6.84/7.08 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A) A)) A))))
% 6.84/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A) A)) A))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))))
% 6.84/7.08 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))
% 6.84/7.08 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y2))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y2) (@ (@ tptp.ord_less_eq_real Y2) B))))))))))
% 6.84/7.08 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (@ tptp.numeral_numeral_nat _let_1)) (= _let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X) tptp.one_one_real))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2) (@ (@ tptp.power_power_real A) N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2) (@ (@ tptp.power_power_int A) N2)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 6.84/7.08 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ P X5) (@ (@ tptp.power_power_real X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X5) (@ (@ P X5) (@ (@ tptp.power_power_int X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.84/7.08 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.84/7.08 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.84/7.08 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.84/7.08 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.84/7.08 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.84/7.08 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N)) (@ (@ tptp.modulo_modulo_nat M6) N)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X) Z)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ 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 N2) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.84/7.08 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N)))))))
% 6.84/7.08 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N)))))))
% 6.84/7.08 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one)))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.84/7.08 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.84/7.08 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.84/7.08 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))))
% 6.84/7.08 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.84/7.08 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K)))))
% 6.84/7.08 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.pred_numeral K)))))
% 6.84/7.08 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) (@ tptp.pred_numeral K))))))
% 6.84/7.08 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N2)))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.84/7.08 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.84/7.08 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.84/7.08 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X5 tptp.num)) (=> (@ P X5) (@ P (@ tptp.inc X5)))) (@ P X)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.84/7.08 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.84/7.08 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.84/7.08 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L2))) (@ tptp.abs_abs_int L2)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 6.84/7.08 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.inc X)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat X)) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X)) tptp.one_one_real))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L2))) (@ _let_2 (@ _let_1 L2)))))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_nat I4) N2)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K)))))))))
% 6.84/7.08 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.84/7.08 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.84/7.08 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K))))))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K))))))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.84/7.08 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))))
% 6.84/7.08 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 6.84/7.08 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K3) _let_1))))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K3) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 6.84/7.08 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 6.84/7.08 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.84/7.08 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.84/7.08 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.84/7.08 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.84/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.84/7.08 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.84/7.08 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N2))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N2))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N2))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.84/7.08 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.84/7.08 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.08 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.84/7.08 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.84/7.08 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.84/7.08 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.84/7.08 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.84/7.08 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.84/7.08 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.84/7.08 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.complex)) (let ((_let_1 (@ tptp.ring_17405671764205052669omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_real (@ tptp.ring_1_of_int_real X)) (@ tptp.ring_1_of_int_real Y)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_int (@ tptp.ring_1_of_int_int X)) (@ tptp.ring_1_of_int_int Y)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_Code_integer (@ tptp.ring_18347121197199848620nteger X)) (@ tptp.ring_18347121197199848620nteger Y)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.08 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N2)) (@ tptp.bit1 (@ tptp.bitM N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.inc (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.inc N2)) (@ tptp.bit1 N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X)))))
% 6.84/7.08 (assert (forall ((D tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N2) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real D))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N2)) tptp.one) (@ tptp.bit0 N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.84/7.08 (assert (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.84/7.08 (assert (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.84/7.08 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.84/7.08 (assert (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.84/7.08 (assert (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.84/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.84/7.08 (assert (= tptp.ord_less_eq_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 6.84/7.08 (assert (= tptp.ord_less_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 6.84/7.08 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.84/7.08 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.84/7.08 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D))) _let_1))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2))) tptp.one_one_complex))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N2))) tptp.one_one_real))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.84/7.08 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))))
% 6.84/7.08 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))))
% 6.84/7.08 (assert (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X))))))
% 6.84/7.08 (assert (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X)))) tptp.one_one_real)))
% 6.84/7.08 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K)))))
% 6.84/7.08 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ _let_1 K)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y)))))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y2)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y2) tptp.one_one_int)))) (= Y2 X5)))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (exists ((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)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N2)) (@ (@ 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 N2)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N2)) (@ (@ 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 N2)))))))
% 6.84/7.08 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.84/7.08 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 tptp.zero_zero_int) (= L tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L) (@ (@ (@ tptp.if_int (= L _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.84/7.08 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 _let_2) (= L _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) B) _let_1))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B))) (= (@ (@ tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) B) _let_1))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) B) _let_1))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) A) A)))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) A) A)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ _let_1 N2)))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.zero_zero_int) A)))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.zero_zero_nat) A)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.zero_zero_int) A) A)))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.zero_zero_nat) A) A)))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.08 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.84/7.08 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.84/7.08 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)))
% 6.84/7.08 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) X)))
% 6.84/7.08 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger _let_1) X) _let_1))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) X) _let_1))))
% 6.84/7.08 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger X) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int X) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N2) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 6.84/7.08 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.84/7.08 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) (and (@ _let_1 K) (@ _let_1 L2))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.84/7.08 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.84/7.08 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int) tptp.one_one_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.zero_zero_int)))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L2)))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.84/7.08 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ tptp.bit_se2000444600071755411sk_int N)))))
% 6.84/7.08 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A4) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Z)) X) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y) X)) (@ (@ tptp.bit_se1409905431419307370or_int Z) X)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y) Z)) X) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) X)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int X))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int Y) Z)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int Y) Z)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int B))) (let ((_let_2 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int B))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat B))) (let ((_let_2 (@ tptp.bit_se1412395901928357646or_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.84/7.08 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B4) A4))))
% 6.84/7.08 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B4) A4))))
% 6.84/7.08 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int B4) A4))))
% 6.84/7.08 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat B4) A4))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int A))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int B) C))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat A))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat B) C))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) (@ (@ tptp.plus_plus_int X) Y))))
% 6.84/7.08 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int X) tptp.zero_zero_int) X)))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.bit_se1409905431419307370or_int A) B) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.bit_se1412395901928357646or_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.08 (assert (forall ((A2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A2))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))))
% 6.84/7.08 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.exp_real A2))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ tptp.bit_se1080825931792720795nteger A))) (let ((_let_3 (@ tptp.bit_se3949692690581998587nteger A))) (=> (= (@ _let_3 X) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 Y) _let_1) (= X Y))))))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_3 (@ tptp.bit_se725231765392027082nd_int A))) (=> (= (@ _let_3 X) tptp.zero_zero_int) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y) tptp.zero_zero_int) (=> (= (@ _let_2 Y) _let_1) (= X Y))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (@ (@ tptp.bit_se3949692690581998587nteger A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.84/7.08 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (= (@ tptp.exp_real X5) Y)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y)))))))
% 6.84/7.08 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L2)))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) X))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Y))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ (@ tptp.times_times_complex Y) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y) (@ (@ tptp.times_times_real Y) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y))))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N2)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N2)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_se2000444600071755411sk_int N2)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 6.84/7.08 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) K))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.84/7.08 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))) tptp.one_one_real)))
% 6.84/7.08 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N2)) (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N2)) (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N2))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1080825931792720795nteger A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X)))))
% 6.84/7.08 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.84/7.08 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ (@ tptp.minus_minus_real Y) tptp.one_one_real)) (= (@ tptp.exp_real X5) Y))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.one_one_int) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N2)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.84/7.08 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ tptp.exp_real X2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.84/7.08 (assert (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))) (let ((_let_2 (@ tptp.exp_complex X2))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.08 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1))) _let_1)))
% 6.84/7.08 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.84/7.08 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N2)) (= N2 tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2)) (= N2 tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N2)) (= N2 tptp.zero_zero_nat))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger A) tptp.one_one_Code_integer) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.one_one_int) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 6.84/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) A) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 6.84/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) A) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 6.84/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))))
% 6.84/7.08 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K3)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.84/7.08 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))
% 6.84/7.08 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))
% 6.84/7.08 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N4 tptp.nat)) (and (not (@ P N4)) (@ P (@ tptp.suc N4))))))))
% 6.84/7.08 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z4)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z4)) X))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z4)))))
% 6.84/7.08 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))
% 6.84/7.08 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (Y 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 Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y)))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X) N2))))
% 6.84/7.08 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) X))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))))
% 6.84/7.08 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) A2)) B2) (and (@ (@ tptp.member_int X) B2) (@ (@ tptp.ord_less_eq_set_int A2) B2)))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (A2 tptp.set_complex) (B2 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.insert_complex X) A2)) B2) (and (@ (@ tptp.member_complex X) B2) (@ (@ tptp.ord_le211207098394363844omplex A2) B2)))))
% 6.84/7.08 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A2)) B2) (and (@ (@ tptp.member8440522571783428010at_nat X) B2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2)))))
% 6.84/7.08 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) A2)) B2) (and (@ (@ tptp.member_real X) B2) (@ (@ tptp.ord_less_eq_set_real A2) B2)))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) A2)) B2) (and (@ (@ tptp.member_nat X) B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2)))))
% 6.84/7.08 (assert (forall ((A tptp.int) (A2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))))
% 6.84/7.08 (assert (forall ((A tptp.real) (A2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= (@ (@ tptp.insert_real A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))))
% 6.84/7.08 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))))
% 6.84/7.08 (assert (forall ((B tptp.int) (A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))))
% 6.84/7.08 (assert (forall ((B tptp.real) (A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= _let_1 (@ (@ tptp.insert_real A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))))
% 6.84/7.08 (assert (forall ((B tptp.nat) (A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.08 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex A2) (@ tptp.uminus8566677241136511917omplex (@ (@ tptp.insert_complex B) tptp.bot_bot_set_complex))) (not (@ (@ tptp.member_complex B) A2)))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A2) (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (not (@ (@ tptp.member8440522571783428010at_nat B) A2)))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B) A2)))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B) A2)))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B) A2)))))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.84/7.08 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.84/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))))
% 6.84/7.08 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_int B) B2))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_real B) B2))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_nat B) B2))))))
% 6.84/7.08 (assert (forall ((B2 tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B2) (@ (@ tptp.insert_int A) B2))))
% 6.84/7.08 (assert (forall ((B2 tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B2) (@ (@ tptp.insert_real A) B2))))
% 6.84/7.08 (assert (forall ((B2 tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.insert_nat A) B2))))
% 6.84/7.08 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B2)) (@ _let_1 B2))))))
% 6.84/7.08 (assert (forall ((X tptp.complex) (A2 tptp.set_complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) B2)) (@ _let_1 B2))))))
% 6.84/7.08 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B2)) (@ _let_1 B2))))))
% 6.84/7.08 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B2)) (@ _let_1 B2))))))
% 6.84/7.08 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B2)) (@ _let_1 B2))))))
% 6.84/7.08 (assert (forall ((C4 tptp.set_int) (D4 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C4) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C4)) (@ _let_1 D4))))))
% 6.84/7.08 (assert (forall ((C4 tptp.set_real) (D4 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C4) D4) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C4)) (@ _let_1 D4))))))
% 6.84/7.08 (assert (forall ((C4 tptp.set_nat) (D4 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C4) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C4)) (@ _let_1 D4))))))
% 6.84/7.08 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.84/7.08 (assert (forall ((X8 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X8) _let_1) (or (= X8 tptp.bot_bot_set_int) (= X8 _let_1))))))
% 6.84/7.08 (assert (forall ((X8 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (= (@ (@ tptp.ord_less_eq_set_real X8) _let_1) (or (= X8 tptp.bot_bot_set_real) (= X8 _let_1))))))
% 6.84/7.08 (assert (forall ((X8 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X8) _let_1) (or (= X8 tptp.bot_bot_set_nat) (= X8 _let_1))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A2) _let_1) (or (= A2 tptp.bot_bot_set_int) (= A2 _let_1))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A2) _let_1) (or (= A2 tptp.bot_bot_set_real) (= A2 _let_1))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (or (= A2 tptp.bot_bot_set_nat) (= A2 _let_1))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (X tptp.int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_int X) A2))))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (X tptp.complex) (C4 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex B2))) (let ((_let_2 (@ tptp.ord_le211207098394363844omplex A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_complex X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_complex X) A2))))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B2))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member8440522571783428010at_nat X) A2))))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (X tptp.real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_real X) A2))))))))
% 6.84/7.08 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (X tptp.nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_nat X) A2))))))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.84/7.08 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) tptp.one) tptp.one)))
% 6.84/7.08 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.84/7.08 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.84/7.09 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.84/7.09 (assert (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S4) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S4) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) S4) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y2 tptp.real)) (=> (@ (@ tptp.member_real Y2) S4) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y2 tptp.real)) (=> (@ (@ tptp.member_real Y2) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S4) (@ (@ tptp.ord_less_eq_int (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S4) (@ (@ tptp.ord_less_eq_int (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B3 tptp.extended_enat) (A7 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A7) (=> (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A7) (@ (@ tptp.ord_le72135733267957522d_enat X3) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_Extended_enat B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B3 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) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B3 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) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B3 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) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B3 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) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B3 tptp.extended_enat) (A7 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A7) (=> (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A7) (@ (@ tptp.ord_le72135733267957522d_enat B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_Extended_enat B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B3 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A7) (@ (@ tptp.ord_less_real B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B3 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) A7) (@ (@ tptp.ord_less_num B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B3 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A7) (@ (@ tptp.ord_less_nat B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B3 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A7) (@ (@ tptp.ord_less_int B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B3) A7)))))) (@ P A2))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F3) A2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A3 tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A3))) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat A3) F4))))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A3 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A3))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le211207098394363844omplex F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A3) F4))))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A3 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A3))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_int F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A3) F4))))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A3 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A3))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_real F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A3) F4))))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A3) F4))))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F3) A2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A3 tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A3))) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat A3) F4)))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A3 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A3))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A3) F4)))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A3 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A3))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A3) F4)))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A3 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A3))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A3) F4)))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((F3 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A3) F4)))))))) (@ P F3)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (let ((_let_2 (@ (@ tptp.member_complex X) A2))) (let ((_let_3 (@ tptp.insert_complex X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X) A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X) A2))) (let ((_let_3 (@ tptp.insert_int X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X) A2))) (let ((_let_3 (@ tptp.insert_real X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X) A2))) (let ((_let_3 (@ tptp.insert_nat X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B2) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) B2) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B2) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B2))))))
% 6.84/7.09 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I2) X))) (@ (@ tptp.insert_int X) (@ tptp.set_int2 Xs2)))))
% 6.84/7.09 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X))) (@ (@ tptp.insert_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.84/7.09 (assert (forall ((Xs2 tptp.list_real) (I2 tptp.nat) (X tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I2) X))) (@ (@ tptp.insert_real X) (@ tptp.set_real2 Xs2)))))
% 6.84/7.09 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I2) X))) (@ (@ tptp.insert_nat X) (@ tptp.set_nat2 Xs2)))))
% 6.84/7.09 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.84/7.09 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.84/7.09 (assert (forall ((P (-> tptp.set_Pr1261947904930325089at_nat Bool)) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (=> (not (@ tptp.finite6177210948735845034at_nat B2)) _let_1) (=> (forall ((A7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A7) (=> (not (= A7 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A7) B2) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A7) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A7) (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))) (@ P A7)))))) _let_1))))))
% 6.84/7.09 (assert (forall ((P (-> tptp.set_complex Bool)) (B2 tptp.set_complex)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_complex) (=> (=> (not (@ tptp.finite3207457112153483333omplex B2)) _let_1) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (not (= A7 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A7) B2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X3) tptp.bot_bot_set_complex))))) (@ P A7)))))) _let_1))))))
% 6.84/7.09 (assert (forall ((P (-> tptp.set_int Bool)) (B2 tptp.set_int)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B2)) _let_1) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (not (= A7 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) B2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))) (@ P A7)))))) _let_1))))))
% 6.84/7.09 (assert (forall ((P (-> tptp.set_real Bool)) (B2 tptp.set_real)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_real) (=> (=> (not (@ tptp.finite_finite_real B2)) _let_1) (=> (forall ((A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (not (= A7 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A7) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))) (@ P A7)))))) _let_1))))))
% 6.84/7.09 (assert (forall ((P (-> tptp.set_nat Bool)) (B2 tptp.set_nat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B2)) _let_1) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (not (= A7 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) B2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))) (@ P A7)))))) _let_1))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A7) (=> (not (= A7 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A7) B2) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A7) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A7) (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))) (@ P A7)))))) (@ P B2))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (not (= A7 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A7) B2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X3) tptp.bot_bot_set_complex))))) (@ P A7)))))) (@ P B2))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (not (= A7 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) B2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))) (@ P A7)))))) (@ P B2))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (not (= A7 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A7) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))) (@ P A7)))))) (@ P B2))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (not (= A7 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) B2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))) (@ P A7)))))) (@ P B2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_complex X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_complex A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A2) B2)))))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2)))))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B2)))))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B2)))))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B2)))))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N2)) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N2)) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N2)) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N2)) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))
% 6.84/7.09 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bit1 M5)))))) (=> (=> _let_3 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N4 tptp.num)) (= X (@ tptp.bit0 N4))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit0 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit0 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (=> (=> (exists ((N4 tptp.num)) (= X (@ tptp.bit1 N4))) _let_2) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit1 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (not (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit1 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))))))))))))))))))
% 6.84/7.09 (assert (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 6.84/7.09 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.84/7.09 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.84/7.09 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.84/7.09 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.84/7.09 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L2))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L2) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L2)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.log _let_1) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X)))))))
% 6.84/7.09 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))))))))
% 6.84/7.09 (assert (= tptp.arctan (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X2) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 X) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y)) (= X Y))))
% 6.84/7.09 (assert (= (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) tptp.bot_bot_nat_o))
% 6.84/7.09 (assert (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.84/7.09 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.09 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 6.84/7.09 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.84/7.09 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))))
% 6.84/7.09 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.84/7.09 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))))
% 6.84/7.09 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X) (= (@ _let_2 (@ (@ tptp.log A) X)) (@ _let_1 X))))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_real A) X)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) A))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y)))))))))
% 6.84/7.09 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) A) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N2))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real A) X))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) A))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N2))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))))
% 6.84/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))))
% 6.84/7.09 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N2)))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N2) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N2) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.nat_set_encode A2)))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N4)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N4)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N4)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N4)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2))))))
% 6.84/7.09 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.84/7.09 (assert (forall ((M tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (= _let_1 _let_1))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 6.84/7.09 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int A) B)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))))
% 6.84/7.09 (assert (forall ((K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (= M N2))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (= M N2))))))
% 6.84/7.09 (assert (forall ((K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N2) (= N2 tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N2) (= N2 tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N4)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N4)))) (= (@ (@ tptp.plus_plus_int A) B) (@ (@ tptp.bit_se1409905431419307370or_int A) B)))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N4)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N4)))) (= (@ (@ tptp.plus_plus_nat A) B) (@ (@ tptp.bit_se1412395901928357646or_nat A) B)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.84/7.09 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (= tptp.log (lambda ((A4 tptp.real) (X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real A4)))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) A) (@ (@ tptp.bit_se2923211474154528505it_int N2) A)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real X) _let_1) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))))))
% 6.84/7.09 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.84/7.09 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N2) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))
% 6.84/7.09 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (A4 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A4) N)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N) A4))))
% 6.84/7.09 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N tptp.nat) (A4 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A4) N)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N) A4))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 B))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.84/7.09 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc N2)) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) N2))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N2))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N4) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))
% 6.84/7.09 (assert (forall ((A tptp.int)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N4) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))
% 6.84/7.09 (assert (forall ((A tptp.nat)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N4) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.84/7.09 (assert (forall ((K tptp.int)) (not (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N4) M2) (= (@ _let_1 M2) (@ _let_1 N4))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (not (@ _let_1 N4)))))))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.84/7.09 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A4) (@ (@ tptp.power_8256067586552552935nteger _let_1) N))))))))
% 6.84/7.09 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A4) (@ (@ tptp.power_power_int _let_1) N))))))))
% 6.84/7.09 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A4) (@ (@ tptp.power_power_nat _let_1) N))))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X) Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y)))))))
% 6.84/7.09 (assert (forall ((U tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) U) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) U))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X) (= Y tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D) _let_1))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.log A) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X)))))))))))
% 6.84/7.09 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N))))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N2) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) Z)) (@ (@ tptp.insert_nat N2) _let_1))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X) Y))))))))
% 6.84/7.09 (assert (forall ((N2 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) N2) (= (@ tptp.sqrt (@ _let_3 N2)) (@ _let_3 (@ (@ tptp.divide_divide_nat N2) _let_2)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.sqrt X)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N2))))))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N2))))))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N2))))))))))
% 6.84/7.09 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A4) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 6.84/7.09 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A4) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 6.84/7.09 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A4) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N2) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.84/7.09 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A12)))))
% 6.84/7.09 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.84/7.09 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.arcosh_real X) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 6.84/7.09 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I4 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J2) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)) (@ (@ P I4) J2)))) (@ (@ P A0) A12)))))
% 6.84/7.09 (assert (= tptp.arsinh_real (lambda ((X2 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 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)) N2)) (=> (@ (@ 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 N2)))))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_2)))) (= (@ (@ tptp.divide_divide_real tptp.pi) _let_3) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_3) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_2)))))) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))))))))))))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.bit1 tptp.one))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1))) (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_3)))))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real _let_3)) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2))))))))) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_2)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N2)) (= M N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N2)) (= M N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) (@ tptp.semiri4939895301339042750nteger N2)) (= M N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.84/7.09 (assert (= (@ tptp.semiri4216267220026989637d_enat tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat))
% 6.84/7.09 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.84/7.09 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.84/7.09 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.84/7.09 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.84/7.09 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.semiri4216267220026989637d_enat N2)) (= tptp.zero_zero_nat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.semiri4939895301339042750nteger N2)) (= tptp.zero_zero_nat N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat M) tptp.zero_z5237406670263579293d_enat) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera1916890842035813515d_enat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_real N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6690914467698888265omplex N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6620942414471956472nteger N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat N2) tptp.one_on7984719198319812577d_enat) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N2) tptp.one_one_Code_integer) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.semiri4216267220026989637d_enat N2)) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (= N2 tptp.one_one_nat))))
% 6.84/7.09 (assert (= (@ tptp.semiri4216267220026989637d_enat tptp.one_one_nat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.09 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.84/7.09 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.84/7.09 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.84/7.09 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.84/7.09 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger M)) N2))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W) (@ tptp.semiri4939895301339042750nteger X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger X) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.84/7.09 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 6.84/7.09 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.84/7.09 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.semiri4216267220026989637d_enat M)) tptp.zero_z5237406670263579293d_enat) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc M)) (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.semiri4216267220026989637d_enat M)))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.84/7.09 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X)) N2) (@ tptp.semiri4216267220026989637d_enat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.84/7.09 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.84/7.09 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.84/7.09 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 6.84/7.09 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.84/7.09 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2) (@ tptp.semiri4939895301339042750nteger Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.84/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat Y) (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.84/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.84/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.84/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 6.84/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.84/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.84/7.09 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat W)))))
% 6.84/7.09 (assert (forall ((N2 tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) M))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N4)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N4)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger X))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.semiri4939895301339042750nteger M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.ring_18347121197199848620nteger X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (= N2 tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc N2)) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc N2)) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.09 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (@ tptp.divide6298287555418463151nteger A))) (= (@ _let_3 (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_3 _let_2)) _let_1)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.84/7.09 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger I2)) (@ tptp.semiri4939895301339042750nteger J)))))
% 6.84/7.09 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.84/7.09 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.84/7.09 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X)) (@ tptp.semiri4216267220026989637d_enat Y)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_Code_integer (@ tptp.semiri4939895301339042750nteger X)) (@ tptp.semiri4939895301339042750nteger Y)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se1412395901928357646or_nat M) N2)) (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se1412395901928357646or_nat M) N2)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se1412395901928357646or_nat M) N2)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ tptp.bit_se2119862282449309892nteger N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) X))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N2))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) X)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N2))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y2 tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) X)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X)))))
% 6.84/7.09 (assert (forall ((D tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real D))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.84/7.09 (assert (= tptp.ord_less_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.84/7.09 (assert (= tptp.ord_less_eq_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log B) _let_1)))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D))) _let_1))))))
% 6.84/7.09 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N4 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) E)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N2)))) N2) (@ tptp.exp_real X)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N2)))) N2) (@ tptp.exp_complex X)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M5)) X)) C))) (= X tptp.zero_zero_real)))))))
% 6.84/7.09 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X)))) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N2)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ln_ln_real X))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_1 X)))))))
% 6.84/7.09 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ 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 N2))))))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) tptp.pi))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N2))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ 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 N2))))))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.zero_zero_real))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.84/7.09 (assert (forall ((Y 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 Y))))
% 6.84/7.09 (assert (forall ((N2 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)) N2)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.84/7.09 (assert (forall ((N2 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)) N2)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ 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 N2)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real X)))))))
% 6.84/7.09 (assert (= tptp.semiri4216267220026989637d_enat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.produc2676513652042109336d_enat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ tptp.semiri4216267220026989637d_enat M6)))) (@ (@ (@ tptp.if_Extended_enat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M6)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M6)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (= N tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M6)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (= tptp.semiri4939895301339042750nteger (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1830744345554046123nteger (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.semiri4939895301339042750nteger M6)))) (@ (@ (@ tptp.if_Code_integer (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M6)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))
% 6.84/7.09 (assert (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)))) (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) N2)) (@ _let_4 N2))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 6.84/7.09 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (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) N2)) (@ _let_3 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 6.84/7.09 (assert (forall ((N2 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)) N2)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N))))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((N2 tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ F tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ F tptp.zero_zero_nat))))
% 6.84/7.09 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.84/7.09 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.84/7.09 (assert (forall ((N2 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 N2))) tptp.zero_zero_real)))
% 6.84/7.09 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 6.84/7.09 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.84/7.09 (assert (forall ((Z tptp.int)) (=> (forall ((N4 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N4)))) (not (forall ((N4 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))))
% 6.84/7.09 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N4))) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))) (@ P Z)))))
% 6.84/7.09 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.09 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.84/7.09 (assert (forall ((B tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B) A))) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex A))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2))) Z))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.84/7.09 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.84/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.84/7.09 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.84/7.09 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) (@ tptp.sin_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((M tptp.int)) (=> (forall ((N4 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N4)))) (not (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))
% 6.84/7.09 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.84/7.09 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.pi) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) tptp.pi))))))
% 6.84/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= K (@ tptp.semiri1314217659103216013at_int N4)))))))
% 6.84/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N4)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4))))))))
% 6.84/7.09 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N4 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N4)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4)))) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4)))))))))
% 6.84/7.09 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)))
% 6.84/7.09 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N4 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.84/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4))))))))
% 6.84/7.09 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2)))))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.84/7.09 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y)) (= X Y))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 6.84/7.09 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X) Y))))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_eq_real X5) _let_1) (= (@ tptp.sin_real X5) Y) (forall ((Y2 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)) Y2) (@ (@ tptp.ord_less_eq_real Y2) _let_1) (= (@ tptp.sin_real Y2) Y)) (= Y2 X5)))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.84/7.09 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.84/7.09 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.84/7.09 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.84/7.09 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 6.84/7.09 (assert (forall ((W tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) (@ tptp.real_V1022390504157884413omplex A)))))
% 6.84/7.09 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.84/7.09 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.84/7.09 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.84/7.09 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.84/7.09 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N2))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N2))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.84/7.09 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))))
% 6.84/7.09 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (N2 tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N2) (@ (@ tptp.power_power_real Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (N2 tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N2) (@ (@ tptp.power_power_complex Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S3) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real R) S3))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S3) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real R) S3))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))))
% 6.84/7.09 (assert (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S3) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real R) S3))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S3) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real R) S3))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N2))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N2))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (R tptp.real) (B tptp.real) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R) S3))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (R tptp.real) (B tptp.complex) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R) S3))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))) E))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))) E))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.84/7.09 (assert (forall ((W tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N2) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N2) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z) M)) (@ (@ tptp.power_power_real W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W))))))))
% 6.84/7.09 (assert (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z) M)) (@ (@ tptp.power_power_complex W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W))))))))
% 6.84/7.09 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (= (@ tptp.suminf_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.84/7.09 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (= (@ tptp.suminf_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (K tptp.nat) (N2 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 N2)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T4)) (not (= Y (@ tptp.sin_real T4))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)) X) (exists ((N tptp.int)) (= X (@ tptp.ring_1_of_int_real N))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ tptp.summable_real F))))
% 6.84/7.09 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.84/7.09 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.09 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.84/7.09 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 6.84/7.09 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.84/7.09 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) Z))))
% 6.84/7.09 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.84/7.09 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.84/7.09 (assert (forall ((X tptp.num) (N2 tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))))
% 6.84/7.09 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (@ tptp.power_power_real C)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (@ tptp.power_power_complex C)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))))
% 6.84/7.09 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.84/7.09 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.84/7.09 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.84/7.09 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.cos_real X))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))))
% 6.84/7.09 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) tptp.one_one_complex))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) tptp.one_one_complex))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((N2 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 N2))) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.84/7.09 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) tptp.zero_zero_real))
% 6.84/7.09 (assert (forall ((N2 tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (N3 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N4))) (@ G N4)))) (@ tptp.summable_real F)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (N3 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N4))) (@ G N4)))) (@ tptp.summable_complex F)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ tptp.summable_real F))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ G N4))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ G N4))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ G N4))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))))
% 6.84/7.09 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 6.84/7.09 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 6.84/7.09 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.84/7.09 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.84/7.09 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex F)) C) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C)))))))
% 6.84/7.09 (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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) (@ tptp.suminf_complex F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (= (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex F)) (@ tptp.suminf_complex G)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N)))))))))
% 6.84/7.09 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))))))))
% 6.84/7.09 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))))))))
% 6.84/7.09 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_real)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_nat)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_int)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N4))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N4))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F N)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X (@ _let_1 (@ tptp.cos_real A3))) (= Y (@ _let_1 (@ tptp.sin_real A3))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I5))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I5))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I5))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.sin_complex Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.sin_complex Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.84/7.09 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real C)))))
% 6.84/7.09 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex C)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) A))))
% 6.84/7.09 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y)) (= X Y)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ _let_1 X))))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) (@ (@ tptp.plus_plus_real R) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) tptp.one_one_real)) R)))
% 6.84/7.09 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X)))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (=> (@ tptp.summable_real F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N9)))))) R))))))))
% 6.84/7.09 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (=> (@ tptp.summable_complex F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N9)))))) R))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I4)) tptp.one_one_real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ (@ tptp.power_power_real Z) I5))))))))))
% 6.84/7.09 (assert (forall ((R tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_real R) R0) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N4))) (@ (@ tptp.power_power_real R0) N4))) M7)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N))) (@ (@ tptp.power_power_real R) N)))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X))) (@ tptp.cos_complex X))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X))) (@ tptp.cos_real X))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1)))))
% 6.84/7.09 (assert (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.archim7802044766580827645g_real X) Z))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1))))))
% 6.84/7.09 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I5 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I5))) (=> (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 I5)))))))
% 6.84/7.09 (assert (forall ((C tptp.real) (N3 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N4)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N4)))))) (@ tptp.summable_real F)))))
% 6.84/7.09 (assert (forall ((C tptp.real) (N3 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N4)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N4)))))) (@ tptp.summable_complex F)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.84/7.09 (assert (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X5) tptp.zero_zero_real) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y2) tptp.zero_zero_real)) (= Y2 X5))))))
% 6.84/7.09 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) tptp.pi) (= (@ tptp.cos_real X5) Y) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (= (@ tptp.cos_real Y2) Y)) (= Y2 X5)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (exists ((Y5 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y5) (@ (@ tptp.ord_less_eq_real Y5) tptp.pi) (= (@ tptp.sin_real Y5) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y5) (@ tptp.cos_real X))))))
% 6.84/7.09 (assert (forall ((Q2 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real P5) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P5) Q2)))) Q2)))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1))))))
% 6.84/7.09 (assert (forall ((Q2 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P5) Q2)))) tptp.one_one_real)) Q2)) P5))))
% 6.84/7.09 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X))) tptp.one_one_real))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X)))))))
% 6.84/7.09 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.84/7.09 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.cos_complex W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))))
% 6.84/7.09 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.cos_real W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.cos_real X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z) W)) _let_1)))))))
% 6.84/7.09 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z) W)) _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_2)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_2)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X2 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X2 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.84/7.09 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.sin_complex W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.84/7.09 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.sin_real W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.pi) (= X (@ tptp.cos_real T4)) (= Y (@ tptp.sin_real T4)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T4)) (= Y (@ tptp.sin_real T4)))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T4)) (= Y (@ tptp.sin_real T4))))))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ 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 N2)) tptp.one_one_int))))))))
% 6.84/7.09 (assert (forall ((N2 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) N2) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.84/7.09 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T4)) (@ tptp.sin_real T4)))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.84/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) A)) (not (= X tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.84/7.09 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N2))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y)) Y)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X)) X)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (I2 tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.84/7.09 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N2))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real A) B))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.09 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.numera6690914467698888265omplex W)) (and (= A (@ tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X) Y)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) tptp.one_one_real)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) B))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X) A)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.powr_real B))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) B)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.09 (assert (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (@ tptp.powr_real W))) (= (@ _let_1 (@ (@ tptp.minus_minus_real Z1) Z22)) (@ (@ tptp.divide_divide_real (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C)) (@ _let_1 D))) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C))))))))
% 6.84/7.09 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))
% 6.84/7.09 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) N2)))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X)))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) A))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X))))))
% 6.84/7.09 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y)))))))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ tptp.sqrt _let_1))))
% 6.84/7.09 (assert (= tptp.powr_real (lambda ((X2 tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= X2 tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X2)))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y) (@ tptp.tan_real X5)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) Y) (forall ((Y2 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)) Y2) (@ (@ tptp.ord_less_real Y2) _let_1) (= (@ tptp.tan_real Y2) Y)) (= Y2 X5)))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y))) (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 Y) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) Y))))))
% 6.84/7.09 (assert (= (@ tptp.tan_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y)))))
% 6.84/7.09 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N2)))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X5) Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X))) tptp.one_one_real))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y) (= (@ tptp.arctan Y) X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X)) X))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arctan Y))) (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) Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.plus_plus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z4 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)) Z4) (@ (@ tptp.ord_less_real Z4) _let_1) (= (@ tptp.tan_real Z4) X)))))))
% 6.84/7.09 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.84/7.09 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.84/7.09 (assert (= tptp.arcosh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) 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 N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.84/7.09 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 6.84/7.09 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.one_one_complex) (= X tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.84/7.09 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X)) N2))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X)) N2))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.84/7.09 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A2))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.09 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A2))))
% 6.84/7.09 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.84/7.09 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 6.84/7.09 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.84/7.09 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y)))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y)) Y)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups7108830773950497114d_enat 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_z5237406670263579293d_enat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5)))) A2) tptp.zero_zero_complex))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5)))) A2) tptp.zero_zero_real))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) _let_1))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real B))))))
% 6.84/7.09 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.09 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5))) (@ D I5)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5))) (@ D I5)))) A2) tptp.zero_zero_complex))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5))) (@ D I5)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5))) (@ D I5)))) A2) tptp.zero_zero_real))))))
% 6.84/7.09 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.84/7.09 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 6.84/7.09 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.84/7.09 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 6.84/7.09 (assert (= (@ tptp.arcsin (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I5)))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I5)))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I5)))) A2))))
% 6.84/7.09 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S))) (@ (@ tptp.groups8097168146408367636l_real G) S)))))
% 6.84/7.09 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S))) (@ (@ tptp.groups8778361861064173332t_real G) S)))))
% 6.84/7.09 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.complex)) (G (-> tptp.product_prod_nat_nat tptp.real))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6381953495645901045omplex F) S))) (@ (@ tptp.groups4567486121110086003t_real G) S)))))
% 6.84/7.09 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S))) (@ (@ tptp.groups6591440286371151544t_real G) S)))))
% 6.84/7.09 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S))) (@ (@ tptp.groups5808333547571424918x_real G) S)))))
% 6.84/7.09 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S))) (@ (@ tptp.groups6591440286371151544t_real G) S)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) K5)) (@ (@ tptp.groups3542108847815614940at_nat G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) K5)) (@ (@ tptp.groups6591440286371151544t_real G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4538972089207619220nt_int F) K5)) (@ (@ tptp.groups4538972089207619220nt_int G) K5)))))
% 6.84/7.09 (assert (forall ((K5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat)) (G (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups977919841031483927at_nat F) K5)) (@ (@ tptp.groups977919841031483927at_nat G) K5)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I5)) (@ G J3)))) B2))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I5)) (@ G J3)))) B2))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B2 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ G J3)))) B2))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B2 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I5)) (@ G J3)))) B2))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F N)) R))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.times_times_complex (@ F N)) R))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) R))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int (@ F N)) R))) A2))))
% 6.84/7.09 (assert (forall ((R tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat R) (@ F N)))) A2))))
% 6.84/7.09 (assert (forall ((R tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.times_times_complex R) (@ F N)))) A2))))
% 6.84/7.09 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R) (@ F N)))) A2))))
% 6.84/7.09 (assert (forall ((R tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int R) (@ F N)))) A2))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) R))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) R))) A2))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.84/7.09 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups7108830773950497114d_enat F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2800946370649118462d_enat F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups4225252721152677374d_enat F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups1752964319039525884d_enat F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups2800946370649118462d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups4225252721152677374d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((F (-> tptp.real tptp.nat)) (I6 tptp.set_real) (G (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I6) (@ (@ tptp.groups1935376822645274424al_nat G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I2) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.int tptp.nat)) (I6 tptp.set_int) (G (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I6) (@ (@ tptp.groups4541462559716669496nt_nat G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I2) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.complex tptp.nat)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I6) (@ (@ tptp.groups5693394587270226106ex_nat G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.real tptp.int)) (I6 tptp.set_real) (G (-> tptp.real tptp.int)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I6) (@ (@ tptp.groups1932886352136224148al_int G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I2) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I6) (@ (@ tptp.groups3539618377306564664at_int G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.complex tptp.int)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.int)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) I6) (@ (@ tptp.groups5690904116761175830ex_int G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) I6) (@ (@ tptp.groups3542108847815614940at_nat G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.real)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real F) I6) (@ (@ tptp.groups6591440286371151544t_real G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.int tptp.int)) (I6 tptp.set_int) (G (-> tptp.int tptp.int)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4538972089207619220nt_int F) I6) (@ (@ tptp.groups4538972089207619220nt_int G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I2) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.nat)) (I6 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (I2 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.groups977919841031483927at_nat F) I6) (@ (@ tptp.groups977919841031483927at_nat G) I6)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member8440522571783428010at_nat I2) I6) (=> (@ tptp.finite6177210948735845034at_nat I6) (= (@ F I2) (@ G I2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.suc X5))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.suc X5))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A2) (@ (@ tptp.groups6591440286371151544t_real G) A2))))))
% 6.84/7.09 (assert (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (R tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R)) (@ (@ tptp.times_times_real Y) R)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I2 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S3)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I2 (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S3)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I2 (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S3)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S3)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S3)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) S3)) (@ (@ tptp.groups5693394587270226106ex_nat G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S3) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) S3)) (@ (@ tptp.groups3539618377306564664at_int G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.int)) (I2 (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S3) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) S3)) (@ (@ tptp.groups5690904116761175830ex_int G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) S3)) (@ (@ tptp.groups3539618377306564664at_int G) T))))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.int)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) S3)) (@ (@ tptp.groups5690904116761175830ex_int G) T))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups2800946370649118462d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_z5237406670263579293d_enat))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups4225252721152677374d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_z5237406670263579293d_enat))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups7108830773950497114d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_z5237406670263579293d_enat))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups1752964319039525884d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_z5237406670263579293d_enat))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.extended_enat tptp.extended_enat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.extended_enat)) (G (-> tptp.nat tptp.extended_enat))) (=> (@ (@ R2 tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat) (=> (forall ((X15 tptp.extended_enat) (Y15 tptp.extended_enat) (X23 tptp.extended_enat) (Y23 tptp.extended_enat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_p3455044024723400733d_enat X15) Y15)) (@ (@ tptp.plus_p3455044024723400733d_enat X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups7108830773950497114d_enat H2) S)) (@ (@ tptp.groups7108830773950497114d_enat G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.extended_enat tptp.extended_enat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ (@ R2 tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat) (=> (forall ((X15 tptp.extended_enat) (Y15 tptp.extended_enat) (X23 tptp.extended_enat) (Y23 tptp.extended_enat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_p3455044024723400733d_enat X15) Y15)) (@ (@ tptp.plus_p3455044024723400733d_enat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups1752964319039525884d_enat H2) S)) (@ (@ tptp.groups1752964319039525884d_enat G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups2073611262835488442omplex H2) S)) (@ (@ tptp.groups2073611262835488442omplex G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups5808333547571424918x_real H2) S)) (@ (@ tptp.groups5808333547571424918x_real G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R2 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups5693394587270226106ex_nat H2) S)) (@ (@ tptp.groups5693394587270226106ex_nat G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.int tptp.int Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R2 tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_int X15) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups3539618377306564664at_int H2) S)) (@ (@ tptp.groups3539618377306564664at_int G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.int tptp.int Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ (@ R2 tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_int X15) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups5690904116761175830ex_int H2) S)) (@ (@ tptp.groups5690904116761175830ex_int G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ (@ R2 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups3542108847815614940at_nat H2) S)) (@ (@ tptp.groups3542108847815614940at_nat G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups7754918857620584856omplex H2) S)) (@ (@ tptp.groups7754918857620584856omplex G) S))))))))
% 6.84/7.09 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups6591440286371151544t_real H2) S)) (@ (@ tptp.groups6591440286371151544t_real G) S))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups1752964319039525884d_enat F) A2)) (@ (@ tptp.groups1752964319039525884d_enat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (G (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups7108830773950497114d_enat F) A2)) (@ (@ tptp.groups7108830773950497114d_enat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups4225252721152677374d_enat F) A2)) (@ (@ tptp.groups4225252721152677374d_enat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (G (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups2800946370649118462d_enat F) A2)) (@ (@ tptp.groups2800946370649118462d_enat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) (@ (@ tptp.groups8097168146408367636l_real G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_complex (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_complex (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_complex (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y))))))
% 6.84/7.09 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (B2 tptp.extended_enat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2800946370649118462d_enat F) S3) B2) (=> (@ (@ tptp.member_real I2) S3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (B2 tptp.extended_enat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups4225252721152677374d_enat F) S3) B2) (=> (@ (@ tptp.member_int I2) S3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (B2 tptp.extended_enat) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups7108830773950497114d_enat F) S3) B2) (=> (@ (@ tptp.member_nat I2) S3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (B2 tptp.extended_enat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups1752964319039525884d_enat F) S3) B2) (=> (@ (@ tptp.member_complex I2) S3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S3) B2) (=> (@ (@ tptp.member_real I2) S3) (@ (@ tptp.ord_less_eq_real (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.real)) (B2 tptp.real) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S3) B2) (=> (@ (@ tptp.member_int I2) S3) (@ (@ tptp.ord_less_eq_real (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (B2 tptp.real) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S3) B2) (=> (@ (@ tptp.member_complex I2) S3) (@ (@ tptp.ord_less_eq_real (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.nat)) (B2 tptp.nat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S3) B2) (=> (@ (@ tptp.member_real I2) S3) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.nat)) (B2 tptp.nat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S3) B2) (=> (@ (@ tptp.member_int I2) S3) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B2 tptp.nat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S3) B2) (=> (@ (@ tptp.member_complex I2) S3) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B2)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2800946370649118462d_enat F) S3) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_real I2) S3) (= (@ F I2) tptp.zero_z5237406670263579293d_enat)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups4225252721152677374d_enat F) S3) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_int I2) S3) (= (@ F I2) tptp.zero_z5237406670263579293d_enat)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups7108830773950497114d_enat F) S3) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_nat I2) S3) (= (@ F I2) tptp.zero_z5237406670263579293d_enat)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups1752964319039525884d_enat F) S3) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_complex I2) S3) (= (@ F I2) tptp.zero_z5237406670263579293d_enat)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.real)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S3) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I2) S3) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.real)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S3) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I2) S3) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S3) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I2) S3) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S3) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I2) S3) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S3) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I2) S3) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.84/7.09 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S3) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I2) S3) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))))
% 6.84/7.09 (assert (forall ((X tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real) (R tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X) R)) Y))))
% 6.84/7.09 (assert (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R) X)) Y))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y)) (= X Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2800946370649118462d_enat F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4225252721152677374d_enat F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups7108830773950497114d_enat F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1752964319039525884d_enat F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups1752964319039525884d_enat F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups7108830773950497114d_enat F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups4225252721152677374d_enat F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2800946370649118462d_enat F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y)) (= X Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4225252721152677374d_enat G) T3) (@ (@ tptp.groups4225252721152677374d_enat H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1752964319039525884d_enat G) T3) (@ (@ tptp.groups1752964319039525884d_enat H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3049146728041665814omplex G) T3) (@ (@ tptp.groups3049146728041665814omplex H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) T3) (@ (@ tptp.groups8778361861064173332t_real H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T3) (@ (@ tptp.groups5808333547571424918x_real H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) T3) (@ (@ tptp.groups4541462559716669496nt_nat H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) T3) (@ (@ tptp.groups5693394587270226106ex_nat H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) T3) (@ (@ tptp.groups5690904116761175830ex_int H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2800946370649118462d_enat G) T3) (@ (@ tptp.groups2800946370649118462d_enat H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T3) (@ (@ tptp.groups5754745047067104278omplex H2) S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.extended_enat)) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4225252721152677374d_enat G) S) (@ (@ tptp.groups4225252721152677374d_enat H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1752964319039525884d_enat G) S) (@ (@ tptp.groups1752964319039525884d_enat H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S) (@ (@ tptp.groups3049146728041665814omplex H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S) (@ (@ tptp.groups8778361861064173332t_real H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S) (@ (@ tptp.groups5808333547571424918x_real H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) S) (@ (@ tptp.groups4541462559716669496nt_nat H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) S) (@ (@ tptp.groups5690904116761175830ex_int H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.extended_enat)) (G (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ H2 X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2800946370649118462d_enat G) S) (@ (@ tptp.groups2800946370649118462d_enat H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ H2 X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S) (@ (@ tptp.groups5754745047067104278omplex H2) T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_complex))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((T3 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.groups4225252721152677374d_enat H2))) (let ((_let_2 (@ tptp.groups4225252721152677374d_enat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat H2))) (let ((_let_2 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H2))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H2))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat H2))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat H2))) (let ((_let_2 (@ tptp.groups2800946370649118462d_enat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.groups4225252721152677374d_enat H2))) (let ((_let_2 (@ tptp.groups4225252721152677374d_enat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat H2))) (let ((_let_2 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H2))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H2))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat H2))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat H2))) (let ((_let_2 (@ tptp.groups2800946370649118462d_enat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (F (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex F))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_complex (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_complex (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups2073611262835488442omplex G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ G M)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_complex (@ F _let_1)) (@ F M)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.groups4225252721152677374d_enat F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B2) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B3)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B3)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B3)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) tptp.pi)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X)) X)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y))))
% 6.84/7.09 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real B)) (@ tptp.real_V1803761363581548252l_real A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.84/7.09 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.84/7.09 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2073611262835488442omplex 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_complex (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I6)) (@ tptp.suminf_int F)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (I6 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I6)) (@ tptp.suminf_nat F)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (I6 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I6)) (@ tptp.suminf_real F)))))))
% 6.84/7.09 (assert (forall ((S 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 S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S 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 S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S 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 S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex)) (C (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.groups3049146728041665814omplex C) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S 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 S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat)) (C (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups4541462559716669496nt_nat C) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex)) (C (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.groups5754745047067104278omplex C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups8097168146408367636l_real C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.nat)) (C (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1935376822645274424al_nat C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.int)) (C (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.groups1932886352136224148al_int C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.09 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B2) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B2) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B2) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B2) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))))))
% 6.84/7.09 (assert (forall ((I2 tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ (@ tptp.member_complex I2) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) (@ (@ tptp.groups1752964319039525884d_enat F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I2) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ (@ tptp.member_int I2) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) (@ (@ tptp.groups4225252721152677374d_enat F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I2) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ (@ tptp.member_real I2) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) (@ (@ tptp.groups2800946370649118462d_enat F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I2) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ (@ tptp.member_nat I2) A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) (@ (@ tptp.groups7108830773950497114d_enat F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ (@ tptp.member_complex I2) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int I2) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))))
% 6.84/7.09 (assert (forall ((I2 tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ (@ tptp.member_real I2) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (X (-> tptp.product_prod_nat_nat tptp.real)) (A (-> tptp.product_prod_nat_nat tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups4567486121110086003t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups4567486121110086003t_real (lambda ((I5 tptp.product_prod_nat_nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.int)) (A (-> tptp.nat tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups3539618377306564664at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.int)) (A (-> tptp.real tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups1932886352136224148al_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups1932886352136224148al_int (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.int)) (A (-> tptp.complex tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups5690904116761175830ex_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups5690904116761175830ex_int (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (X (-> tptp.product_prod_nat_nat tptp.int)) (A (-> tptp.product_prod_nat_nat tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups975429370522433651at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups975429370522433651at_int (lambda ((I5 tptp.product_prod_nat_nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (A (-> tptp.nat tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups6591440286371151544t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.int)) (A (-> tptp.int tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups4538972089207619220nt_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X)) tptp.zero_zero_real))))))
% 6.84/7.09 (assert (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X)))))))
% 6.84/7.09 (assert (forall ((M tptp.int) (X tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X))))))
% 6.84/7.09 (assert (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X)))))))
% 6.84/7.09 (assert (forall ((M tptp.int) (X tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X) (= (@ tptp.arccos (@ tptp.cos_real X)) (@ tptp.uminus_uminus_real X))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X)) tptp.zero_zero_real))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_complex (@ F N2)) (@ F M))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N8 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M2) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N9)))) E)))))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N8 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M2) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N9)))) E)))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.complex)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X))))))
% 6.84/7.09 (assert (= tptp.cos_real (lambda ((X2 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)))) X2)))))
% 6.84/7.09 (assert (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X2)))))
% 6.84/7.09 (assert (= tptp.sin_real (lambda ((X2 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)))) X2)))))
% 6.84/7.09 (assert (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (forall ((A tptp.extended_enat) (D tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 A)) (@ (@ tptp.times_7803423173614009249d_enat _let_1) D))))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (D tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 A)) (@ (@ tptp.times_3573771949741848930nteger _let_1) D))))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (D tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I5) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N2) D)))) _let_1)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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 Y))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X)) X))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D)))) _let_1))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) 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 N2))))) (@ _let_1 X)))))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (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)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y))))))))
% 6.84/7.09 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X))))))))))
% 6.84/7.09 (assert (forall ((Theta tptp.real)) (not (forall ((K2 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (= tptp.arsinh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.84/7.09 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ 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)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q4)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.84/7.09 (assert (forall ((H2 tptp.real) (Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ 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)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q4)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.84/7.09 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_real (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.set_real))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_set_real (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo2489691266198938127t_real X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_set_nat (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_num (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_nat (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_int (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_real (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.set_real))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_set_real (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo2489691266198938127t_real X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_num (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_nat (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_int (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.84/7.09 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X4 N)) (@ X4 M6))))))))
% 6.84/7.09 (assert (= tptp.topolo2489691266198938127t_real (lambda ((X4 (-> tptp.nat tptp.set_real))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_real (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_real (@ X4 N)) (@ X4 M6))))))))
% 6.84/7.09 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X4 (-> tptp.nat tptp.set_nat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_nat (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_nat (@ X4 N)) (@ X4 M6))))))))
% 6.84/7.09 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X4 N)) (@ X4 M6))))))))
% 6.84/7.09 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X4 N)) (@ X4 M6))))))))
% 6.84/7.09 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X4 N)) (@ X4 M6))))))))
% 6.84/7.09 (assert (forall ((I2 tptp.extended_enat) (K tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I2) (@ tptp.set_or8419480210114673929d_enat K)) (@ (@ tptp.ord_le72135733267957522d_enat I2) K))))
% 6.84/7.09 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I2) K))))
% 6.84/7.09 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I2) K))))
% 6.84/7.09 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I2) K))))
% 6.84/7.09 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I2) K))))
% 6.84/7.09 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.84/7.09 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.84/7.09 (assert (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.84/7.09 (assert (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.84/7.09 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N2 tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N2))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.84/7.09 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S3 tptp.real) (T tptp.real)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ G N4))) (=> (@ (@ tptp.sums_real F) S3) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S3) T))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S3 tptp.nat) (T tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ G N4))) (=> (@ (@ tptp.sums_nat F) S3) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S3) T))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S3 tptp.int) (T tptp.int)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ G N4))) (=> (@ (@ tptp.sums_int F) S3) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S3) T))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))) (@ (@ tptp.times_times_complex A) C)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))) (@ (@ tptp.times_times_real A) C)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) A)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) A)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (G (-> tptp.nat tptp.complex)) (B tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (=> (@ (@ tptp.sums_complex G) B) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_complex A) B))))))
% 6.84/7.09 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_real A) B))))))
% 6.84/7.09 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 6.84/7.09 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_int A) B))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.84/7.09 (assert (= tptp.set_or8419480210114673929d_enat (lambda ((U2 tptp.extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X2 tptp.extended_enat)) (@ (@ tptp.ord_le72135733267957522d_enat X2) U2))))))
% 6.84/7.09 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U2))))))
% 6.84/7.09 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U2))))))
% 6.84/7.09 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U2))))))
% 6.84/7.09 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U2))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (S3 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S3) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S3) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S3 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S3) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S3) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (S3 tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.sums_complex F) S3) (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_complex S3) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (S3 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.sums_real F) S3) (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_real S3) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (S3 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_complex S3) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_complex F) S3))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S3 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_real S3) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_real F) S3))))
% 6.84/7.09 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2529575680413868914d_enat (@ tptp.set_or8419480210114673929d_enat M)) (@ tptp.set_or8419480210114673929d_enat N2)) (@ (@ tptp.ord_le72135733267957522d_enat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.09 (assert (forall ((M tptp.real) (N2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N2)) (@ (@ tptp.ord_less_real M) N2))))
% 6.84/7.09 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))))
% 6.84/7.09 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 6.84/7.09 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))))
% 6.84/7.09 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 6.84/7.09 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups977919841031483927at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups977919841031483927at_nat F) A2)) (@ (@ tptp.groups977919841031483927at_nat G) A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) A2) (=> (not (= X2 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A2) (=> (not (= X2 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N2)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) A2) (=> (not (= X2 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.84/7.09 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A2) (=> (not (= X2 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.84/7.09 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.84/7.09 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (S3 tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S3) (@ (@ tptp.sums_complex F) S3)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (S3 tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S3) (@ (@ tptp.sums_real F) S3)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (L2 tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex L2) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L2) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (L2 tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L2) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (L2 tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L2) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (S3 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S3) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S3) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (S3 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S3) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S3) (@ F tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.complex)) (S3 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (= (@ F I4) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S3) (@ (@ tptp.sums_complex F) S3)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (S3 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (= (@ F I4) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S3) (@ (@ tptp.sums_real F) S3)))))
% 6.84/7.09 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))) tptp.zero_zero_complex))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.power_power_complex Z) M))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.power_power_real Z) M))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N)))) (@ (@ tptp.power_power_int Z) M))))
% 6.84/7.09 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ A tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ A tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2))))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.complex)) (S tptp.complex) (A2 tptp.set_nat) (S5 tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.sums_complex G) S) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_complex S) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ G N)))) A2))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat N) A2)) (@ F N)) (@ G N)))) S5))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (S tptp.real) (A2 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) A2))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N) A2)) (@ F N)) (@ G N)))) S5))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (X tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_complex (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (R tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) R)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I5)) R))) _let_1)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (R tptp.complex)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex F) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) R)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F I5)) R))) _let_1)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (N2 tptp.nat) (R tptp.code_integer)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger F) _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) R)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger (@ F I5)) R))) _let_1)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (R tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) R)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I5)) R))) _let_1)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ tptp.summable_int F)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ tptp.summable_nat F)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ tptp.summable_real F)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.09 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex F) (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K))))) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.84/7.09 (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 ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.84/7.09 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.84/7.09 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P4)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.84/7.09 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P4)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P4)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P4)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_complex X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.09 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_int X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_real X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.09 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.84/7.09 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.84/7.09 (assert (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N)))) tptp.one_one_real))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.code_integer)) (K5 tptp.code_integer) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F P7)) K5))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) K5) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) K5))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) K5))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) K5))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) K5))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) X))))
% 6.84/7.09 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ F (@ (@ tptp.divide_divide_nat N) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X) Y))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ F I5)) (@ G I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) tptp.one_one_nat)))) _let_1))))))
% 6.84/7.09 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D3))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F (@ _let_2 _let_1))) (@ F (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real F))))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.set_real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo2489691266198938127t_real X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.set_real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo2489691266198938127t_real X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.84/7.09 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.84/7.09 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.84/7.09 (assert (= tptp.topolo2489691266198938127t_real (lambda ((X4 (-> tptp.nat tptp.set_real))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.84/7.09 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X4 (-> tptp.nat tptp.set_nat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.84/7.09 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.84/7.09 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.84/7.09 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.84/7.09 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ C N))) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N))))))))
% 6.84/7.09 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ C N))) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 6.84/7.09 (assert (= (@ tptp.semiri4449623510593786356d_enat tptp.zero_zero_nat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.09 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.84/7.09 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.84/7.09 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.84/7.09 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.84/7.09 (assert (= (@ tptp.semiri4449623510593786356d_enat tptp.one_one_nat) tptp.one_on7984719198319812577d_enat))
% 6.84/7.09 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.84/7.09 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.84/7.09 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.84/7.09 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.84/7.09 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.84/7.09 (assert (= (@ tptp.semiri4449623510593786356d_enat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat))
% 6.84/7.09 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.84/7.09 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.84/7.09 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.84/7.09 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri3624122377584611663nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ tptp.semiri3624122377584611663nteger N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri4449623510593786356d_enat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera1916890842035813515d_enat _let_1))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.84/7.09 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N2))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N2))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N2))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N2))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real M)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat N2) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N2) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.84/7.09 (assert (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))))
% 6.84/7.09 (assert (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))))
% 6.84/7.09 (assert (= tptp.diffs_complex (lambda ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C2 _let_1))))))
% 6.84/7.09 (assert (= tptp.diffs_Code_integer (lambda ((C2 (-> tptp.nat tptp.code_integer)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ C2 _let_1))))))
% 6.84/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.semiri4449623510593786356d_enat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.semiri4449623510593786356d_enat (@ tptp.pred_numeral K))))))
% 6.84/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K))))))
% 6.84/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K))))))
% 6.84/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real K)) (@ tptp.semiri2265585572941072030t_real (@ tptp.pred_numeral K))))))
% 6.84/7.09 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.semiri1408675320244567234ct_nat (@ tptp.pred_numeral K)))))))
% 6.84/7.09 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((X5 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X5) N))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N)))))))
% 6.84/7.09 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((X5 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X5) N))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ 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))) N2))))))
% 6.84/7.09 (assert (= tptp.cos_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ tptp.semiri2265585572941072030t_real N))) tptp.zero_zero_real)))))
% 6.84/7.09 (assert (= tptp.semiri4449623510593786356d_enat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M6 tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat M6)) (@ tptp.semiri4449623510593786356d_enat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M6)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (= tptp.semiri3624122377584611663nteger (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M6 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M6)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M6)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M6)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1406184849735516958ct_int N2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri5044797733671781792omplex N2) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri3624122377584611663nteger N2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri2265585572941072030t_real N2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1408675320244567234ct_nat N2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.extended_enat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_z5237406670263579293d_enat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.84/7.09 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) K5) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X5)) K5) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X5) N)))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N))))))))
% 6.84/7.09 (assert (forall ((X tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) K5) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X5)) K5) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X5) N)))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real X) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.cos_real X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T4 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N2))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N2)))))))))
% 6.84/7.09 (assert (forall ((R tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R)))) (@ (@ tptp.power_power_nat N2) R)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N2)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N2))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.84/7.09 (assert (= tptp.sin_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) 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 N) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N)))))))
% 6.84/7.09 (assert (forall ((B tptp.nat) (K tptp.nat) (N2 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 N2)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.84/7.09 (assert (forall ((Z tptp.real) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N2)))))))))
% 6.84/7.09 (assert (forall ((Z tptp.complex) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))))
% 6.84/7.09 (assert (= tptp.semiri4216267220026989637d_enat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8563196900006977889d_enat (lambda ((I5 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat I5) tptp.one_on7984719198319812577d_enat))) N) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.09 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I5 tptp.real)) (@ (@ tptp.plus_plus_real I5) tptp.one_one_real))) N) tptp.zero_zero_real))))
% 6.84/7.09 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I5 tptp.int)) (@ (@ tptp.plus_plus_int I5) tptp.one_one_int))) N) tptp.zero_zero_int))))
% 6.84/7.09 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat I5) tptp.one_one_nat))) N) tptp.zero_zero_nat))))
% 6.84/7.09 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.plus_plus_complex I5) tptp.one_one_complex))) N) tptp.zero_zero_complex))))
% 6.84/7.09 (assert (= tptp.semiri4939895301339042750nteger (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri4055485073559036834nteger (lambda ((I5 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger I5) tptp.one_one_Code_integer))) N) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.09 (assert (forall ((R tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R) _let_1))))))
% 6.84/7.09 (assert (forall ((R tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R) _let_1))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X)) X) (exists ((N tptp.int)) (= X (@ tptp.ring_1_of_int_real N))))))
% 6.84/7.09 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.84/7.09 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.84/7.09 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.84/7.09 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.84/7.09 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.84/7.09 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.84/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.84/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.84/7.09 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 6.84/7.09 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) tptp.zero_zero_nat) tptp.one_on7984719198319812577d_enat)))
% 6.84/7.09 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.84/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.84/7.09 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.84/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real V)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int))))
% 6.84/7.09 (assert (forall ((X tptp.num) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))))
% 6.84/7.09 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))))
% 6.84/7.09 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.09 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.84/7.09 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))))
% 6.84/7.09 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))))
% 6.84/7.09 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))) X)))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N2))))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N2))))))
% 6.84/7.09 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N2))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N2) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_complex)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_real)))))))
% 6.84/7.09 (assert (= tptp.semiri4449623510593786356d_enat (@ tptp.comm_s3181272606743183617d_enat tptp.one_on7984719198319812577d_enat)))
% 6.84/7.09 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.84/7.09 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.84/7.09 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.84/7.09 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.84/7.09 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z))))))
% 6.84/7.09 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X)))))
% 6.84/7.09 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L2))) (@ (@ tptp.divide_divide_int K) L2))))
% 6.84/7.09 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A4)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.84/7.09 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A4)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.84/7.09 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.84/7.09 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (=> (= X (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N2)))))
% 6.84/7.09 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N2)))))
% 6.84/7.09 (assert (forall ((X tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N2)))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s3181272606743183617d_enat tptp.zero_z5237406670263579293d_enat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on7984719198319812577d_enat)) (=> (not _let_2) (= _let_1 tptp.zero_z5237406670263579293d_enat)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.84/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.84/7.09 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_2) (@ (@ tptp.plus_plus_complex (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ _let_1 tptp.one_one_complex)) K))))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K)) (@ (@ tptp.gbinomial_real A) K))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real A) _let_3) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex A) _let_3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real _let_3) A) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex _let_3) A) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.84/7.09 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N2))))))
% 6.84/7.09 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 6.84/7.09 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 6.84/7.09 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 6.84/7.09 (assert (forall ((A tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat A) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.one_on7984719198319812577d_enat)) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N2)))))
% 6.84/7.09 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.84/7.09 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.84/7.09 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N2)))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2)))))))
% 6.84/7.09 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger N2)))))))
% 6.84/7.09 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) (@ _let_1 N2))))))
% 6.84/7.09 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))))
% 6.84/7.09 (assert (forall ((Z tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))))
% 6.84/7.09 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ _let_1 N2))))))
% 6.84/7.09 (assert (forall ((Z tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N2))) (@ _let_1 N2))))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N2) K))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N2) K))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N2) K))))
% 6.84/7.09 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N2) K))))
% 6.84/7.09 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 6.84/7.09 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex)))))
% 6.84/7.09 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.09 (assert (forall ((Z tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) M))))))
% 6.84/7.09 (assert (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) M))))))
% 6.84/7.09 (assert (forall ((Z tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) M))))))
% 6.84/7.09 (assert (forall ((Z tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) M))))))
% 6.84/7.09 (assert (forall ((Z tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N2))) M))))))
% 6.84/7.09 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I5 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I5))) (=> (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 I5)))))))
% 6.84/7.09 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.84/7.09 (assert (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) Z))))))
% 6.84/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.84/7.10 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N2))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A) K)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_2)) (@ (@ tptp.gbinomial_complex _let_1) _let_2)) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.gbinomial_complex A) K)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A) _let_1)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) K))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ (@ tptp.gbinomial_complex A) _let_1)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) K))))))
% 6.84/7.10 (assert (forall ((B tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B)))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.84/7.10 (assert (forall ((Q2 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P5) Q2)))) Q2)) P5))))
% 6.84/7.10 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K)))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))))
% 6.84/7.10 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K3)) A4)) tptp.one_one_real)) K3)))))
% 6.84/7.10 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K3)) A4)) tptp.one_one_complex)) K3)))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 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 N2))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N2))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 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 N2))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N2))))))
% 6.84/7.10 (assert (forall ((R tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.84/7.10 (assert (forall ((R tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.84/7.10 (assert (forall ((R tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.84/7.10 (assert (forall ((R tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.84/7.10 (assert (forall ((Q2 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real P5) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P5) Q2)))) tptp.one_one_real)) Q2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ tptp.semiri5044797733671781792omplex N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.84/7.10 (assert (= tptp.archim8280529875227126926d_real (lambda ((X2 tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (K tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (K tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.84/7.10 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K)))))
% 6.84/7.10 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K)))))
% 6.84/7.10 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K)))))
% 6.84/7.10 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K)))))
% 6.84/7.10 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 6.84/7.10 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 6.84/7.10 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 6.84/7.10 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K)))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 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) N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X) (@ (@ tptp.ord_less_real X) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.84/7.10 (assert (forall ((N2 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) N2) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) _let_2))))) tptp.one_one_int))))))))
% 6.84/7.10 (assert (forall ((N2 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)) N2))) (= (@ 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)) N2))) (@ tptp.semiri5044797733671781792omplex N2))))))))
% 6.84/7.10 (assert (forall ((N2 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)) N2))) (= (@ 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)) N2))) (@ tptp.semiri2265585572941072030t_real N2))))))))
% 6.84/7.10 (assert (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ 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 N2))))))))
% 6.84/7.10 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))
% 6.84/7.10 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))
% 6.84/7.10 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.84/7.10 (assert (= tptp.comm_s3181272606743183617d_enat (lambda ((A4 tptp.extended_enat) (N tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((O tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A4) (@ tptp.semiri4216267220026989637d_enat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_on7984719198319812577d_enat)))))
% 6.84/7.10 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N tptp.nat)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.84/7.10 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.84/7.10 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N tptp.nat)) (@ (@ (@ tptp.if_complex (= N tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.84/7.10 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A4 tptp.code_integer) (N tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((O tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.semiri4939895301339042750nteger O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_Code_integer)))))
% 6.84/7.10 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.84/7.10 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I2) K))))
% 6.84/7.10 (assert (forall ((I2 tptp.set_real) (K tptp.set_real)) (= (@ (@ tptp.member_set_real I2) (@ tptp.set_or5092868708245317595t_real K)) (@ (@ tptp.ord_less_eq_set_real I2) K))))
% 6.84/7.10 (assert (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I2) K))))
% 6.84/7.10 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I2) K))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I2) K))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I2) K))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.extended_enat))) (= (@ (@ tptp.groups7961826882256487087d_enat G) tptp.bot_bot_set_nat) tptp.one_on7984719198319812577d_enat)))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 6.84/7.10 (assert (forall ((G (-> tptp.int tptp.extended_enat))) (= (@ (@ tptp.groups5078248829458667347d_enat G) tptp.bot_bot_set_int) tptp.one_on7984719198319812577d_enat)))
% 6.84/7.10 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 6.84/7.10 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 6.84/7.10 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.extended_enat))) (= (@ (@ tptp.groups7973222482632965587d_enat G) tptp.bot_bot_set_real) tptp.one_on7984719198319812577d_enat)))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.extended_enat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups7961826882256487087d_enat G) A2) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups8780218893797010257d_enat G) A2) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups861055069439313189ex_nat G) A2) tptp.one_one_nat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups858564598930262913ex_int G) A2) tptp.one_one_int))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups708209901874060359at_nat G) A2) tptp.one_one_nat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups705719431365010083at_int G) A2) tptp.one_one_int))))
% 6.84/7.10 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (@ (@ tptp.ord_le3558479182127378552t_real (@ tptp.set_or5092868708245317595t_real X)) (@ tptp.set_or5092868708245317595t_real Y)) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 6.84/7.10 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X)) (@ tptp.set_or4236626031148496127et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.84/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.84/7.10 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real X)) (@ tptp.set_ord_atMost_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.84/7.10 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups7973222482632965587d_enat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_Extended_enat (= A K3)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7973222482632965587d_enat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_Extended_enat (= A K3)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups5078248829458667347d_enat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Extended_enat (= A K3)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5078248829458667347d_enat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Extended_enat (= A K3)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups7961826882256487087d_enat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= A K3)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7961826882256487087d_enat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= A K3)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups8780218893797010257d_enat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (= A K3)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8780218893797010257d_enat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (= A K3)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups7973222482632965587d_enat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_Extended_enat (= K3 A)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7973222482632965587d_enat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_Extended_enat (= K3 A)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups5078248829458667347d_enat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Extended_enat (= K3 A)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5078248829458667347d_enat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Extended_enat (= K3 A)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups7961826882256487087d_enat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= K3 A)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7961826882256487087d_enat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= K3 A)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups8780218893797010257d_enat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (= K3 A)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8780218893797010257d_enat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (= K3 A)) (@ B K3)) tptp.one_on7984719198319812577d_enat))) S) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S) tptp.one_one_real)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 A2))))))))
% 6.84/7.10 (assert (forall ((L2 tptp.set_real) (H2 tptp.set_real) (H3 tptp.set_real)) (= (@ (@ tptp.ord_le3558479182127378552t_real (@ (@ tptp.set_or7743017856606604397t_real L2) H2)) (@ tptp.set_or5092868708245317595t_real H3)) (or (not (@ (@ tptp.ord_less_eq_set_real L2) H2)) (@ (@ tptp.ord_less_eq_set_real H2) H3)))))
% 6.84/7.10 (assert (forall ((L2 tptp.set_nat) (H2 tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L2) H2)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L2) H2)) (@ (@ tptp.ord_less_eq_set_nat H2) H3)))))
% 6.84/7.10 (assert (forall ((L2 tptp.num) (H2 tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L2) H2)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L2) H2)) (@ (@ tptp.ord_less_eq_num H2) H3)))))
% 6.84/7.10 (assert (forall ((L2 tptp.nat) (H2 tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) H2)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (@ (@ tptp.ord_less_eq_nat H2) H3)))))
% 6.84/7.10 (assert (forall ((L2 tptp.int) (H2 tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L2) H2)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L2) H2)) (@ (@ tptp.ord_less_eq_int H2) H3)))))
% 6.84/7.10 (assert (forall ((L2 tptp.real) (H2 tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L2) H2)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L2) H2)) (@ (@ tptp.ord_less_eq_real H2) H3)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_complex (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_complex (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups7961826882256487087d_enat 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_on7984719198319812577d_enat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_7803423173614009249d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (= (@ G X5) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A2) tptp.one_one_nat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (= (@ G X5) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A2) tptp.one_one_int))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (= (@ G X5) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A2) tptp.one_one_int))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.extended_enat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups7961826882256487087d_enat G) A2) tptp.one_on7984719198319812577d_enat)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.extended_enat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups7973222482632965587d_enat G) A2) tptp.one_on7984719198319812577d_enat)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.int tptp.extended_enat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups5078248829458667347d_enat G) A2) tptp.one_on7984719198319812577d_enat)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (= (@ G A3) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.complex tptp.extended_enat)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups8780218893797010257d_enat G) A2) tptp.one_on7984719198319812577d_enat)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (= (@ G A3) tptp.one_on7984719198319812577d_enat)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex)) (not (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (= (@ G A3) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (= (@ G A3) tptp.one_one_real)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A2)) (@ (@ tptp.groups708209901874060359at_nat H2) A2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A2)) (@ (@ tptp.groups705719431365010083at_int H2) A2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A2)) (@ (@ tptp.groups1705073143266064639nt_int H2) A2)))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X2)) N2))) A2))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N2) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_int (@ F X2)) N2))) A2))))
% 6.84/7.10 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.power_power_int (@ F X2)) N2))) A2))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))))
% 6.84/7.10 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) U2))))))
% 6.84/7.10 (assert (= tptp.set_or5092868708245317595t_real (lambda ((U2 tptp.set_real)) (@ tptp.collect_set_real (lambda ((X2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real X2) U2))))))
% 6.84/7.10 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X2) U2))))))
% 6.84/7.10 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) U2))))))
% 6.84/7.10 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) U2))))))
% 6.84/7.10 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) U2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ (@ tptp.groups7961826882256487087d_enat F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ (@ tptp.groups7973222482632965587d_enat F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ (@ tptp.groups5078248829458667347d_enat F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ (@ tptp.groups8780218893797010257d_enat F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups7961826882256487087d_enat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.times_7803423173614009249d_enat (@ F A4)) __flatten_var_0))) A) B) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups5078248829458667347d_enat G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups5078248829458667347d_enat (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_Extended_enat (@ P X2)) (@ G X2)) tptp.one_on7984719198319812577d_enat))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups7973222482632965587d_enat G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups7973222482632965587d_enat (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_Extended_enat (@ P X2)) (@ G X2)) tptp.one_on7984719198319812577d_enat))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups7961826882256487087d_enat G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ P X2)) (@ G X2)) tptp.one_on7984719198319812577d_enat))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups8780218893797010257d_enat G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups8780218893797010257d_enat (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_Extended_enat (@ P X2)) (@ G X2)) tptp.one_on7984719198319812577d_enat))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups7440179247065528705omplex G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups7440179247065528705omplex (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups713298508707869441omplex G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups713298508707869441omplex (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups3708469109370488835omplex G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups2316167850115554303t_real G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1681761925125756287l_real G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups1681761925125756287l_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.84/7.10 (assert (forall ((H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H2)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))))
% 6.84/7.10 (assert (forall ((H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H2)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.10 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_real C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_real C) (@ F A4)))) A2))))
% 6.84/7.10 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_complex C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_complex C) (@ F A4)))) A2))))
% 6.84/7.10 (assert (forall ((C tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_nat C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A4)))) A2))))
% 6.84/7.10 (assert (forall ((C tptp.int) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A4 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A4)))) A2))))
% 6.84/7.10 (assert (forall ((C tptp.int) (F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A4 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A4)))) A2))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7961826882256487087d_enat F) A2)) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7973222482632965587d_enat F) A2)) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups5078248829458667347d_enat F) A2)) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_complex X5) A2) (and (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) _let_1) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups8780218893797010257d_enat F) A2)) tptp.one_on7984719198319812577d_enat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_complex X5) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) tptp.one_one_nat))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) tptp.one_one_nat))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.extended_enat tptp.extended_enat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.extended_enat)) (G (-> tptp.nat tptp.extended_enat))) (=> (@ (@ R2 tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (=> (forall ((X15 tptp.extended_enat) (Y15 tptp.extended_enat) (X23 tptp.extended_enat) (Y23 tptp.extended_enat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_7803423173614009249d_enat X15) Y15)) (@ (@ tptp.times_7803423173614009249d_enat X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups7961826882256487087d_enat H2) S)) (@ (@ tptp.groups7961826882256487087d_enat G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.extended_enat tptp.extended_enat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ (@ R2 tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (=> (forall ((X15 tptp.extended_enat) (Y15 tptp.extended_enat) (X23 tptp.extended_enat) (Y23 tptp.extended_enat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_7803423173614009249d_enat X15) Y15)) (@ (@ tptp.times_7803423173614009249d_enat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups8780218893797010257d_enat H2) S)) (@ (@ tptp.groups8780218893797010257d_enat G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups6464643781859351333omplex H2) S)) (@ (@ tptp.groups6464643781859351333omplex G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ (@ R2 tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_complex X15) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups3708469109370488835omplex H2) S)) (@ (@ tptp.groups3708469109370488835omplex G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups129246275422532515t_real H2) S)) (@ (@ tptp.groups129246275422532515t_real G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.real tptp.real Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.one_one_real) tptp.one_one_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_real X15) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups766887009212190081x_real H2) S)) (@ (@ tptp.groups766887009212190081x_real G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R2 tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_nat X15) Y15)) (@ (@ tptp.times_times_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups861055069439313189ex_nat H2) S)) (@ (@ tptp.groups861055069439313189ex_nat G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.int tptp.int Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ (@ R2 tptp.one_one_int) tptp.one_one_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_int X15) Y15)) (@ (@ tptp.times_times_int X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups858564598930262913ex_int H2) S)) (@ (@ tptp.groups858564598930262913ex_int G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ (@ R2 tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_nat X15) Y15)) (@ (@ tptp.times_times_nat X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups708209901874060359at_nat H2) S)) (@ (@ tptp.groups708209901874060359at_nat G) S))))))))
% 6.84/7.10 (assert (forall ((R2 (-> tptp.int tptp.int Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R2 tptp.one_one_int) tptp.one_one_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.times_times_int X15) Y15)) (@ (@ tptp.times_times_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups705719431365010083at_int H2) S)) (@ (@ tptp.groups705719431365010083at_int G) S))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_complex (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_complex (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_complex (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_complex (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ G X)) _let_2)))))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.code_integer))) (let ((_let_1 (@ tptp.groups8682486955453173170nteger F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.code_integer))) (let ((_let_1 (@ tptp.groups6225526099057966256nteger F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups3827104343326376752nteger F) A2)) (@ (@ tptp.groups3827104343326376752nteger G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.code_integer)) (G (-> tptp.complex tptp.code_integer))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups8682486955453173170nteger F) A2)) (@ (@ tptp.groups8682486955453173170nteger G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.code_integer)) (G (-> tptp.real tptp.code_integer))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups6225526099057966256nteger F) A2)) (@ (@ tptp.groups6225526099057966256nteger G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups3455450783089532116nteger F) A2)) (@ (@ tptp.groups3455450783089532116nteger G) B2)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) B2)))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S tptp.set_real) (I2 (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T3 tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups7973222482632965587d_enat G) S) (@ (@ tptp.groups7973222482632965587d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_int) (S tptp.set_real) (I2 (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T3 tptp.set_int) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups7973222482632965587d_enat G) S) (@ (@ tptp.groups5078248829458667347d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_real) (S tptp.set_int) (I2 (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T3 tptp.set_real) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S5)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_int (@ I2 B3)) (@ (@ tptp.minus_minus_set_int S) S5)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5078248829458667347d_enat G) S) (@ (@ tptp.groups7973222482632965587d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_int) (S tptp.set_int) (I2 (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T3 tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S5)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_int (@ I2 B3)) (@ (@ tptp.minus_minus_set_int S) S5)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5078248829458667347d_enat G) S) (@ (@ tptp.groups5078248829458667347d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_complex) (S tptp.set_real) (I2 (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups7973222482632965587d_enat G) S) (@ (@ tptp.groups8780218893797010257d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (S tptp.set_int) (I2 (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S) S5)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_int (@ I2 B3)) (@ (@ tptp.minus_minus_set_int S) S5)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5078248829458667347d_enat G) S) (@ (@ tptp.groups8780218893797010257d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_real) (S tptp.set_complex) (I2 (-> tptp.real tptp.complex)) (J (-> tptp.complex tptp.real)) (T3 tptp.set_real) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8780218893797010257d_enat G) S) (@ (@ tptp.groups7973222482632965587d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_int) (S tptp.set_complex) (I2 (-> tptp.int tptp.complex)) (J (-> tptp.complex tptp.int)) (T3 tptp.set_int) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8780218893797010257d_enat G) S) (@ (@ tptp.groups5078248829458667347d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_complex) (S tptp.set_complex) (I2 (-> tptp.complex tptp.complex)) (J (-> tptp.complex tptp.complex)) (T3 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_complex (@ I2 B3)) (@ (@ tptp.minus_811609699411566653omplex S) S5)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T5) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8780218893797010257d_enat G) S) (@ (@ tptp.groups8780218893797010257d_enat H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S tptp.set_real) (I2 (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S5)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T3) T5)))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T3) T5)) (= (@ J (@ I2 B3)) B3))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real T3) T5)) (@ (@ tptp.member_real (@ I2 B3)) (@ (@ tptp.minus_minus_set_real S) S5)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T5) (= (@ H2 B3) tptp.one_one_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups713298508707869441omplex G) S) (@ (@ tptp.groups713298508707869441omplex H2) T3)))))))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 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))) N2)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 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))) N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 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))) N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7973222482632965587d_enat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_on7984719198319812577d_enat))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8780218893797010257d_enat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_on7984719198319812577d_enat))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_real))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_real))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ G X2) tptp.one_one_int))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_int))))) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.84/7.10 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_or8332593352340944941d_enat A)) (@ tptp.set_or8419480210114673929d_enat B)) (@ (@ tptp.ord_le72135733267957522d_enat A) B))))
% 6.84/7.10 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A)) (@ tptp.set_ord_lessThan_num B)) (@ (@ tptp.ord_less_num A) B))))
% 6.84/7.10 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B)) (@ (@ tptp.ord_less_int A) B))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B)) (@ (@ tptp.ord_less_nat A) B))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B)) (@ (@ tptp.ord_less_real A) B))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.extended_enat)) (H2 (-> tptp.nat tptp.extended_enat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups7961826882256487087d_enat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_Extended_enat (= J3 K)) tptp.one_on7984719198319812577d_enat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups7961826882256487087d_enat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ 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 P5)) (@ (@ 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 P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ 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 P5)) (@ (@ 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 P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ 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 P5)) (@ (@ 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 P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ 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 P5)) (@ (@ 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 P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (I2 tptp.product_prod_nat_nat) (F (-> tptp.product_prod_nat_nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite6177210948735845034at_nat I6) (=> (@ (@ tptp.member8440522571783428010at_nat I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups6036352826371341000t_real F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4694064378042380927al_int F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (I2 tptp.product_prod_nat_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite6177210948735845034at_nat I6) (=> (@ (@ tptp.member8440522571783428010at_nat I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4075276357253098568at_int F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups858564598930262913ex_int F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups705719431365010083at_int F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1705073143266064639nt_int F) I6)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.real))) (=> (@ tptp.finite6177210948735845034at_nat I6) (=> (not (= I6 tptp.bot_bo2099793752762293965at_nat)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups6036352826371341000t_real F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (=> (@ tptp.finite6177210948735845034at_nat I6) (=> (not (= I6 tptp.bot_bo2099793752762293965at_nat)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups4075276357253098568at_int F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups858564598930262913ex_int F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups705719431365010083at_int F) I6)))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I4)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups1705073143266064639nt_int F) I6)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ _let_1 B2))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.groups5078248829458667347d_enat H2))) (let ((_let_2 (@ tptp.groups5078248829458667347d_enat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8780218893797010257d_enat H2))) (let ((_let_2 (@ tptp.groups8780218893797010257d_enat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex H2))) (let ((_let_2 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real H2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat H2))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat H2))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int H2))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_int))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_one_int))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7973222482632965587d_enat H2))) (let ((_let_2 (@ tptp.groups7973222482632965587d_enat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.groups5078248829458667347d_enat H2))) (let ((_let_2 (@ tptp.groups5078248829458667347d_enat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8780218893797010257d_enat H2))) (let ((_let_2 (@ tptp.groups8780218893797010257d_enat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex H2))) (let ((_let_2 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H2))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_complex))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_one_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real H2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_one_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat H2))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat H2))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int H2))) (let ((_let_2 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.one_one_int))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.one_one_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7973222482632965587d_enat H2))) (let ((_let_2 (@ tptp.groups7973222482632965587d_enat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.one_on7984719198319812577d_enat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8780218893797010257d_enat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_on7984719198319812577d_enat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7973222482632965587d_enat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_on7984719198319812577d_enat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 S) (@ _let_1 T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups8780218893797010257d_enat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_on7984719198319812577d_enat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7973222482632965587d_enat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_on7984719198319812577d_enat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.extended_enat)) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.one_on7984719198319812577d_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5078248829458667347d_enat G) S) (@ (@ tptp.groups5078248829458667347d_enat H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.one_on7984719198319812577d_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8780218893797010257d_enat G) S) (@ (@ tptp.groups8780218893797010257d_enat H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S) (@ (@ tptp.groups7440179247065528705omplex H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S) (@ (@ tptp.groups3708469109370488835omplex H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.one_one_real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2316167850115554303t_real G) S) (@ (@ tptp.groups2316167850115554303t_real H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.one_one_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups766887009212190081x_real G) S) (@ (@ tptp.groups766887009212190081x_real H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) S) (@ (@ tptp.groups1707563613775114915nt_nat H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) S) (@ (@ tptp.groups861055069439313189ex_nat H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.one_one_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups858564598930262913ex_int G) S) (@ (@ tptp.groups858564598930262913ex_int H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.extended_enat)) (G (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ H2 X5) tptp.one_on7984719198319812577d_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups7973222482632965587d_enat G) S) (@ (@ tptp.groups7973222482632965587d_enat H2) T3))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.one_on7984719198319812577d_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5078248829458667347d_enat G) T3) (@ (@ tptp.groups5078248829458667347d_enat H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_on7984719198319812577d_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8780218893797010257d_enat G) T3) (@ (@ tptp.groups8780218893797010257d_enat H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups7440179247065528705omplex G) T3) (@ (@ tptp.groups7440179247065528705omplex H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) T3) (@ (@ tptp.groups3708469109370488835omplex H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.one_one_real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2316167850115554303t_real G) T3) (@ (@ tptp.groups2316167850115554303t_real H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups766887009212190081x_real G) T3) (@ (@ tptp.groups766887009212190081x_real H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) T3) (@ (@ tptp.groups1707563613775114915nt_nat H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups861055069439313189ex_nat G) T3) (@ (@ tptp.groups861055069439313189ex_nat H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.one_one_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups858564598930262913ex_int G) T3) (@ (@ tptp.groups858564598930262913ex_int H2) S))))))))
% 6.84/7.10 (assert (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.one_on7984719198319812577d_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups7973222482632965587d_enat G) T3) (@ (@ tptp.groups7973222482632965587d_enat H2) S))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_complex (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_complex (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups6464643781859351333omplex G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ G M)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G M)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.complex)) (I2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_complex (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X2) I5)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I5)) (@ (@ tptp.power_power_complex X2) I5)))) _let_1)))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) (@ D I5)))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X2) I5)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ D I5)) (@ (@ tptp.power_power_real X2) I5)))) _let_1)))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) (@ D I5)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.int)) (B2 tptp.int)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int A) (@ tptp.set_ord_atMost_nat N4))) B2)) (@ tptp.summable_int A)))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.nat)) (B2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat A) (@ tptp.set_ord_atMost_nat N4))) B2)) (@ tptp.summable_nat A)))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real A) (@ tptp.set_ord_atMost_nat N4))) B2)) (@ tptp.summable_real A)))))
% 6.84/7.10 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))))
% 6.84/7.10 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))))
% 6.84/7.10 (assert (= tptp.semiri3624122377584611663nteger (lambda ((N tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))))
% 6.84/7.10 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))))
% 6.84/7.10 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I4 tptp.complex)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_complex I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I4 tptp.real)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_real I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I4 tptp.nat)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_nat I4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I4)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) A2)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3455450783089532116nteger F) A2)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.code_integer))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups8682486955453173170nteger F) A2)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups858564598930262913ex_int F) A2)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups705719431365010083at_int F) A2)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_complex (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.84/7.10 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X Xa2) Xc))))))))))
% 6.84/7.10 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F5 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B4 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B4) A4)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F5) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B4) (@ (@ F5 A4) Acc2))))))
% 6.84/7.10 (assert (forall ((S tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex)) (C (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.groups3708469109370488835omplex C) (@ (@ tptp.minus_811609699411566653omplex S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex)) (C (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.groups7440179247065528705omplex C) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex)) (C (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.groups713298508707869441omplex C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex)) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.groups6464643781859351333omplex C) (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_2 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C) (@ (@ tptp.minus_811609699411566653omplex S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups2316167850115554303t_real C) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real)) (C (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.groups129246275422532515t_real C) (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_2 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups861055069439313189ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat)) (C (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1707563613775114915nt_nat C) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.times_times_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_real) (Z (-> tptp.real tptp.real)) (W (-> tptp.real tptp.real))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups1681761925125756287l_real Z) I6)) (@ (@ tptp.groups1681761925125756287l_real W) I6)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_int) (Z (-> tptp.int tptp.real)) (W (-> tptp.int tptp.real))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups2316167850115554303t_real Z) I6)) (@ (@ tptp.groups2316167850115554303t_real W) I6)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_complex) (Z (-> tptp.complex tptp.real)) (W (-> tptp.complex tptp.real))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups766887009212190081x_real Z) I6)) (@ (@ tptp.groups766887009212190081x_real W) I6)))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (Z (-> tptp.product_prod_nat_nat tptp.real)) (W (-> tptp.product_prod_nat_nat tptp.real))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6036352826371341000t_real Z) I6)) (@ (@ tptp.groups6036352826371341000t_real W) I6)))) (@ (@ tptp.groups4567486121110086003t_real (lambda ((I5 tptp.product_prod_nat_nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_real) (Z (-> tptp.real tptp.complex)) (W (-> tptp.real tptp.complex))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups713298508707869441omplex Z) I6)) (@ (@ tptp.groups713298508707869441omplex W) I6)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_int) (Z (-> tptp.int tptp.complex)) (W (-> tptp.int tptp.complex))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7440179247065528705omplex Z) I6)) (@ (@ tptp.groups7440179247065528705omplex W) I6)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_complex) (Z (-> tptp.complex tptp.complex)) (W (-> tptp.complex tptp.complex))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups3708469109370488835omplex Z) I6)) (@ (@ tptp.groups3708469109370488835omplex W) I6)))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (Z (-> tptp.product_prod_nat_nat tptp.complex)) (W (-> tptp.product_prod_nat_nat tptp.complex))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups8110221916422527690omplex Z) I6)) (@ (@ tptp.groups8110221916422527690omplex W) I6)))) (@ (@ tptp.groups4567486121110086003t_real (lambda ((I5 tptp.product_prod_nat_nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_nat) (Z (-> tptp.nat tptp.real)) (W (-> tptp.nat tptp.real))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups129246275422532515t_real Z) I6)) (@ (@ tptp.groups129246275422532515t_real W) I6)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_nat) (Z (-> tptp.nat tptp.complex)) (W (-> tptp.nat tptp.complex))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I4))) tptp.one_one_real))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I4))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups6464643781859351333omplex Z) I6)) (@ (@ tptp.groups6464643781859351333omplex W) I6)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex W2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_complex)))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real W2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) tptp.zero_zero_complex))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) tptp.zero_zero_real))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_complex (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) N2))))
% 6.84/7.10 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) N2))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.real))) (let ((_let_1 (@ tptp.groups6036352826371341000t_real F))) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (forall ((B3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat B3) (@ (@ tptp.minus_1356011639430497352at_nat B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups4075276357253098568at_int F))) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (forall ((B3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat B3) (@ (@ tptp.minus_1356011639430497352at_nat B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B3)))) (=> (forall ((A3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B3)))) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B3)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B3)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B3)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (A tptp.int)) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (A tptp.real)) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_nat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (A tptp.int)) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (A tptp.real)) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_int _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (A tptp.real)) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_int _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.84/7.10 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.complex)) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z5) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.real)) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z5 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z5) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I5) N2) (not (= (@ C I5) tptp.zero_zero_complex)))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I5) N2) (not (= (@ C I5) tptp.zero_zero_real)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N2)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex) (not (forall ((B3 (-> tptp.nat tptp.complex))) (not (forall ((Z3 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z3) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z3) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I5)) (@ (@ tptp.power_power_complex Z3) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int) (not (forall ((B3 (-> tptp.nat tptp.int))) (not (forall ((Z3 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int Z3) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z3) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I5)) (@ (@ tptp.power_power_int Z3) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real) (not (forall ((B3 (-> tptp.nat tptp.real))) (not (forall ((Z3 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z3) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z3) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I5)) (@ (@ tptp.power_power_real Z3) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (A tptp.complex)) (exists ((B3 (-> tptp.nat tptp.complex))) (forall ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z3) I5)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z3) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I5)) (@ (@ tptp.power_power_complex Z3) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex A) I5)))) _let_1))))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.int)) (N2 tptp.nat) (A tptp.int)) (exists ((B3 (-> tptp.nat tptp.int))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int Z3) I5)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z3) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I5)) (@ (@ tptp.power_power_int Z3) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int A) I5)))) _let_1))))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (A tptp.real)) (exists ((B3 (-> tptp.nat tptp.real))) (forall ((Z3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z3) I5)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z3) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I5)) (@ (@ tptp.power_power_real Z3) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real A) I5)))) _let_1))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.84/7.10 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.84/7.10 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N tptp.nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.84/7.10 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A4 tptp.code_integer) (N tptp.nat)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat N) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.84/7.10 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.84/7.10 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ tptp.summable_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)) (@ tptp.suminf_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.extended_enat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups7108830773950497114d_enat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2538466533108834004d_enat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ F A4)) __flatten_var_0))) A) B) tptp.zero_z5237406670263579293d_enat))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_complex))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N2 tptp.nat) (B (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B J3)) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R4) K3))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_complex X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N2 tptp.nat) (B (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B J3)) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R4) K3))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_int X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N2 tptp.nat) (B (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B J3)) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R4) K3))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_real X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N2)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.complex)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X2) tptp.zero_zero_complex)))))))
% 6.84/7.10 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.real)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X2) tptp.zero_zero_real)))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) M)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) M)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) M)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) M)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N2 tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I5)) (@ (@ tptp.power_power_nat X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R4 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R4) K3))))) (@ tptp.set_ord_atMost_nat R4))) (@ (@ tptp.power_power_nat X) R4)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ (@ tptp.sums_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ (@ tptp.sums_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_1) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups6464643781859351333omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.84/7.10 (assert (forall ((A tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinom8545251970709558553nteger A) _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.groups3455450783089532116nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.semiri4939895301339042750nteger I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri3624122377584611663nteger _let_1))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.84/7.10 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.extended_enat)) (H2 (-> tptp.nat tptp.extended_enat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups7108830773950497114d_enat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_Extended_enat (= J3 K)) tptp.zero_z5237406670263579293d_enat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups7108830773950497114d_enat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_complex (= J3 K)) tptp.zero_zero_complex) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.zero_zero_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.zero_zero_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((P5 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P5) (=> (@ (@ tptp.ord_less_eq_nat K) P5) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.zero_zero_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P5)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P5) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Z tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_int Z) N2) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I5 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I5 N2)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_complex Z) N2) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I5 tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I5 N2)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_8256067586552552935nteger Z) N2) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I5 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I5 N2)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Z tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_real Z) N2) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I5 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I5 N2)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) M))))
% 6.84/7.10 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) M))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex K3)) A)) tptp.one_one_complex)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real K3)) A)) tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex X) I5)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex Y) I5)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_complex Y) K3))) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int X) I5)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int Y) I5)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_int Y) K3))) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real X) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real Y) I5)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_real Y) K3))) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.10 (assert (forall ((E tptp.real) (C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z3))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z3) I5)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))))
% 6.84/7.10 (assert (forall ((E tptp.real) (C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z3 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z3))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z3) I5)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex X) I5)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex Y) I5)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I5) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2))) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int X) I5)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int Y) I5)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I5) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2))) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real X) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real Y) I5)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I5) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2))) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.84/7.10 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.84/7.10 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.84/7.10 (assert (= tptp.semiri3624122377584611663nteger (lambda ((N tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.84/7.10 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.84/7.10 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.84/7.10 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (= (@ (@ tptp.groups2073611262835488442omplex (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) (@ tptp.semiri8010041392384452111omplex M))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.84/7.10 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ (@ tptp.groups6591440286371151544t_real (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) (@ tptp.semiri5074537144036343181t_real M))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I5))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I5))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))))
% 6.84/7.10 (assert (= tptp.archim8280529875227126926d_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.archim2898591450579166408c_real X2))) (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim6058952711729229775r_real X2)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex B)))))
% 6.84/7.10 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.84/7.10 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.inverse_inverse_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X) tptp.one_one_complex) (= X tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_1) N2) _let_1))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) N2) tptp.one_one_nat)))
% 6.84/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ _let_1 A)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_real B) A)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) (@ tptp.suc tptp.zero_zero_nat)) N2)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N2))) (= (@ (@ tptp.binomial (@ tptp.suc N2)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.one_one_nat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.one_one_nat)))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups708209901874060359at_nat F) A2) tptp.one_one_nat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.one_one_nat)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real A) (@ tptp.inverse_inverse_real A)) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 6.84/7.10 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X2))))))))
% 6.84/7.10 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 6.84/7.10 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real A)) N2) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real A) N2)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N2) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N2)))))
% 6.84/7.10 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y))) (let ((_let_2 (@ tptp.times_times_real X))) (=> (= (@ (@ tptp.times_times_real Y) X) (@ _let_2 Y)) (= (@ (@ tptp.times_times_real _let_1) X) (@ _let_2 _let_1)))))))
% 6.84/7.10 (assert (forall ((Y tptp.complex) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y))) (let ((_let_2 (@ tptp.times_times_complex X))) (=> (= (@ (@ tptp.times_times_complex Y) X) (@ _let_2 Y)) (= (@ (@ tptp.times_times_complex _let_1) X) (@ _let_2 _let_1)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.one_one_nat) N2)))
% 6.84/7.10 (assert (forall ((R tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R) (@ tptp.real_V7735802525324610683m_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X))) (@ tptp.inverse_inverse_real R))))))
% 6.84/7.10 (assert (forall ((R tptp.real) (X tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R) (@ tptp.real_V1022390504157884413omplex X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X))) (@ tptp.inverse_inverse_real R))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ _let_1 tptp.zero_zero_real) (@ _let_1 A))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (=> (not (= A tptp.zero_zero_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.inverse_inverse_real A)) (=> (not (= A tptp.zero_zero_real)) (@ _let_1 A))))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_real A))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A)))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B)) (@ tptp.invers8013647133539491842omplex A)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2) K)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.84/7.10 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 6.84/7.10 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 6.84/7.10 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B4)) A4))))
% 6.84/7.10 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B4)) A4))))
% 6.84/7.10 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B4)))))
% 6.84/7.10 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B4)))))
% 6.84/7.10 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B4)))))
% 6.84/7.10 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B4)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (R tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.10 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 6.84/7.10 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 6.84/7.10 (assert (forall ((R tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R)) (@ (@ tptp.power_power_nat N2) R)))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X) (@ (@ tptp.times_times_real X) _let_1)))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X) (@ (@ tptp.times_times_complex X) _let_1)))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X) (@ (@ tptp.times_times_real X) _let_1)))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.int) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X) (@ (@ tptp.times_times_complex X) _let_1)))))
% 6.84/7.10 (assert (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y3)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X)) tptp.one_one_real)))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.plus_plus_real A) B))) _let_1))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.plus_plus_complex A) B))) _let_1))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_2)) _let_1))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_2)) _let_1))))))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real B) A))) _let_1))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex B) A))) _let_1))))))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real A) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 6.84/7.10 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K))) _let_1))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 6.84/7.10 (assert (forall ((Y tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y) A))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) B)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)))))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real A) B))) _let_1)))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex A) B))) _let_1)))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) X)))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) K))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.binomial N2) K)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.84/7.10 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.84/7.10 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N4 tptp.nat)) (=> (not (= N4 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.84/7.10 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N)))) (and (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real _let_1) X) (@ tptp.inverse_inverse_real _let_1))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X))))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex (@ tptp.semiri5044797733671781792omplex N))) (@ (@ tptp.power_power_complex X) N))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))
% 6.84/7.10 (assert (forall ((R tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R) K3)) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R) N2))) N2))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) M))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N2)))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ 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)) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N2) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4))) X))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X)) M))))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X)) M))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) X) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups1681761925125756287l_real F) I6)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X2 tptp.real)) (@ tptp.ln_ln_real (@ F X2)))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups2316167850115554303t_real F) I6)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X2 tptp.int)) (@ tptp.ln_ln_real (@ F X2)))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.real))) (=> (@ tptp.finite6177210948735845034at_nat I6) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups6036352826371341000t_real F) I6)) (@ (@ tptp.groups4567486121110086003t_real (lambda ((X2 tptp.product_prod_nat_nat)) (@ tptp.ln_ln_real (@ F X2)))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups766887009212190081x_real F) I6)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X2 tptp.complex)) (@ tptp.ln_ln_real (@ F X2)))) I6))))))
% 6.84/7.10 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (= (@ tptp.ln_ln_real (@ (@ tptp.groups129246275422532515t_real F) I6)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.ln_ln_real (@ F X2)))) I6))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N2)) M)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N2)) R))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N2) _let_1))) (let ((_let_3 (@ tptp.binomial N2))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.binomial N2) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N2)) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) _let_1)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))))))
% 6.84/7.10 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) N2) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_8256067586552552935nteger A) K3))) (@ (@ tptp.power_8256067586552552935nteger B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X)))))
% 6.84/7.10 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) B)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s2602460028002588243omplex A) K3))) (@ (@ tptp.comm_s2602460028002588243omplex B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) N2) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s8582702949713902594nteger A) K3))) (@ (@ tptp.comm_s8582702949713902594nteger B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N2) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) N2))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real _let_2)) _let_1)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.tan_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex _let_2)) _let_1)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I5)) (@ tptp.semiri1314217659103216013at_int I5))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I5)) (@ tptp.semiri8010041392384452111omplex I5))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I5)) (@ tptp.semiri4939895301339042750nteger I5))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ tptp.semiri5074537144036343181t_real I5))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat I5) (@ (@ tptp.binomial N2) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I5)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I5)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I5)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))
% 6.84/7.10 (assert (= tptp.binomial (lambda ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) K3))) (let ((_let_2 (@ tptp.ord_less_nat N))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) N2)))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P4) (not (@ _let_2 N)))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N))))) (@ tptp.semiri2265585572941072030t_real P4)))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P4) (not (@ _let_2 N)))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N))))) (@ tptp.semiri2265585572941072030t_real P4)))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) P4)) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P4)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat _let_1) P4)) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P4)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P4) (@ _let_2 N))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P4) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P4) (@ _let_2 N))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P4) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P4) N))))) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P4) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P4)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y)))))
% 6.84/7.10 (assert (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 6.84/7.10 (assert (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) X2)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1)))))))))
% 6.84/7.10 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) N)))
% 6.84/7.10 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ _let_2 Y)) (@ _let_2 (@ _let_1 Y)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (A tptp.real) (Y tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ _let_2 Y)) (@ _let_2 (@ _let_1 Y)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) Y))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_complex X) Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real tptp.one_one_real) X) X)))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex tptp.one_one_real) X) X)))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real A) (@ (@ tptp.real_V1485227260804924795R_real B) X)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.times_times_real A) B)) X))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex A) (@ (@ tptp.real_V2046097035970521341omplex B) X)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.times_times_real A) B)) X))))
% 6.84/7.10 (assert (forall ((B tptp.real) (U tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real U))) (= (= (@ (@ tptp.plus_plus_real B) (@ _let_1 A)) (@ (@ tptp.plus_plus_real A) (@ _let_1 B))) (or (= A B) (= U tptp.one_one_real))))))
% 6.84/7.10 (assert (forall ((B tptp.complex) (U tptp.real) (A tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex U))) (= (= (@ (@ tptp.plus_plus_complex B) (@ _let_1 A)) (@ (@ tptp.plus_plus_complex A) (@ _let_1 B))) (or (= A B) (= U tptp.one_one_real))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.real_V1485227260804924795R_real X) Y)) N2) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.real_V2046097035970521341omplex X) Y)) N2) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_complex Y) N2)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ tptp.uminus_uminus_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ tptp.uminus1482373934393186551omplex X))))
% 6.84/7.10 (assert (forall ((U tptp.real) (A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real tptp.one_one_real) U)) A)) (@ (@ tptp.real_V1485227260804924795R_real U) A)) A)))
% 6.84/7.10 (assert (forall ((U tptp.real) (A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.minus_minus_real tptp.one_one_real) U)) A)) (@ (@ tptp.real_V2046097035970521341omplex U) A)) A)))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.real_V7735802525324610683m_real X)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex A) X)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.real_V1022390504157884413omplex X)))))
% 6.84/7.10 (assert (forall ((U tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.numeral_numeral_real U))) (= (@ (@ tptp.real_V1485227260804924795R_real _let_2) (@ (@ tptp.times_times_real _let_1) A)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.times_times_real _let_2) _let_1)) A))))))
% 6.84/7.10 (assert (forall ((U tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (= (@ (@ tptp.real_V2046097035970521341omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.times_times_real _let_1) (@ tptp.numeral_numeral_real W))) A)))))
% 6.84/7.10 (assert (forall ((V tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.times_times_real _let_2) A)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real _let_2) _let_1)) A))))))
% 6.84/7.10 (assert (forall ((V tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real W)) _let_1)) A)))))
% 6.84/7.10 (assert (forall ((U tptp.num) (V tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real W))) (let ((_let_3 (@ tptp.numeral_numeral_real U))) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real _let_3) _let_1)) (@ (@ tptp.times_times_real _let_2) A)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real _let_3) _let_2)) _let_1)) A)))))))
% 6.84/7.10 (assert (forall ((U tptp.num) (V tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real U))) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real _let_2) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real _let_2) (@ tptp.numeral_numeral_real W))) _let_1)) A))))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_real A) A)) A)))
% 6.84/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_complex A) A)) A)))
% 6.84/7.10 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ _let_1 X)) (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X) Y)) Xa2) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X) Xa2)) (@ (@ tptp.real_V1485227260804924795R_real Y) Xa2)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real X) Y)) Xa2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex X) Xa2)) (@ (@ tptp.real_V2046097035970521341omplex Y) Xa2)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real A) B)) X) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) X)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.plus_plus_real A) B)) X) (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex A) X)) (@ (@ tptp.real_V2046097035970521341omplex B) X)))))
% 6.84/7.10 (assert (= tptp.real_V1485227260804924795R_real (lambda ((R4 tptp.real) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real R4)) __flatten_var_0))))
% 6.84/7.10 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R4 tptp.real) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R4)) __flatten_var_0))))
% 6.84/7.10 (assert (= tptp.real_V1803761363581548252l_real (lambda ((R4 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real R4) tptp.one_one_real))))
% 6.84/7.10 (assert (= tptp.real_V4546457046886955230omplex (lambda ((R4 tptp.real)) (@ (@ tptp.real_V2046097035970521341omplex R4) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.real_V2046097035970521341omplex R) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 6.84/7.10 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) C)) (@ (@ tptp.real_V1485227260804924795R_real B) C))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) X))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.84/7.10 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.84/7.10 (assert (forall ((U tptp.real) (V tptp.real) (A tptp.real) (X tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (@ (@ tptp.real_V1485227260804924795R_real U) A) (@ (@ tptp.real_V1485227260804924795R_real V) X))))))))
% 6.84/7.10 (assert (forall ((U tptp.real) (V tptp.real) (A tptp.complex) (X tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (@ (@ tptp.real_V2046097035970521341omplex U) A) (@ (@ tptp.real_V2046097035970521341omplex V) X))))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (U tptp.real) (V tptp.real) (A tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (@ (@ tptp.real_V1485227260804924795R_real V) X) (@ (@ tptp.real_V1485227260804924795R_real U) A))))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (U tptp.real) (V tptp.real) (A tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (@ (@ tptp.real_V2046097035970521341omplex V) X) (@ (@ tptp.real_V2046097035970521341omplex U) A))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (= A tptp.zero_zero_real))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) B)) tptp.zero_zero_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B)) (= A tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 B) (=> (@ _let_1 X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) Y)))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) C)) (@ (@ tptp.real_V1485227260804924795R_real B) D)))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 X))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) B))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) X)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.real_V1485227260804924795R_real A) B))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) X)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_real X) X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_complex X) X))))
% 6.84/7.10 (assert (forall ((M tptp.real) (X tptp.real) (C tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X)) C) Y) (= X (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ _let_1 C))))))))
% 6.84/7.10 (assert (forall ((M tptp.real) (X tptp.complex) (C tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex M) X)) C) Y) (= X (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ _let_1 C))))))))
% 6.84/7.10 (assert (forall ((M tptp.real) (Y tptp.real) (X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X)) C)) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ _let_1 C)) X))))))
% 6.84/7.10 (assert (forall ((M tptp.real) (Y tptp.complex) (X tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex M) X)) C)) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ _let_1 C)) X))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.84/7.10 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.84/7.10 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X) N)))) (@ tptp.sin_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X) N)))) (@ tptp.sin_complex X))))
% 6.84/7.10 (assert (= tptp.sin_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X2) N)))))))
% 6.84/7.10 (assert (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X2) N)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X) N)))) (@ tptp.cos_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X) N)))) (@ tptp.cos_complex X))))
% 6.84/7.10 (assert (= tptp.cos_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X2) N)))))))
% 6.84/7.10 (assert (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X2) N)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X) N)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X) N)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X) N)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X) N)))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.84/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))) (@ tptp.exp_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N)))) (@ tptp.exp_complex X))))
% 6.84/7.10 (assert (= tptp.exp_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))
% 6.84/7.10 (assert (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X2) N)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) N))))) (@ tptp.sin_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) N))))) (@ tptp.sin_complex X))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) N)))) (@ tptp.cos_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) N)))) (@ tptp.cos_complex X))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B)) _let_2)))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) (@ (@ tptp.times_times_real Y) X)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) I5))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real I5))) (@ (@ tptp.power_power_real X) I5))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real Y) _let_1)))))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ (@ tptp.times_times_complex Y) X)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) N2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) I5))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real I5))) (@ (@ tptp.power_power_complex X) I5))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex Y) _let_1)))))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 6.84/7.10 (assert (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1)))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (= tptp.exp_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (= tptp.exp_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X2) N)))) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X2) _let_1))))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_real) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))) (@ tptp.sinh_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_complex) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N))))) (@ tptp.sinh_complex X))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))) tptp.zero_zero_real))) (@ tptp.cosh_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N))) tptp.zero_zero_complex))) (@ tptp.cosh_complex X))))
% 6.84/7.10 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) tptp.one_one_complex))
% 6.84/7.10 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.real_V4546457046886955230omplex tptp.pi))) tptp.imaginary_unit)) tptp.one_one_complex))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.84/7.10 (assert (= (@ tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.84/7.10 (assert (= (@ tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real))
% 6.84/7.10 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.84/7.10 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))))
% 6.84/7.10 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2)))))
% 6.84/7.10 (assert (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sinh_complex X2)) (@ tptp.cosh_complex X2)))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.cosh_complex X)) (@ tptp.sinh_complex X)) (@ tptp.exp_complex X))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.cosh_real X)) (@ tptp.sinh_real X)) (@ tptp.exp_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex X)) (@ tptp.exp_complex X))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X)) (@ tptp.exp_real X))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cosh_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X)) (@ tptp.sinh_complex Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sinh_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X)) (@ tptp.sinh_complex Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.sinh_real Y))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cosh_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X)) (@ tptp.sinh_complex Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sinh_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X)) (@ tptp.sinh_complex Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.sinh_real Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ _let_1 X)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sinh_complex X))) (@ tptp.cosh_complex X))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sinh_real X))) (@ tptp.cosh_real X))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1)) tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1)) tptp.one_one_complex)))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1)) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1)) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1)) tptp.one_one_complex)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1)) tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X) Y) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y tptp.one_one_real)))))
% 6.84/7.10 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_2)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_2)))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tanh_real Y))) (let ((_let_2 (@ tptp.tanh_real X))) (=> (not (= (@ tptp.cosh_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cosh_real Y) tptp.zero_zero_real)) (= (@ tptp.tanh_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tanh_complex Y))) (let ((_let_2 (@ tptp.tanh_complex X))) (=> (not (= (@ tptp.cosh_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cosh_complex Y) tptp.zero_zero_complex)) (= (@ tptp.tanh_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.sinh_real X) tptp.zero_zero_real) (@ (@ tptp.member_real (@ tptp.exp_real X)) (@ (@ tptp.insert_real tptp.one_one_real) (@ (@ tptp.insert_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.bot_bot_set_real))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (= (= (@ tptp.sinh_complex X) tptp.zero_zero_complex) (@ (@ tptp.member_complex (@ tptp.exp_complex X)) (@ (@ tptp.insert_complex tptp.one_one_complex) (@ (@ tptp.insert_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.bot_bot_set_complex))))))
% 6.84/7.10 (assert (= tptp.cosh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.10 (assert (= tptp.cosh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.84/7.10 (assert (= tptp.sinh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.84/7.10 (assert (= tptp.sinh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.cosh_real X) tptp.zero_zero_real) (= (@ (@ tptp.power_power_real (@ tptp.exp_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (= (= (@ tptp.cosh_complex X) tptp.zero_zero_complex) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A))))) tptp.one_one_real)))
% 6.84/7.10 (assert (= tptp.cosh_real (lambda ((X2 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))))))
% 6.84/7.10 (assert (= tptp.cosh_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.84/7.10 (assert (= tptp.sinh_real (lambda ((X2 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))))))
% 6.84/7.10 (assert (= tptp.sinh_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.84/7.10 (assert (= (@ tptp.arg (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.10 (assert (= (@ tptp.csqrt tptp.imaginary_unit) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.imaginary_unit)) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.84/7.10 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.84/7.10 (assert (= (@ tptp.cis (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 6.84/7.10 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.84/7.10 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.84/7.10 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.plus_plus_real A) B)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N2))))) (@ tptp.set_ord_lessThan_nat N2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X)) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X))))
% 6.84/7.10 (assert (= tptp.arctan (lambda ((Y3 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.tan_real X2) Y3))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X2 tptp.real)) false))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (H2 (-> tptp.real tptp.real)) (S tptp.set_real) (T3 tptp.set_real) (G (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ (@ tptp.bij_betw_real_real H2) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.minus_minus_set_real T3) T5)) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups7973222482632965587d_enat (lambda ((X2 tptp.real)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups7973222482632965587d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_int) (H2 (-> tptp.real tptp.int)) (S tptp.set_real) (T3 tptp.set_int) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ (@ tptp.bij_betw_real_int H2) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.minus_minus_set_int T3) T5)) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups7973222482632965587d_enat (lambda ((X2 tptp.real)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups5078248829458667347d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_real) (H2 (-> tptp.int tptp.real)) (S tptp.set_int) (T3 tptp.set_real) (G (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ (@ tptp.bij_betw_int_real H2) (@ (@ tptp.minus_minus_set_int S) S5)) (@ (@ tptp.minus_minus_set_real T3) T5)) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups5078248829458667347d_enat (lambda ((X2 tptp.int)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups7973222482632965587d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_int) (H2 (-> tptp.int tptp.int)) (S tptp.set_int) (T3 tptp.set_int) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ (@ tptp.bij_betw_int_int H2) (@ (@ tptp.minus_minus_set_int S) S5)) (@ (@ tptp.minus_minus_set_int T3) T5)) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups5078248829458667347d_enat (lambda ((X2 tptp.int)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups5078248829458667347d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_complex) (H2 (-> tptp.real tptp.complex)) (S tptp.set_real) (T3 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ (@ tptp.bij_be1067425076133476306omplex H2) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups7973222482632965587d_enat (lambda ((X2 tptp.real)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups8780218893797010257d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (H2 (-> tptp.int tptp.complex)) (S tptp.set_int) (T3 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ (@ tptp.bij_betw_int_complex H2) (@ (@ tptp.minus_minus_set_int S) S5)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups5078248829458667347d_enat (lambda ((X2 tptp.int)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups8780218893797010257d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_real) (H2 (-> tptp.complex tptp.real)) (S tptp.set_complex) (T3 tptp.set_real) (G (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ (@ tptp.bij_be1121013576637796946x_real H2) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (@ (@ tptp.minus_minus_set_real T3) T5)) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups8780218893797010257d_enat (lambda ((X2 tptp.complex)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups7973222482632965587d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_int) (H2 (-> tptp.complex tptp.int)) (S tptp.set_complex) (T3 tptp.set_int) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ (@ tptp.bij_betw_complex_int H2) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (@ (@ tptp.minus_minus_set_int T3) T5)) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups8780218893797010257d_enat (lambda ((X2 tptp.complex)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups5078248829458667347d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (S tptp.set_complex) (T3 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ (@ tptp.bij_be1856998921033663316omplex H2) (@ (@ tptp.minus_811609699411566653omplex S) S5)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) S5) (= (@ G (@ H2 A3)) tptp.one_on7984719198319812577d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) T5) (= (@ G B3) tptp.one_on7984719198319812577d_enat))) (= (@ (@ tptp.groups8780218893797010257d_enat (lambda ((X2 tptp.complex)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups8780218893797010257d_enat G) T3)))))))))
% 6.84/7.10 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (H2 (-> tptp.real tptp.real)) (S tptp.set_real) (T3 tptp.set_real) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ (@ tptp.bij_betw_real_real H2) (@ (@ tptp.minus_minus_set_real S) S5)) (@ (@ tptp.minus_minus_set_real T3) T5)) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S5) (= (@ G (@ H2 A3)) tptp.one_one_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) T5) (= (@ G B3) tptp.one_one_complex))) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((X2 tptp.real)) (@ G (@ H2 X2)))) S) (@ (@ tptp.groups713298508707869441omplex G) T3)))))))))
% 6.84/7.10 (assert (= tptp.cot_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))))
% 6.84/7.10 (assert (= tptp.cot_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X2)) (@ tptp.sin_complex X2)))))
% 6.84/7.10 (assert (= tptp.arccos (lambda ((Y3 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.cos_real X2) Y3)))))))
% 6.84/7.10 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real))))))
% 6.84/7.10 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.cot_real X))))
% 6.84/7.10 (assert (= tptp.arcsin (lambda ((Y3 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.sin_real X2) Y3))))))))
% 6.84/7.10 (assert (forall ((L2 tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N2 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 N2) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))) _let_1)))))))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (I2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real I2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I2)))))))))))))
% 6.84/7.10 (assert (forall ((L2 tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N2))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N2 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 N2) M)))))))))))))))))))
% 6.84/7.10 (assert (forall ((Xs2 tptp.list_int) (X8 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) X8) (=> (@ tptp.finite_finite_int X8) (= (@ (@ tptp.groups4541462559716669496nt_nat (@ tptp.count_list_int Xs2)) X8) (@ tptp.size_size_list_int Xs2))))))
% 6.84/7.10 (assert (forall ((Xs2 tptp.list_real) (X8 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) X8) (=> (@ tptp.finite_finite_real X8) (= (@ (@ tptp.groups1935376822645274424al_nat (@ tptp.count_list_real Xs2)) X8) (@ tptp.size_size_list_real Xs2))))))
% 6.84/7.10 (assert (forall ((Xs2 tptp.list_nat) (X8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) X8) (=> (@ tptp.finite_finite_nat X8) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.count_list_nat Xs2)) X8) (@ tptp.size_size_list_nat Xs2))))))
% 6.84/7.10 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.84/7.10 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.84/7.10 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 6.84/7.10 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.84/7.10 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 6.84/7.10 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.84/7.10 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 6.84/7.10 (assert (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.84/7.10 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.84/7.10 (assert (forall ((V tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) tptp.one_one_nat) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) tptp.one_one_int)))))
% 6.84/7.10 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.84/7.10 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.84/7.10 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.84/7.10 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.84/7.10 (assert (= tptp.numeral_numeral_nat (lambda ((I5 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I5)))))
% 6.84/7.10 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y)))))
% 6.84/7.10 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.84/7.10 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.84/7.10 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 6.84/7.10 (assert (forall ((X tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N2) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B))) (@ (@ tptp.plus_plus_nat A) B))))
% 6.84/7.10 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (@ (@ tptp.dvd_dvd_int L2) K)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.modulo_modulo_int K) L2)) (@ tptp.sgn_sgn_int L2))))))
% 6.84/7.10 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 6.84/7.10 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.84/7.10 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.84/7.10 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.84/7.10 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 6.84/7.10 (assert (= tptp.divide_divide_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.84/7.10 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.84/7.10 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 6.84/7.10 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) K)))))
% 6.84/7.10 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z6)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))))
% 6.84/7.10 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))
% 6.84/7.10 (assert (= tptp.suc (lambda ((A4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) tptp.one_one_int)))))
% 6.84/7.10 (assert (forall ((K tptp.int) (L2 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L2)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))))
% 6.84/7.10 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.84/7.10 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.84/7.10 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N2)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))))
% 6.84/7.10 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.84/7.10 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))))
% 6.84/7.10 (assert (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.84/7.10 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K))))))
% 6.84/7.10 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))))
% 6.84/7.10 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.84/7.10 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L) K3))))))))))))
% 6.84/7.10 (assert (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K3))))) _let_2)))))))))))
% 6.84/7.10 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.84/7.10 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 6.84/7.10 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.84/7.10 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z6)))))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))))
% 6.84/7.10 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.nat2 K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (N2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N2)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N2)))))))))))))
% 6.84/7.10 (assert (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N2) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N2)))))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X))))))
% 6.84/7.10 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) 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)) N2)) tptp.one_one_complex))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.root N2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X)) (@ _let_1 X)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) tptp.one_one_real) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N2) X)) (@ tptp.sgn_sgn_real X)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N2))) (= (@ _let_1 (@ _let_2 X)) (@ _let_2 (@ _let_1 X)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N2)) X) (@ (@ tptp.root M) (@ (@ tptp.root N2) X)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ _let_1 X))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N2) X))))))
% 6.84/7.10 (assert (= tptp.sgn_sgn_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real X2) (@ tptp.abs_abs_real X2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2))) Y))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N2) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N2)) X)))))
% 6.84/7.10 (assert (forall ((P (-> tptp.real Bool)) (N2 tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N2) X)) (and (=> (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (forall ((Y3 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y3)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y3)) N2)) X) (@ P Y3))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N2) X)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N3) X)) (@ (@ tptp.root N2) X)))))))
% 6.84/7.10 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.84/7.10 (assert (= tptp.sgn_sgn_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (= A4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.abs_abs_real (@ (@ tptp.root N2) (@ (@ tptp.power_power_real Y) N2))) (@ tptp.abs_abs_real Y)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N2) X))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N3) X))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N3) X)) (@ (@ tptp.root N2) X)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X) N2)) X))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (= (@ (@ tptp.power_power_real Y) N2) X) (= (@ (@ tptp.root N2) X) Y)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N2) X) (= (@ (@ tptp.root N2) X) Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X) N2)) X)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N3) X))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (X tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arg Z) X))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N2) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N2) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N2) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) X)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) 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)) N2)) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) 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)) N2)) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis _let_1)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.84/7.10 (assert (= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= Z5 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.84/7.10 (assert (forall ((Bs tptp.list_o)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) _let_1) Bs)) (@ (@ tptp.power_power_int _let_1) (@ tptp.size_size_list_o Bs))))))
% 6.84/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 6.84/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.84/7.10 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 6.84/7.10 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.84/7.10 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 6.84/7.10 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.84/7.10 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X4 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X4 M6)) (@ X4 N)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ _let_1 K)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N2) L2))))
% 6.84/7.10 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) (= (@ _let_1 K) (@ _let_1 L2))))))
% 6.84/7.10 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.84/7.10 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))))
% 6.84/7.10 (assert (forall ((K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N2) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N2) K)))))
% 6.84/7.10 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y)))))))
% 6.84/7.10 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.84/7.10 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.84/7.10 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.84/7.10 (assert (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L)))))
% 6.84/7.10 (assert (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L)))))
% 6.84/7.10 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))))
% 6.84/7.10 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.10 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.84/7.10 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y)) _let_1)))))))
% 6.84/7.10 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K3)) (not (@ _let_2 L)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.84/7.10 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L)) (@ (@ (@ tptp.if_int (= L _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.10 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.size_size_VEBT_VEBT) X13)) (@ tptp.size_size_VEBT_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))))
% 6.84/7.10 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K)) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.84/7.10 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.84/7.10 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.84/7.10 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.84/7.10 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.84/7.10 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L))))))
% 6.84/7.10 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.84/7.10 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.84/7.10 (assert (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat N2) (@ _let_1 N2))))))
% 6.84/7.10 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))))
% 6.84/7.10 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L)))))
% 6.84/7.10 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_ri7919022796975470100ot_int K)) _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K) _let_1))))))
% 6.84/7.10 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int K)) (not (@ _let_1 K))))))
% 6.84/7.10 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int)))
% 6.84/7.10 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) _let_1))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.84/7.10 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N2) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N2))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N2) M))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N2) (@ _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ 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 N2)))))))
% 6.84/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.zero_zero_int)))
% 6.84/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K)))) (let ((_let_3 (@ tptp.pred_numeral K))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ 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 N2)))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ 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 N2)))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ 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 N2)))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ 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 N2))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ 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 N2))))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ 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 N2))))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ 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 N2))))))))
% 6.84/7.10 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K3))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K3) _let_1))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J2))))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I5)) (@ B I5)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.84/7.10 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_size_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.vEBT_size_VEBT) X13)) (@ tptp.vEBT_size_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.84/7.10 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.84/7.10 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.84/7.10 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.84/7.10 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.84/7.10 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.84/7.10 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))
% 6.84/7.10 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (R tptp.real)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) R))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.numeral_numeral_real W)))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X)) (@ tptp.real_V1022390504157884413omplex X))))
% 6.84/7.10 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y)))))
% 6.84/7.10 (assert (forall ((R tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R) X)) (@ (@ tptp.times_times_real R) (@ tptp.re X)))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.84/7.10 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.re Z))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2)))))
% 6.84/7.10 (assert (= tptp.csqrt (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z5))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z5))) (let ((_let_4 (@ tptp.im Z5))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.im Z))) (= (@ tptp.im (@ tptp.csqrt Z)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_1 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_1))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.84/7.10 (assert (= tptp.code_integer_of_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (R tptp.real)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) R))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_real (@ tptp.re X)) N2)))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.numeral_numeral_real W)))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.im X))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.84/7.10 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y)))))
% 6.84/7.10 (assert (forall ((R tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R) X)) (@ (@ tptp.times_times_real R) (@ tptp.im X)))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.im Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.re Y))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.abs_abs_real (@ tptp.im Y)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.abs_abs_real (@ tptp.re Y)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.84/7.10 (assert (= tptp.plus_plus_complex (lambda ((X2 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y3))) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y3))))))
% 6.84/7.10 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R4 tptp.real) (X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R4))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X2))) (@ _let_1 (@ tptp.im X2)))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.csqrt Z))) (let ((_let_2 (@ tptp.re _let_1))) (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (and (= _let_2 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im _let_1))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2)))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.cos_real (@ tptp.im Z))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.sin_real (@ tptp.im Z))))))
% 6.84/7.10 (assert (= tptp.times_times_complex (lambda ((X2 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.re Y3))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X2)))) (let ((_let_3 (@ tptp.im Y3))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X2)))) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_4 _let_1)) (@ _let_2 _let_3))) (@ (@ tptp.plus_plus_real (@ _let_4 _let_3)) (@ _let_2 _let_1))))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X))) (@ tptp.im X))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)) tptp.zero_zero_real)))))
% 6.84/7.10 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z5)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z5)) _let_1)))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.84/7.10 (assert (forall ((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))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.84/7.10 (assert (forall ((B tptp.complex)) (let ((_let_1 (@ tptp.re B))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B)))))
% 6.84/7.10 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.re W))) (=> (= (@ (@ tptp.power_power_complex W) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im W)))) (= (@ tptp.csqrt Z) W))))))
% 6.84/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.84/7.10 (assert (forall ((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))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))))
% 6.84/7.10 (assert (= tptp.invers8013647133539491842omplex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (let ((_let_3 (@ tptp.re X2))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 6.84/7.10 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y3))) (let ((_let_3 (@ tptp.re Y3))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X2)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X2)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 6.84/7.10 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) R)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.re R))))))
% 6.84/7.10 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) R)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.re R))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.84/7.10 (assert (= tptp.code_num_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A) B))) (and (= (@ _let_2 (@ tptp.re _let_3)) (@ _let_2 (@ tptp.re _let_1))) (= (@ _let_2 (@ tptp.im _let_3)) (@ _let_2 (@ tptp.im _let_1)))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z) (@ tptp.cnj Z)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z)))) tptp.imaginary_unit))))
% 6.84/7.10 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A4) (@ tptp.cnj B4))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z) (@ tptp.cnj W)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z)) W)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 6.84/7.10 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.ord_less_nat I5) N2)))) N2)))
% 6.84/7.10 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I5) N2)))) (@ tptp.suc N2))))
% 6.84/7.10 (assert (forall ((K tptp.code_integer)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.code_nat_of_integer K)) (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) K))))
% 6.84/7.10 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.ord_max_Code_integer K) L2)) (@ (@ tptp.ord_max_int (@ tptp.code_int_of_integer K)) (@ tptp.code_int_of_integer L2)))))
% 6.84/7.10 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L2))))
% 6.84/7.10 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I2))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.84/7.10 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I2)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.84/7.10 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2)))))) tptp.zero_zero_nat)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A2))))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (= A2 _let_1)))))
% 6.84/7.10 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.84/7.10 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.84/7.10 (assert (forall ((N3 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N3)) N2))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) S))))
% 6.84/7.10 (assert (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))) N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) N2))))
% 6.84/7.10 (assert (= tptp.archim6058952711729229775r_real (lambda ((X2 tptp.real)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z5)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 6.84/7.10 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) (@ _let_1 K)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N2) _let_1) _let_1))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.84/7.10 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.84/7.10 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.84/7.10 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N2) M)) K)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N2))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M3) N2)))) M)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M3)))) M)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N2))))))
% 6.84/7.10 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)))))
% 6.84/7.10 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.84/7.10 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.84/7.10 (assert (forall ((K tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.84/7.10 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.84/7.10 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M6 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M6) K3)) (@ (@ tptp.product_Pair_nat_nat M6) (@ (@ tptp.minus_minus_nat K3) M6))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M6) _let_1)))))))
% 6.84/7.10 (assert (forall ((K tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.divide_divide_nat M) N2))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2)))))))
% 6.84/7.10 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2))))))))))))))
% 6.84/7.10 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y3) (@ (@ tptp.modulo_modulo_nat X2) Y3)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y3 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y3)))))))))))
% 6.84/7.10 (assert (forall ((Y tptp.nat) (X 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.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 6.84/7.10 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (=> Y (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))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _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))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (@ _let_2 X) (=> (=> (= X _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.84/7.10 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R4) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R4)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.84/7.10 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K3) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K3)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M6 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.member_nat N) S)))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (S tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N9) (@ (@ tptp.member_nat N9) S))))) (not (@ tptp.finite_finite_nat S)))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M6 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ (@ tptp.member_nat N) S)))))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S))) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N9) (@ tptp.finite_card_nat S)) (@ (@ tptp.member_nat (@ R3 N9)) S))))))))
% 6.84/7.10 (assert (forall ((K tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)) K)))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N2)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))))
% 6.84/7.10 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y3) X2))) (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_nat Y3) X2))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 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 Y3))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X)))))
% 6.84/7.10 (assert (forall ((Z tptp.int)) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X5) Y5))))))))
% 6.84/7.10 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.84/7.10 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat)))))
% 6.84/7.10 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y3) X2))) X)))))
% 6.84/7.10 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y3)))) __flatten_var_0))) Xa2) X))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y3)))) __flatten_var_0))) Xa2) X))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y3) V4)))) __flatten_var_0))) Xa2) X)))))
% 6.84/7.10 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y3) U2)))) __flatten_var_0))) Xa2) X)))))
% 6.84/7.10 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y3 tptp.nat) (Z5 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 Y3) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa3)))))
% 6.84/7.10 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y3 tptp.nat) (Z5 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 Y3) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa3)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N2)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N2)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.84/7.10 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.84/7.10 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N2) N2)) (@ tptp.bit0 (@ tptp.num_of_nat N2))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N2))))))))
% 6.84/7.10 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y3) X2))))))
% 6.84/7.10 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 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 Y3))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.84/7.10 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y3) U2)))) __flatten_var_0))))))
% 6.84/7.10 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y3) V4)))) __flatten_var_0))))))
% 6.84/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X)))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N2))))))
% 6.84/7.10 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.84/7.10 (assert (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))
% 6.84/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N2)) N2))))))
% 6.84/7.10 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.84/7.10 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.84/7.10 (assert (forall ((M7 tptp.set_nat) (N3 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N3) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N3))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I2)) (@ tptp.suc J)))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I2) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I2)) (@ tptp.suc J)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2))))))
% 6.84/7.10 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.84/7.10 (assert (= tptp.comple4887499456419720421f_real (lambda ((X4 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X4))))))
% 6.84/7.10 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I4))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I5)))) tptp.top_top_set_nat)))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.84/7.10 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.84/7.10 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.84/7.10 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A)) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))))
% 6.84/7.10 (assert (= tptp.root (lambda ((N tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y3 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y3)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y3)) N)))) X2)))))
% 6.84/7.10 (assert (= (@ tptp.finite_card_char tptp.top_top_set_char) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))
% 6.84/7.10 (assert (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))
% 6.84/7.10 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.84/7.10 (assert (forall ((C tptp.char)) (@ (@ tptp.ord_less_nat (@ tptp.comm_s629917340098488124ar_nat C)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.84/7.10 (assert (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.84/7.10 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 6.84/7.10 (assert (forall ((C tptp.char)) (= (@ tptp.comm_s629917340098488124ar_nat (@ tptp.ascii_of C)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ tptp.comm_s629917340098488124ar_nat C)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ 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))) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K))) (@ (@ tptp.cons_nat K) tptp.nil_nat)))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ (@ tptp.minus_minus_real B) A)) K)))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.minus_minus_real X) H4))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X) H4))) (@ F X)))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.plus_plus_real X) H4))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X) H4))) (@ F X)))))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X5)))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ G A)) (@ G B)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z4) (@ (@ tptp.ord_less_real Z4) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F6 Z4)))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (= (@ F X) (@ F Y5)))) (= L2 tptp.zero_zero_real))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.84/7.10 (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 ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (@ (@ tptp.ord_less_eq_real (@ F Y5)) (@ F X)))) (= L2 tptp.zero_zero_real))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y5)))) (= L2 tptp.zero_zero_real))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real) (S3 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real X2) N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S3))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ G X2)) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ G X)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) M)) _let_1)))))
% 6.84/7.10 (assert (forall ((Z tptp.real) (R tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) R))) (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) R))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (F (-> tptp.real tptp.real)) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (let ((_let_3 (@ F X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) (@ F X2)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))
% 6.84/7.10 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2))))
% 6.84/7.10 (assert (forall ((X tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))
% 6.84/7.10 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.84/7.10 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.84/7.10 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.84/7.10 (assert (forall ((H2 tptp.real) (N2 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) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))))
% 6.84/7.10 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2)))))))))))
% 6.84/7.10 (assert (forall ((H2 tptp.real) (N2 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) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real H2) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))))
% 6.84/7.10 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))))
% 6.84/7.10 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C)) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T4))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T4) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T4) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N2))))))))))))))))))))
% 6.84/7.10 (assert (forall ((N2 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) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real C) T4) (@ (@ tptp.ord_less_real T4) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N2)))))))))))))
% 6.84/7.10 (assert (forall ((N2 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) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real A) T4) (@ (@ tptp.ord_less_real T4) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N2)))))))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B2 tptp.real)) (=> (forall ((M5 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (= N2 (@ tptp.suc K)) (forall ((M2 tptp.nat) (T6 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N2) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P4)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real U2) P4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T6)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P4)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P4))) (@ (@ tptp.power_power_real T6) P4)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T6) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real))))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 6.84/7.10 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) (@ (@ tptp.power_power_real X5) N)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X2) (@ tptp.suc N))))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) (@ (@ tptp.power_power_real X0) N))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X) _let_1) (=> (@ (@ tptp.member_real Y) _let_1) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (= (@ F X) (@ F Y)))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F6 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F6 X0))) (=> (forall ((N4 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ F X2) N4))) (@ (@ F6 X0) N4)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X5)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N4 tptp.nat) (X5 tptp.real) (Y5 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X5) _let_1) (=> (@ (@ tptp.member_real Y5) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X5) N4)) (@ (@ F Y5) N4)))) (@ (@ tptp.times_times_real (@ L5 N4)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X5) Y5)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (@ F X2)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.84/7.10 (assert (= tptp.upto_aux (lambda ((I5 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I5)) Js) (@ (@ (@ tptp.upto_aux I5) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.84/7.10 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L2)))))
% 6.84/7.10 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) F))) (exists ((L6 tptp.real) (M8 tptp.real)) (and (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M8))))) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y2) (@ (@ tptp.ord_less_eq_real Y2) M8)) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B) (= (@ F X5) Y2)))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((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))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L2 tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((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))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((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)))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.sqrt)))
% 6.84/7.10 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ tptp.root N2))))
% 6.84/7.10 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (= (@ G (@ F Z4)) Z4)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G)))))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y5) (=> (@ (@ tptp.ord_less_real Y5) B) (= (@ F (@ G Y5)) Y5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arccos)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.84/7.10 (assert (forall ((B tptp.real) (X tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real B) X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.84/7.10 (assert (forall ((D tptp.real) (X tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z4) X))) D) (= (@ G (@ F Z4)) Z4))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z4) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) G)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z4) (=> (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z4)) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z4) (=> (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 Z4)) (@ (@ tptp.topolo2177554685111907308n_real Z4) 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))) (@ F6 C3))))))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N9 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N9 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ 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)))))))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.84/7.10 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C)) tptp.at_top_nat) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I4))) B2)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.root N) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N4))) (@ G N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ G N4))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N9)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N9))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.84/7.10 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_real R3) (@ X8 N4)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.84/7.10 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.root N) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.84/7.10 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) L2)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N9)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X) N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((C tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real C))) (=> (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real _let_1)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.84/7.10 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real C)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real C)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X) N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N)))) N))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_nat)))
% 6.84/7.10 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.84/7.10 (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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ A N))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ A N)))))))))
% 6.84/7.10 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K2 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.84/7.10 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K2 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.84/7.10 (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 ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat))))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ 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))))) _let_1) tptp.at_top_nat)))))))))
% 6.84/7.10 (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 ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ 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))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat)))))
% 6.84/7.10 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ 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))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat))))))
% 6.84/7.10 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F5 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F5 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C2)))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y3 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y3))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y3)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) tptp.at_bot_real))
% 6.84/7.10 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.84/7.10 (assert (let ((_let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N2))) tptp.at_bot_real) F3))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N2))) tptp.at_top_real) F3))))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.84/7.10 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) K)) (@ tptp.exp_real X2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.84/7.10 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y3 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y3))) Y3))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 6.84/7.10 (assert (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))
% 6.84/7.10 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X5) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.84/7.10 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.at_top_real))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.84/7.10 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I5 tptp.nat)) (@ P (@ tptp.suc I5)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X5) (@ P X5))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ P N)))))))
% 6.84/7.10 (assert (forall ((F3 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F3) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N6)) F3)))))
% 6.84/7.10 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I5 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I5) K)))) tptp.at_top_nat))))
% 6.84/7.10 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 6.84/7.10 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ (@ tptp.plus_plus_real X2) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F3) _let_1))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F3) _let_1))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_1) tptp.at_top_real)))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.84/7.10 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (F3 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 ((X2 tptp.real)) (not (= (@ G0 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X2)) (@ G0 X2)))) F3) _let_1))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F3) _let_1))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.84/7.10 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F6 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X)) tptp.at_top_nat)))))
% 6.84/7.10 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.84/7.10 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.84/7.10 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.84/7.10 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.84/7.10 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B2) (@ X8 I4))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.84/7.10 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B2) (@ X8 I4))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X8 I)))))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.84/7.10 (assert (forall ((J tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J) I2) (= (@ (@ tptp.upto I2) J) tptp.nil_int))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J)) (@ (@ tptp.ord_less_int J) I2))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I2) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I2))))
% 6.84/7.10 (assert (forall ((I2 tptp.int)) (= (@ (@ tptp.upto I2) I2) (@ (@ tptp.cons_int I2) tptp.nil_int))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J)) K) _let_1)))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I2)) tptp.one_one_int)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.84/7.10 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3)))))
% 6.84/7.10 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I5) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.84/7.10 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I5) J3)))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I2) J))))
% 6.84/7.10 (assert (= tptp.upto (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I5) J3) tptp.nil_int))))
% 6.84/7.10 (assert (= tptp.upto_aux (lambda ((I5 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I5) J3)) __flatten_var_0))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 6.84/7.10 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.84/7.10 (assert (= tptp.upto (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I5) J3)) (@ (@ tptp.cons_int I5) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.84/7.10 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ (@ tptp.upto I2) J) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J))))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 6.84/7.10 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.84/7.10 (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 ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) F))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X5) (@ (@ tptp.ord_less_real X5) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) G))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X5) (@ (@ tptp.ord_less_real X5) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.84/7.10 (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 ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z4) (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arcosh_real))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.arcosh_real (@ F X2)))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (exists ((C3 tptp.real) (D3 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C3) D3)) (@ (@ tptp.ord_less_eq_real C3) D3)))))))
% 6.84/7.10 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.84/7.10 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.artanh_real))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.member_real (@ F X5)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.artanh_real (@ F X2)))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> 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 ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F6 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z4) (@ (@ tptp.ord_less_real Z4) B) (= (@ F6 Z4) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F6 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) 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)) (@ (@ F6 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))))
% 6.84/7.10 (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 ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))))
% 6.84/7.10 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X) (=> (@ (@ tptp.ord_less_eq_real X) B) (= (@ F X) (@ F A)))))))))
% 6.84/7.10 (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 ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z4) (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ 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) N2))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))))
% 6.84/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.84/7.10 (assert (forall ((R tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ 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 N2) M)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))))
% 6.84/7.10 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ 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 R)) M)))))
% 6.84/7.10 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M))))))
% 6.84/7.10 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ 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 N2))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ 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 N2))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))) N2))))
% 6.84/7.10 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N2) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ tptp.some_num tptp.one))) N2))))
% 6.84/7.10 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num tptp.one))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N2)) tptp.none_num)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))) N2))))
% 6.84/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int Q2)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ (@ 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) N2)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N2) M)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.84/7.10 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (= Y (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (not (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))
% 6.84/7.10 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList2) Summary)) Deg4) (and (= Deg Deg4) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima2)))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.84/7.10 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A4 tptp.nat) (X2 tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P4 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num O) P4)))) (lambda ((P4 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P4))))) X2))) A4))) (@ (@ tptp.product_Pair_nat_num N) M6)))))
% 6.84/7.10 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 6.84/7.10 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B2)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.84/7.10 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B2)) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I)) L6))))))))))
% 6.84/7.10 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M6)) M6))))))
% 6.84/7.10 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa2) Y) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N4 tptp.num)) (= Xa2 (@ tptp.bit0 N4))) (not (= Y (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N4 tptp.num)) (= Xa2 (@ tptp.bit1 N4))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M5) N4)))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4))))))))))))))))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G) (= (@ (@ tptp.bfun_nat_real (lambda ((X2 tptp.nat)) (@ F (@ G X2)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.84/7.10 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa2) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N4 tptp.num)) (= Xa2 (@ tptp.bit0 N4))) _let_4)) (=> (=> _let_5 (=> (exists ((N4 tptp.num)) (= Xa2 (@ tptp.bit1 N4))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X (@ tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4)))))))) (=> (=> (exists ((M5 tptp.num)) (= X (@ tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4)))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4)))))))))))))))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa2) Y) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y (@ tptp.some_num (@ tptp.bit1 N4))))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y (@ tptp.some_num (@ tptp.bit0 N4))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4)))))))))))))))))))))
% 6.84/7.10 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.84/7.10 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N2)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num tptp.one))))
% 6.84/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N2)) tptp.none_num)))
% 6.84/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num (@ tptp.bit1 N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num (@ tptp.bit0 N2)))))
% 6.84/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.84/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.84/7.10 (assert (forall ((F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F6 X5))) (@ tptp.order_7092887310737990675l_real F)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))))
% 6.84/7.10 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.84/7.10 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.inj_on_real_real (lambda ((Y3 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y3)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y3)) N2)))) tptp.top_top_set_real))))
% 6.84/7.10 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((N3 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N3)))
% 6.84/7.10 (assert (forall ((N3 tptp.set_nat) (K tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) N3) (@ (@ tptp.ord_less_eq_nat K) N4))) (@ (@ tptp.inj_on_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) K))) N3))))
% 6.84/7.10 (assert (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.84/7.10 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 6.84/7.10 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.84/7.10 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.84/7.10 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G)))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G))) (@ tptp.suminf_real F)))))))
% 6.84/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (=> (forall ((X5 tptp.nat)) (=> (not (@ (@ tptp.member_nat X5) (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat))) (= (@ F X5) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G)) (@ tptp.suminf_real F))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N2))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) I2))))
% 6.84/7.10 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.upt I2) J) tptp.nil_nat))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.upt M) N2))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I2) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I2)))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J)) K) _let_1)))))
% 6.84/7.10 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat)) (= (@ (@ tptp.upt I2) tptp.zero_zero_nat) tptp.nil_nat)))
% 6.84/7.10 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) M6)))))
% 6.84/7.10 (assert (= tptp.set_ord_lessThan_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N)))))
% 6.84/7.10 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I5) J3)))))
% 6.84/7.10 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N) (@ tptp.suc M6))))))
% 6.84/7.10 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) (@ tptp.suc M6))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N2) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I2) J))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat I5) N2))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N2) (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N2)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.84/7.10 (assert (= tptp.set_ord_atMost_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N))))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.upt M) N2))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat X) Xs2)) (and (@ (@ tptp.ord_less_nat I2) J) (= I2 X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J) Xs2)))))
% 6.84/7.10 (assert (= tptp.upt (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I5) J3)) (@ (@ tptp.cons_nat I5) (@ (@ tptp.upt (@ tptp.suc I5)) J3))) tptp.nil_nat))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N3))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L) N3)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L)) tptp.one_one_nat) N3))))))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N3))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N3) M)) tptp.one_one_nat)) N3))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N2))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N2))))
% 6.84/7.10 (assert (forall ((Ns tptp.list_nat) (I2 tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.nth_nat Ns) I2))))))
% 6.84/7.10 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J))))
% 6.84/7.10 (assert (forall ((M tptp.int) (N2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N2))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.upt (@ tptp.suc M)) N2))))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J)) I2))))
% 6.84/7.10 (assert (forall ((X tptp.real) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (or (not (= X tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2)) (= (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.power_int_real X) N2))))))
% 6.84/7.10 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X2) Y3)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.84/7.10 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X2 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X2) Y3)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.84/7.10 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R4 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R4)))))))
% 6.84/7.10 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N6 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ P (@ (@ tptp.product_Pair_nat_nat N) M6))))))))))
% 6.84/7.10 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M6)))))))
% 6.84/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) A))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) (@ tptp.pred_numeral K))))))
% 6.84/7.10 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N2)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N2)) Q2) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N2) Q2)))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N2) Q2)) (@ (@ tptp.ord_min_nat (@ _let_1 N2)) (@ _let_1 Q2))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I2)) (@ (@ tptp.minus_minus_nat N2) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N2)) I2))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int) (L2 tptp.int) (R tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N2) K) L2)) R) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N2)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N2)) L2) R)))))
% 6.84/7.10 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N2) K) L2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N2)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N2)) L2)))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) M3)))) M))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M3) N2)))) M))))
% 6.84/7.10 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.10 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 6.84/7.10 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N2) (= (@ (@ tptp.take_nat M) (@ _let_2 N2)) (@ _let_2 _let_1)))))))
% 6.84/7.10 (assert (forall ((M tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I2) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M)) J))))
% 6.84/7.10 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.84/7.10 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I5 tptp.int) (N tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I5)) (@ tptp.semiri5074537144036343181t_real N))) (not (= N tptp.zero_zero_nat))))))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X) X5)))))
% 6.84/7.10 (assert (forall ((X tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X5) X)))))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X) X5) (@ (@ tptp.ord_less_real X5) Y))))))
% 6.84/7.10 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I5 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I5)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N2)) A2)) (@ (@ tptp.insert_nat N2) (@ _let_1 A2))))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A2)) (@ _let_1 A2)))))
% 6.84/7.10 (assert (forall ((F3 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F3)) (@ tptp.finite_finite_nat F3))))
% 6.84/7.10 (assert (forall ((X tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X)))))
% 6.84/7.10 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.84/7.10 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S))))))
% 6.84/7.10 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N)) M6))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N2) (@ (@ tptp.ord_less_nat Y3) N2) (@ (@ tptp.ord_less_eq_nat X2) Y3)))))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N2))))))
% 6.84/7.10 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N2)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N2)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N2) (@ (@ tptp.ord_less_nat Y3) N2) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))))
% 6.84/7.10 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 6.84/7.10 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2)) (lambda ((Uu3 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N2) (@ (@ tptp.ord_less_nat Y3) N2) (@ (@ tptp.ord_less_eq_nat X2) Y3))))))))
% 6.84/7.10 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N2))))))
% 6.84/7.10 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M))))
% 6.84/7.10 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.84/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.84/7.10 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N))) M6)))))
% 6.84/7.10 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X5) Xs3)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs2)))))))
% 6.84/7.10 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X5) Xs3))) (=> (= X _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.84/7.10 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 6.84/7.10 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X4 tptp.real)) (@ P X4)))))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (@ (@ (@ tptp.if_set_real false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (@ (@ (@ tptp.if_set_real true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)))
% 6.84/7.10 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 6.84/7.10 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 8.97/9.20 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 8.97/9.20 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 8.97/9.20 (assert (forall ((X (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X) Y) Y)))
% 8.97/9.20 (assert (forall ((X (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int true) X) Y) X)))
% 8.97/9.20 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat false) X) Y) Y)))
% 8.97/9.20 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat true) X) Y) X)))
% 8.97/9.20 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y) Y)))
% 8.97/9.20 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y) X)))
% 8.97/9.20 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 8.97/9.20 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)))
% 8.97/9.20 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)))
% 8.97/9.20 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (not (@ (@ tptp.ord_less_nat (@ (@ (@ tptp.if_nat (= _let_3 tptp.ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))) _let_4))))) tptp.ma)) (@ _let_2 tptp.deg))))))))
% 8.97/9.20 (set-info :filename cvc5---1.0.5_22629)
% 8.97/9.20 (check-sat-assuming ( true ))
% 8.97/9.20 ------- get file name : TPTP file name is ITP269^1
% 8.97/9.20 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22629.smt2...
% 8.97/9.20 --- Run --ho-elim --full-saturate-quant at 10...
% 8.97/9.20 % SZS status Theorem for ITP269^1
% 8.97/9.20 % SZS output start Proof for ITP269^1
% 8.97/9.20 (
% 8.97/9.20 (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_nat _let_2))) (let ((_let_4 (@ _let_3 tptp.deg))) (let ((_let_5 (@ _let_3 tptp.na))) (let ((_let_6 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) _let_5)) tptp.lx))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_high _let_6) tptp.na))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low _let_6) tptp.na))) (let ((_let_9 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_10 (@ (@ tptp.vEBT_vebt_delete (@ _let_9 _let_7)) _let_8))) (let ((_let_11 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_7) _let_10))) (let ((_let_12 (@ (@ tptp.nth_VEBT_VEBT _let_11) _let_7))) (let ((_let_13 (@ (@ tptp.divide_divide_nat tptp.deg) _let_2))) (let ((_let_14 (@ _let_3 _let_13))) (let ((_let_15 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_14)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt _let_12))))) (let ((_let_16 (= _let_6 tptp.ma))) (let ((_let_17 (@ (@ (@ tptp.if_nat _let_16) _let_15) tptp.ma))) (let ((_let_18 (@ (@ tptp.ord_less_nat _let_17) _let_4))) (let ((_let_19 (not _let_18))) (let ((_let_20 (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat)))) (let ((_let_21 (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (let ((_let_22 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (let ((_let_23 (@ tptp.bit0 _let_1))) (let ((_let_24 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_23))))))))) (let ((_let_25 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_24))) (let ((_let_26 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_27 (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real _let_26) tptp.one_one_real)))) (let ((_let_28 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_29 (@ tptp.divide_divide_real tptp.pi))) (let ((_let_30 (@ _let_29 _let_28))) (let ((_let_31 (@ tptp.filterlim_real_real tptp.arctan))) (let ((_let_32 (@ tptp.topolo2177554685111907308n_real _let_30))) (let ((_let_33 (@ tptp.filterlim_real_real tptp.tan_real))) (let ((_let_34 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_35 (@ tptp.topolo2177554685111907308n_real tptp.one_one_real))) (let ((_let_36 (@ tptp.filterlim_real_real tptp.artanh_real))) (let ((_let_37 (@ tptp.topolo2815343760600316023s_real tptp.one_one_real))) (let ((_let_38 (@ tptp.filterlim_real_real tptp.tanh_real))) (let ((_let_39 (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))) (let ((_let_40 (@ tptp.uminus_uminus_real _let_30))) (let ((_let_41 (@ tptp.numera6620942414471956472nteger _let_1))) (let ((_let_42 (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ))) (let ((_let_43 (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) _let_42))) (let ((_let_44 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_45 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_46 (@ tptp.suc _let_45))) (let ((_let_47 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_48 (@ tptp.nat2 tptp.one_one_int))) (let ((_let_49 (@ tptp.times_times_real _let_28))) (let ((_let_50 (@ _let_49 tptp.pi))) (let ((_let_51 (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_52 (@ tptp.sqrt _let_28))) (let ((_let_53 (@ tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_54 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_55 (@ tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_56 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_57 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_58 (@ tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_59 (@ tptp.numeral_numeral_real tptp.one))) (let ((_let_60 (@ tptp.numera1916890842035813515d_enat _let_1))) (let ((_let_61 (@ (@ tptp.divide1717551699836669952omplex _let_55) _let_56))) (let ((_let_62 (@ tptp.real_V1803761363581548252l_real tptp.pi))) (let ((_let_63 (@ (@ tptp.divide_divide_real _let_62) _let_28))) (let ((_let_64 (@ tptp.bit1 tptp.one))) (let ((_let_65 (@ tptp.numeral_numeral_real _let_64))) (let ((_let_66 (@ tptp.sqrt _let_65))) (let ((_let_67 (@ _let_29 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_64))))) (let ((_let_68 (@ tptp.numeral_numeral_real _let_23))) (let ((_let_69 (@ _let_29 _let_68))) (let ((_let_70 (@ _let_29 _let_65))) (let ((_let_71 (@ (@ tptp.divide_divide_real _let_66) _let_28))) (let ((_let_72 (@ _let_57 _let_28))) (let ((_let_73 (@ (@ tptp.divide_divide_real _let_52) _let_28))) (let ((_let_74 (@ tptp.cos_real _let_28))) (let ((_let_75 (@ tptp.power_power_complex tptp.zero_zero_complex))) (let ((_let_76 (@ tptp.power_power_int tptp.zero_zero_int))) (let ((_let_77 (@ tptp.power_power_real tptp.zero_zero_real))) (let ((_let_78 (@ tptp.divide_divide_real _let_65))) (let ((_let_79 (@ (@ tptp.times_times_real (@ _let_78 _let_28)) tptp.pi))) (let ((_let_80 (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_81 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_82 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_83 (@ tptp.ord_less_real tptp.pi))) (let ((_let_84 (@ tptp.bit1 _let_64))) (let ((_let_85 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1)))) (let ((_let_86 (@ tptp.exp_real tptp.one_one_real))) (let ((_let_87 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_88 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_89 (@ tptp.numeral_numeral_int _let_64))) (let ((_let_90 (@ tptp.numera6690914467698888265omplex _let_64))) (let ((_let_91 (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_92 (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_93 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_94 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_95 (@ tptp.ord_le6747313008572928689nteger _let_87))) (let ((_let_96 (@ tptp.ord_less_int _let_88))) (let ((_let_97 (@ tptp.ord_less_real _let_26))) (let ((_let_98 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_99 (@ tptp.ord_less_eq_int _let_88))) (let ((_let_100 (@ tptp.ord_le3102999989581377725nteger _let_87))) (let ((_let_101 (@ tptp.ord_less_eq_real _let_26))) (let ((_let_102 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_103 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_104 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_105 (@ tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_106 (@ tptp.uminus1351360451143612070nteger _let_41))) (let ((_let_107 (@ tptp.uminus1482373934393186551omplex _let_56))) (let ((_let_108 (@ tptp.uminus_uminus_int _let_47))) (let ((_let_109 (@ tptp.uminus_uminus_real _let_28))) (let ((_let_110 (= (@ (@ tptp.modulo364778990260209775nteger _let_87) _let_41) tptp.one_one_Code_integer))) (let ((_let_111 (= (@ (@ tptp.modulo_modulo_int _let_88) _let_47) tptp.one_one_int))) (let ((_let_112 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_113 (@ tptp.minus_minus_int tptp.one_one_int))) (let ((_let_114 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_115 (@ tptp.minus_8373710615458151222nteger _let_87))) (let ((_let_116 (@ tptp.minus_minus_complex _let_54))) (let ((_let_117 (@ tptp.minus_minus_int _let_88))) (let ((_let_118 (@ tptp.minus_minus_real _let_26))) (let ((_let_119 (@ tptp.plus_p5714425477246183910nteger _let_87))) (let ((_let_120 (@ tptp.plus_plus_complex _let_54))) (let ((_let_121 (@ tptp.plus_plus_int _let_88))) (let ((_let_122 (@ tptp.plus_plus_real _let_26))) (let ((_let_123 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_124 (@ tptp.plus_plus_real tptp.one_one_real))) (let ((_let_125 (@ tptp.dvd_dvd_int _let_47))) (let ((_let_126 (@ tptp.dvd_dvd_nat _let_2))) (let ((_let_127 (@ tptp.dvd_dvd_Code_integer _let_41))) (let ((_let_128 (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) _let_47) tptp.one_one_int))) (let ((_let_129 (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) _let_2) tptp.one_one_nat))) (let ((_let_130 (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))) (let ((_let_131 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_132 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_133 (@ tptp.numeral_numeral_nat tptp.one))) (let ((_let_134 (@ _let_123 tptp.one_one_int))) (let ((_let_135 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_136 (@ _let_135 tptp.one_one_nat))) (let ((_let_137 (@ _let_124 tptp.one_one_real))) (let ((_let_138 (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))) (let ((_let_139 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_140 (@ _let_94 tptp.one_one_int))) (let ((_let_141 (@ _let_132 tptp.one_one_nat))) (let ((_let_142 (@ _let_82 tptp.one_one_real))) (let ((_let_143 (@ _let_139 tptp.one_on7984719198319812577d_enat))) (let ((_let_144 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_145 (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat))) (let ((_let_146 (@ _let_98 tptp.one_one_int))) (let ((_let_147 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_148 (@ _let_147 tptp.one_one_nat))) (let ((_let_149 (@ _let_81 tptp.one_one_real))) (let ((_let_150 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_151 (@ _let_150 tptp.one_on7984719198319812577d_enat))) (let ((_let_152 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_153 (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat))) (let ((_let_154 (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) _let_41) tptp.zero_z3403309356797280102nteger))) (let ((_let_155 (= (@ (@ tptp.divide_divide_int tptp.one_one_int) _let_47) tptp.zero_zero_int))) (let ((_let_156 (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) _let_2) tptp.zero_zero_nat))) (let ((_let_157 (@ _let_9 tptp.summin))) (let ((_let_158 (@ tptp.vEBT_vebt_mint tptp.summary))) (let ((_let_159 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary))) (let ((_let_160 (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na))) (let ((_let_161 (= tptp.xa tptp.mi))) (let ((_let_162 (not _let_161))) (let ((_let_163 (@ tptp.the_nat _let_158))) (let ((_let_164 (= _let_136 _let_2))) (let ((_let_165 (= _let_133 tptp.one_one_nat))) (let ((_let_166 (@ tptp.ord_less_eq_nat tptp.mi))) (let ((_let_167 (= tptp.mi tptp.ma))) (let ((_let_168 (not _let_167))) (let ((_let_169 (@ (@ tptp.ord_less_nat tptp.ma) _let_4))) (let ((_let_170 (@ _let_166 tptp.ma))) (let ((_let_171 (@ _let_3 tptp.m))) (let ((_let_172 (@ tptp.size_s6755466524823107622T_VEBT _let_11))) (let ((_let_173 (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList))) (let ((_let_174 (@ tptp.ord_less_nat _let_7))) (let ((_let_175 (and (=> _let_16 (= _let_6 _let_15)) (=> (not _let_16) _let_16)))) (let ((_let_176 (and _let_18 (@ (@ tptp.ord_less_eq_nat _let_6) _let_17)))) (SCOPE (SCOPE (CONTRA (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_176)) (MACRO_SR_EQ_INTRO :args (_let_176 SB_DEFAULT SBA_FIXPOINT))) :args (0)) (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT)))) :args ((= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)) (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)) _let_169 (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)))) (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((Ma tptp.nat) (N2 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 N2) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N2)) (@ _let_1 M))))) (= _let_13 tptp.na) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) Y)))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) X)))) (@ (@ tptp.ord_less_eq_nat _let_2) tptp.deg) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)) X_1)) (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L))) (@ (@ tptp.ord_less_nat tptp.summin) _let_171) (@ (@ tptp.ord_less_nat _let_6) _let_4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ _let_9 _let_160)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na)) (=> (not _let_175) (forall ((I 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.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))))) (let ((_let_6 (@ (@ (@ tptp.if_nat (= _let_3 tptp.ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_5 _let_4))))) tptp.ma))) (=> (@ (@ tptp.ord_less_nat I) (@ _let_2 tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high _let_6) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ _let_5 I)) (@ (@ tptp.vEBT_VEBT_low _let_6) tptp.na))) (forall ((Y2 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.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))))) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y2) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ _let_5 I)) (@ (@ tptp.vEBT_VEBT_low Y2) tptp.na))) (and (@ (@ tptp.ord_less_nat _let_3) Y2) (@ (@ tptp.ord_less_eq_nat Y2) (@ (@ (@ tptp.if_nat (= _let_3 tptp.ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_5 _let_4))))) tptp.ma)))))))))))))))))))) (= _let_12 _let_10) (and (@ _let_174 _let_171) (@ (@ tptp.ord_less_nat _let_8) _let_5)) (exists ((X_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))) X_1))) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (=> (and (not (= I2 _let_4)) (@ (@ tptp.ord_less_nat I2) (@ _let_2 tptp.m))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ _let_1 _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))) I2) (@ _let_1 I2)))))))) (not (@ tptp.vEBT_VEBT_minNull _let_10)) _let_176 _let_170 (= _let_173 _let_171) (= _let_173 _let_172) (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> _let_175 (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))))) (@ _let_174 _let_173) (@ (@ tptp.vEBT_invar_vebt _let_10) tptp.na) (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))))) (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)))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))) (= _let_172 _let_171) (=> _let_168 (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y2) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low Y2) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y2) (@ (@ tptp.ord_less_eq_nat Y2) tptp.ma)))))))) (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))) (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m) (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.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete X3) Xa)) tptp.na))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) Y))))) (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) Xs) (@ (@ tptp.ord_less_eq_nat X2) Y3)))))) (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) Xs) (@ (@ tptp.ord_less_eq_nat Y3) X2)))))) (=> _let_167 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N2))))) (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ tptp.set_complex2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) N2))))) (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N2))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N2))))) (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N2 tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N2))))) (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N2))))) (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs2)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat M) (@ tptp.numera1916890842035813515d_enat N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N2)) (= M N2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X3) tptp.na))) (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))) (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.collec3392354462482085612at_nat P)) (@ P A))) (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))) (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))) (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))) (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))) (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)) (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A2))) A2)) (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)) (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)) (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A2))) A2)) (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collec3392354462482085612at_nat P) (@ tptp.collec3392354462482085612at_nat Q)))) (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))) (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))) (forall ((X tptp.nat)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete tptp.summary) X)) tptp.m)) (@ (@ tptp.vEBT_invar_vebt _let_157) tptp.na) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) _let_160) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((V tptp.num) (W tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat W)) Z)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num V) W))) Z))) (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))) (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))) (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))) (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))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))) (forall ((V tptp.num) (W tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W)) Z)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V) W))) Z))) (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))) (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))) (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))) (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))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N2) (@ tptp.bit0 N2))) (and _let_170 _let_169) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B) _let_1))))) (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))))) (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))))) (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))))) (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))))) (forall ((V tptp.num) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B)) (@ _let_1 C))))) (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))))) (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))))) (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))))) (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))))) (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)))) (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))))) (forall ((Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_low Y) tptp.na))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Y) tptp.na))) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_3)) _let_2) (=> (@ (@ tptp.ord_less_nat _let_3) (@ _let_1 tptp.m)) (and (@ (@ tptp.ord_less_nat tptp.mi) Y) (@ (@ tptp.ord_less_eq_nat Y) tptp.ma) (@ (@ tptp.ord_less_nat _let_2) (@ _let_1 tptp.na))))))))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y2) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low Y2) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y2) (@ (@ tptp.ord_less_eq_nat Y2) tptp.ma))))))) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))))) (@ (@ tptp.vEBT_invar_vebt X3) tptp.na))))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na)))) I)) X4)))) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))) (forall ((A tptp.nat) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L2)))))) (forall ((A tptp.int) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L2)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L2)))))) (forall ((A tptp.code_integer) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger L2)) (@ _let_1 (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num K) L2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N2) K)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))) (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))))) (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))))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2))) M)) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2)) M)) (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N2) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N2)) Q2)))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) (@ tptp.numera1916890842035813515d_enat tptp.one)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat tptp.one)) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) I2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger N2))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B)))) (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)))) (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)))) (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)))) (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)))) (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))) (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))) (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))) (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))) (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))) (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))) (= tptp.vEBT_V5917875025757280293ildren (lambda ((N tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) N))) (@ (@ tptp.vEBT_VEBT_low X2) N)))) (and _let_168 (@ (@ tptp.ord_less_nat tptp.xa) _let_4)) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_VEBT_VEBT2 Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_o2 Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_nat2 Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_int2 Xs2))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) I2) X))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) I2) X))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) I2) X))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) I2) X))) (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I2) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2))) (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I2) (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2))) (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I2) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2))) (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I2) (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) _let_2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.power_8040749407984259932d_enat X) _let_2)) (@ (@ tptp.power_8040749407984259932d_enat Y) _let_2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat _let_1)) X)) Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))) (and (@ _let_166 tptp.xa) (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma)) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary)) N2) (= Deg N2))) (@ _let_152 tptp.na) _let_161 (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X)) I2) Y) (@ _let_1 Y)))) (or _let_162 (not (= tptp.xa tptp.ma))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.one_on7984719198319812577d_enat) N2) tptp.one_on7984719198319812577d_enat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N2) tptp.one_one_real)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N2) tptp.one_one_complex)) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)) (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) (@ tptp.size_size_list_o Xs2))) (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) (@ tptp.size_size_list_nat Xs2))) (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) (@ tptp.size_size_list_int Xs2))) (forall ((Xs2 tptp.list_nat) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ (@ tptp.nth_nat Xs2) I2)) Xs2)) (forall ((Xs2 tptp.list_int) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs2) I2) (@ (@ tptp.nth_int Xs2) I2)) Xs2)) (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) Xs2)) (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J) (@ (@ tptp.nth_nat Xs2) J)))) (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J) (@ (@ tptp.nth_int Xs2) J)))) (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J) (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))) (forall ((N2 tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat N2) tptp.one_on7984719198319812577d_enat) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N2) tptp.one_one_complex) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real N2) tptp.one_one_real) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat N2) tptp.one_one_nat) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int N2) tptp.one_one_int) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.numera1916890842035813515d_enat N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N2)) (= tptp.one N2))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((A tptp.nat) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))) (forall ((A tptp.real) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))) (forall ((A tptp.int) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))) (forall ((A tptp.complex) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))) (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((A tptp.complex) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))) (forall ((A tptp.real) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))) (forall ((A tptp.nat) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))) (forall ((A tptp.int) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))) (forall ((A tptp.complex) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.real) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.nat) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.int) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))) (= _let_138 _let_60) (= (@ _let_53 tptp.one_one_complex) _let_56) (= _let_137 _let_28) _let_164 (= _let_134 _let_47) (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((Xs2 tptp.list_complex) (B2 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) B2) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 (@ tptp.set_complex2 Xs2)) (@ _let_1 B2)))))) (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) B2) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ _let_1 B2)))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (B2 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) B2) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs2)) (@ _let_1 B2)))))) (forall ((Xs2 tptp.list_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) B2) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs2)) (@ _let_1 B2)))))) (forall ((Xs2 tptp.list_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) B2) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 Xs2)) (@ _let_1 B2)))))) (forall ((Xs2 tptp.list_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) B2) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs2)) (@ _let_1 B2)))))) (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))))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N2) (@ (@ tptp.plus_plus_num N2) tptp.one))) (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))) (@ _let_153 tptp.one_on7984719198319812577d_enat) (@ _let_105 tptp.one_one_real) (@ _let_152 tptp.one_one_nat) (@ _let_104 tptp.one_one_int) (not (@ _let_145 tptp.one_on7984719198319812577d_enat)) (not (@ _let_103 tptp.one_one_real)) (not (@ _let_144 tptp.one_one_nat)) (not (@ _let_102 tptp.one_one_int)) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_7803423173614009249d_enat X) Y) tptp.one_on7984719198319812577d_enat) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.power_8040749407984259932d_enat X) N2)) (@ (@ tptp.power_8040749407984259932d_enat Y) N2)) tptp.one_on7984719198319812577d_enat))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) tptp.one_one_complex))) (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) tptp.one_one_real))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))) (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_complex A) N2))))) (forall ((Xs2 tptp.list_complex) (A2 tptp.set_complex) (X tptp.complex) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (=> (@ (@ tptp.member_complex X) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) I2) X))) A2)))) (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) I2) X))) A2)))) (forall ((Xs2 tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I2) X))) A2)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X))) A2)))) (forall ((Xs2 tptp.list_real) (A2 tptp.set_real) (X tptp.real) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A2) (=> (@ (@ tptp.member_real X) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I2) X))) A2)))) (forall ((Xs2 tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I2) X))) A2)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) _let_2))))) (forall ((A tptp.real) (N2 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) N2)))))) (forall ((A tptp.nat) (N2 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) N2)))))) (forall ((A tptp.int) (N2 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) N2)))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))) (forall ((A tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N3)))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N3)))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N3)))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N3)))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N3)))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N3)))))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))) (= (@ tptp.numera1916890842035813515d_enat tptp.one) tptp.one_on7984719198319812577d_enat) (= _let_58 tptp.one_one_complex) (= _let_59 tptp.one_one_real) _let_165 (= _let_93 tptp.one_one_int) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))) _let_165 (forall ((A tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.one_on7984719198319812577d_enat) _let_2) tptp.one_on7984719198319812577d_enat) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) _let_2) tptp.one_one_nat) (= (@ (@ tptp.power_power_real tptp.one_one_real) _let_2) tptp.one_one_real) (= (@ (@ tptp.power_power_int tptp.one_one_int) _let_2) tptp.one_one_int) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) _let_2) tptp.one_one_complex) (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)))) (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)))) (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)))) (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)))) (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N2))) (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N2))) (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N2))) (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N2))) (forall ((I2 tptp.nat) (I3 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X6 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs2))) (=> (not (= I2 I3)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I2) X)) I3) X6) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I3) X6)) I2) X))))) _let_164 (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 ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))))))) (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 ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat)))))))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))) (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N2))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N2))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N2))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N2))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))) (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N2)))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_real (@ _let_1 M)) N2)))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_int (@ _let_1 M)) N2)))) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N2)))) (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))) (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))) (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))) (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))) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N2))))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N2))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I4) (@ (@ tptp.nth_VEBT_VEBT Ys) I4)))) (= Xs2 Ys)))) (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I4) (@ (@ tptp.nth_o Ys) I4)))) (= Xs2 Ys)))) (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I4) (@ (@ tptp.nth_nat Ys) I4)))) (= Xs2 Ys)))) (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I4) (@ (@ tptp.nth_int Ys) I4)))) (= Xs2 Ys)))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.vEBT_VEBT)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_VEBT_VEBT Xs) I5)))))))) (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 Bool)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_o Xs) I5)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.nat)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_nat Xs) I5)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.int)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_int Xs) I5)))))))) (= (lambda ((Y4 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y4 Z2)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I5) (@ (@ tptp.nth_VEBT_VEBT Ys3) I5))))))) (= (lambda ((Y4 tptp.list_o) (Z2 tptp.list_o)) (= Y4 Z2)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I5) (@ (@ tptp.nth_o Ys3) I5))))))) (= (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Ys3) I5))))))) (= (lambda ((Y4 tptp.list_int) (Z2 tptp.list_int)) (= Y4 Z2)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I5) (@ (@ tptp.nth_int Ys3) I5))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N2)) (@ tptp.set_real2 Xs2)))) (forall ((N2 tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N2)) (@ tptp.set_complex2 Xs2)))) (forall ((N2 tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N2)) (@ tptp.set_Pr5648618587558075414at_nat Xs2)))) (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N2)) (@ tptp.set_VEBT_VEBT2 Xs2)))) (forall ((N2 tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N2)) (@ tptp.set_o2 Xs2)))) (forall ((N2 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N2)) (@ tptp.set_nat2 Xs2)))) (forall ((N2 tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N2)) (@ tptp.set_int2 Xs2)))) (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X5))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N2))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs2)) (@ P X5))) (@ P (@ (@ tptp.nth_o Xs2) N2))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs2)) (@ P X5))) (@ P (@ (@ tptp.nth_nat Xs2) N2))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs2)) (@ P X5))) (@ P (@ (@ tptp.nth_int Xs2) N2))))) (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I5) X))))) (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I5) X))))) (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s5460976970255530739at_nat Xs2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I5) X))))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I5) X))))) (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I5) X))))) (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I5) X))))) (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I5) X))))) (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I4)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P X)))) (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I4)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P X)))) (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I4)))) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I4)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X)))) (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I4)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X)))) (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I4)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X)))) (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I4)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I5)))))) (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I5)))))) (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I5)))))) (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I5)))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N2) X))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N2) X))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) N2) X))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N2) X))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N2) X))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N2) X))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N2) X))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool) (J tptp.nat)) (let ((_let_1 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) J) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J)))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J)))))))) (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) X)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_o Xs2) I2) X)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_nat Xs2) I2) X)))) (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_int Xs2) I2) X)))) (forall ((X tptp.complex)) (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X) X)) X)) X))) (forall ((X tptp.real)) (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X) X)) X)) X))) (forall ((X tptp.nat)) (= (@ (@ tptp.power_power_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X) X)) X)) X))) (forall ((X tptp.int)) (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X) X)) X)) X))) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))) (forall ((A tptp.nat) (N2 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) N2)) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1))))) (forall ((A tptp.real) (N2 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) N2)) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1))))) (forall ((A tptp.int) (N2 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) N2)) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1))))) (forall ((A tptp.complex) (N2 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) N2)) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (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)))) (forall ((M tptp.nat) (N2 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 N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_161 (= _let_6 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_163) _let_14)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_9 _let_163)))))) (=> _let_162 (= _let_6 tptp.xa))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))) (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) _let_1) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))) (@ (@ tptp.vEBT_vebt_member tptp.summary) _let_160) (@ (@ tptp.vEBT_vebt_member _let_157) tptp.lx) (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.xa) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat _let_6) _let_17))) tptp.deg) _let_11) tptp.summary)) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N2)) (= M N2))) (forall ((R tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R)) (@ (@ tptp.divide_divide_real A) R)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))) (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit0 N2)))) (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)) (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N2) N2)) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N2) (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))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))) (@ (@ tptp.vEBT_invar_vebt _let_159) tptp.deg) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Newlist 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.product_Pair_nat_nat Mi))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_4 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_2) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) (@ (@ tptp.power_power_nat _let_1) _let_2))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_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.power_power_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xn) _let_2))) (let ((_let_6 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_5 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_6))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_2) L2) (=> (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_159) _let_6) (= (@ tptp.some_nat tptp.summin) _let_158) (= (@ tptp.some_nat tptp.lx) (@ tptp.vEBT_vebt_mint _let_157)) (forall ((S tptp.set_real)) (=> (exists ((X3 tptp.real)) (@ (@ tptp.member_real X3) S)) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real X5) Z3)))) (exists ((Y5 tptp.real)) (and (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S) (@ (@ tptp.ord_less_eq_real X3) Y5))) (forall ((Z3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real X5) Z3))) (@ (@ tptp.ord_less_eq_real Y5) Z3)))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X) N4))))) (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y3) (= X2 Y3)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))) (forall ((I2 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J)) U)) K))) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N2) (=> (= N2 (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))))))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))) (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))) (forall ((X tptp.nat)) (=> (forall ((N4 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N4) N4)))) (not (forall ((N4 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N4) (@ tptp.suc N4)))))))) (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N2))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N2))) TreeList3) S2))))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))) (not (forall ((Summin tptp.nat)) (not (= (@ tptp.some_nat Summin) (@ tptp.vEBT_vebt_mint tptp.summary))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))) (= (@ tptp.suc tptp.na) tptp.m) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))) (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22))) (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)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat X) Maxi))))) (not (forall ((Lx tptp.nat)) (not (= (@ tptp.some_nat Lx) (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ 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))) N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N2) M))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N2)))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.one_one_Code_integer) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N2))))) (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))) (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))) (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))))) (= (@ tptp.suc tptp.one_one_nat) _let_2) (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))) (forall ((P (-> tptp.extended_enat Bool)) (N2 tptp.extended_enat)) (=> (forall ((N4 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N4) (@ P M2))) (@ P N4))) (@ P N2))) (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N2)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N2) Q2)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q2))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N2)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N2) Q2)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q2))))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (or (@ P N2) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N2) (@ P I5)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (and (@ P N2) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N2) (@ P I5)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M) (exists ((M3 tptp.nat)) (and (= M (@ tptp.suc M3)) (@ (@ tptp.ord_less_nat N2) M3))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I2) J))))) (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (=> (= J (@ tptp.suc I4)) (@ P I4))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J) (=> (@ P (@ tptp.suc I4)) (@ P I4)))) (@ P I2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N2 M))))) (forall ((M tptp.nat) (N2 tptp.nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (forall ((X5 tptp.nat)) (@ (@ R2 X5) X5)) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ R2 X5))) (=> (@ _let_1 Y5) (=> (@ (@ R2 Y5) Z4) (@ _let_1 Z4))))) (=> (forall ((N4 tptp.nat)) (@ (@ R2 N4) (@ tptp.suc N4))) (@ (@ R2 M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P M) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N4) (=> (@ P N4) (@ P (@ tptp.suc N4))))) (@ P N2))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N4) (@ P M2))) (@ P N4))) (@ P N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M _let_1)))))) (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2)))) (forall ((F (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_num (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.extended_enat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_real (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_num (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.set_real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_real (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.set_real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_real (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N5))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))) (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P I2) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N4) (=> (@ (@ tptp.ord_less_nat N4) J) (=> (@ P N4) (@ P (@ tptp.suc N4)))))) (@ P J))))) (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P J) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N4) (=> (@ (@ tptp.ord_less_nat N4) J) (=> (@ P (@ tptp.suc N4)) (@ P N4))))) (@ P I2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)) (= N2 M)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (= tptp.ord_less_nat (lambda ((N tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) __flatten_var_0))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (forall ((Q3 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))) (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))) (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))) (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M) N2)))) (= tptp.suc _let_135) (= _let_135 tptp.suc) (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ _let_1 N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ _let_1 N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ _let_1 N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ _let_1 N2))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) A)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) A)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) A)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) A)))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N2))) (forall ((A tptp.real) (N2 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 N2)))))) (forall ((A tptp.nat) (N2 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 N2)))))) (forall ((A tptp.int) (N2 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 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))) (forall ((S3 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S3) T) (not (= S3 T)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N4) (@ P M2))) (@ P N4))) (@ P N2))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (not (@ P N4)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N4) (not (@ P M2)))))) (@ P N2))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y2 tptp.nat)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_nat Y2) X5)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) M))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)) (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))) (forall ((X tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y))) (not (= X Y)))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))) (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))) (forall ((N2 tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N2) Q2))))) (forall ((V tptp.num) (N2 tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N2))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))) (forall ((A tptp.complex) (N2 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) N2))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1)))))) (forall ((A tptp.real) (N2 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) N2))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1)))))) (forall ((A tptp.nat) (N2 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) N2))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1)))))) (forall ((A tptp.int) (N2 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) N2))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1)))))) (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (not (= M6 N))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N) (= M6 N)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J2) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) K) (@ (@ tptp.ord_less_nat I2) K))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2))))) (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))) (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))) (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N4 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N4))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M6) K3))))) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))) (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) L2))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))) (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N4) (@ (@ tptp.ord_less_nat (@ F M5)) (@ F N4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))) (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Ma))))) (forall ((Deg tptp.nat) (X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Mi))))) (= tptp.ord_less_nat (lambda ((Y3 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)))) (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X2)) (@ tptp.some_nat Y3)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z5 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z5) (@ (@ tptp.ord_less_nat X) Z5)) (@ (@ tptp.ord_less_eq_nat Y) Z5)))))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z5 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z5) (@ (@ tptp.ord_less_nat Z5) X)) (@ (@ tptp.ord_less_eq_nat Z5) Y)))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Px)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Sx)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))) (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N2) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M5) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))) (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))) (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))) (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))) (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList2) Summary)))) (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))) (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))) (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y3 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y3))))) (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y3 tptp.nat)) (= X (@ tptp.some_nat Y3))))) (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y3 tptp.num)) (= X (@ tptp.some_num Y3))))) (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y3 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y3)))) (= X tptp.none_P5556105721700978146at_nat))) (forall ((X tptp.option_nat)) (= (forall ((Y3 tptp.nat)) (not (= X (@ tptp.some_nat Y3)))) (= X tptp.none_nat))) (forall ((X tptp.option_num)) (= (forall ((Y3 tptp.num)) (not (= X (@ tptp.some_num Y3)))) (= X tptp.none_num))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (and (@ (@ tptp.ord_le6747313008572928689nteger X) Z) (@ (@ tptp.ord_le6747313008572928689nteger Y) Z)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y)) Z) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Y) Z)))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y)) Z) (and (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (and (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z) (and (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))) (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))) (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))) (forall ((X22 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X22 Y22))) (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y22)) (= X22 Y22))) (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y22)) (= X22 Y22))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_max_nat A) B))) (= (@ (@ tptp.ord_max_nat _let_1) B) _let_1))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) B) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.ord_max_int A) B))) (= (@ (@ tptp.ord_max_int _let_1) B) _let_1))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.ord_max_Code_integer A) B))) (= (@ (@ tptp.ord_max_Code_integer _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) A) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.ord_max_int A) A) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A) A) A)) (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)))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_eq_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X) tptp.none_nat))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N2)) K))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))) (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)))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (and (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ (@ tptp.ord_le3102999989581377725nteger C) A)))) (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)))) (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)))) (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)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))) (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ _let_1 (@ _let_1 I2)) I2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K)))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I2))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) D)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex C) D)))) (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)))) (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)))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I2 tptp.nat)) (=> (@ P K) (=> (forall ((N4 tptp.nat)) (=> (@ P (@ tptp.suc N4)) (@ P N4))) (@ P (@ (@ tptp.minus_minus_nat K) I2))))) (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)))) (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)))) (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)))) (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N2) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M))))))) (forall ((J tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N2)) K))) (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M))))) (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))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)) (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N2) L2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M N2)))))) (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv tptp.option4927543243414619207at_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uu) tptp.none_P5556105721700978146at_nat) Uv) tptp.none_P5556105721700978146at_nat)) (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu) tptp.none_num) Uv) tptp.none_num)) (forall ((Uu (-> tptp.nat tptp.nat tptp.nat)) (Uv tptp.option_nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2))))) (forall ((X tptp.complex) (Y tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y) B))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) A)) B))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N2) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M) N2)))))) (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))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M) N2)) M))) (forall ((J tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I2) K)))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.minus_minus_nat J) I2) K) (= J (@ (@ tptp.plus_plus_nat K) I2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M)) M) (@ (@ tptp.ord_max_nat N2) M))) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)) (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw) (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)) (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)) (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw) (@ tptp.some_nat V)) tptp.none_nat) tptp.none_nat)) (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb) Y) (=> (=> (= 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 ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B3 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B3)) (not (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B3)))))))))))))) (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B3 tptp.num)) (=> (= Xb (@ tptp.some_num B3)) (not (= Y (@ tptp.some_num (@ (@ X A3) B3)))))))))))))) (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B3 tptp.nat)) (=> (= Xb (@ tptp.some_nat B3)) (not (= Y (@ tptp.some_nat (@ (@ X A3) B3)))))))))))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I2) K))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat B))) (let ((_let_2 (@ tptp.ord_max_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat B))) (let ((_let_2 (@ tptp.ord_ma741700101516333627d_enat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int B))) (let ((_let_2 (@ tptp.ord_max_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer B))) (let ((_let_2 (@ tptp.ord_max_Code_integer A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_max_nat B4) A4))) (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ tptp.ord_ma741700101516333627d_enat B4) A4))) (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_max_int B4) A4))) (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.ord_max_Code_integer B4) A4))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A))) (= (@ (@ tptp.ord_max_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_nat B) C))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat A))) (= (@ (@ tptp.ord_ma741700101516333627d_enat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (= (@ (@ tptp.ord_max_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_int B) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer A))) (= (@ (@ tptp.ord_max_Code_integer (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_Code_integer B) C))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X)) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X)) _let_1)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X)) _let_1)))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))) (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))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))) (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))))) (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))))) (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))))) (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))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))) (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))))) (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))))) (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))))) (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4) B4))) (= tptp.ord_le3102999989581377725nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A4) B4) B4))) (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) B4))) (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) B4))) (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) B4))) (= tptp.ord_le2932123472753598470d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4) A4))) (= tptp.ord_le3102999989581377725nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A4) B4) A4))) (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) A4))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) A4))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) A4))) (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.ord_max_Code_integer A) B))) (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))) (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))) (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.ord_max_Code_integer A) B))) (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))) (= tptp.ord_le2932123472753598470d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4)))) (= tptp.ord_le3102999989581377725nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (= A4 (@ (@ tptp.ord_max_Code_integer A4) B4)))) (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= A4 (@ (@ tptp.ord_max_num A4) B4)))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.ord_max_nat A4) B4)))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.ord_max_int A4) B4)))) (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)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A)))) (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)))) (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)))) (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)))) (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)))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (not (@ (@ tptp.ord_le3102999989581377725nteger C) A)))))) (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)))))) (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)))))) (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)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A (@ (@ tptp.ord_max_Code_integer A) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))) (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= A (@ (@ tptp.ord_max_Code_integer A) B)))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))) (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))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger D) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer C) D)) (@ (@ tptp.ord_max_Code_integer A) B))))) (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))))) (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))))) (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))))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (not (@ (@ tptp.ord_le6747313008572928689nteger C) A)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (= tptp.ord_le6747313008572928689nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (and (= A4 (@ (@ tptp.ord_max_Code_integer A4) B4)) (not (= A4 B4))))) (= tptp.ord_le72135733267957522d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (and (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4)) (not (= A4 B4))))) (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B4)) (not (= A4 B4))))) (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B4)) (not (= A4 B4))))) (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.ord_max_nat A4) B4)) (not (= A4 B4))))) (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.ord_max_int A4) B4)) (not (= A4 B4))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X) Y)))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P X) Y)))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B3 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X) Y)))) _let_1))))) (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X) Y)))) _let_1))))) (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P X) Y)))) _let_1))))) (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X) Y)))) _let_1))))) (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X) Y)))) _let_1))))) (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_nat B3)) (@ (@ P X) Y)))) _let_1))))) (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X) Y)))) _let_1))))) (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X7 tptp.option4927543243414619207at_nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P3 tptp.none_P5556105721700978146at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))) (= (lambda ((P2 (-> tptp.option_nat Bool))) (forall ((X7 tptp.option_nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.option_nat Bool))) (and (@ P3 tptp.none_nat) (forall ((X2 tptp.nat)) (@ P3 (@ tptp.some_nat X2)))))) (= (lambda ((P2 (-> tptp.option_num Bool))) (forall ((X7 tptp.option_num)) (@ P2 X7))) (lambda ((P3 (-> tptp.option_num Bool))) (and (@ P3 tptp.none_num) (forall ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))) (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X7 tptp.option4927543243414619207at_nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P3 tptp.none_P5556105721700978146at_nat) (exists ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))) (= (lambda ((P2 (-> tptp.option_nat Bool))) (exists ((X7 tptp.option_nat)) (@ P2 X7))) (lambda ((P3 (-> tptp.option_nat Bool))) (or (@ P3 tptp.none_nat) (exists ((X2 tptp.nat)) (@ P3 (@ tptp.some_nat X2)))))) (= (lambda ((P2 (-> tptp.option_num Bool))) (exists ((X7 tptp.option_num)) (@ P2 X7))) (lambda ((P3 (-> tptp.option_num Bool))) (or (@ P3 tptp.none_num) (exists ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))) (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X23))))))) (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (@ tptp.some_nat X23))))))) (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))) (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))) (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))) (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))) (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))) (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))) (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))) (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)) (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)) (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)) (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)))))) (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)))))) (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)))))) (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))) (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))) (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))) (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))) (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))) (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))) (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))) (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))) (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))) (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)) (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)) (forall ((M tptp.nat) (N2 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 N2))))) (forall ((M tptp.nat) (N2 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 N2)))))) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) B) A)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex C))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_complex A) B)))) (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)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) A) B)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))) (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (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)))) (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)))) (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)))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.one_on7984719198319812577d_enat) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex A) B))) (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))) (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))) (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))) (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))) (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (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)))))) (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)))))) (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)))))) (= tptp.times_times_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.times_times_complex B4) A4))) (= tptp.times_times_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real B4) A4))) (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.times_times_nat B4) A4))) (= tptp.times_times_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int B4) A4))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (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))))) (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))))) (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))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (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))))) (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))))) (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))))) (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (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)))) (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)))) (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)))) (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex B))) (let ((_let_2 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (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)))))) (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)))))) (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)))))) (= tptp.plus_plus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex B4) A4))) (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real B4) A4))) (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A4))) (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A4))) (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))) (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))))) (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))))) (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))))) (forall ((B2 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (let ((_let_2 (@ tptp.plus_plus_complex K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))) (forall ((B2 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))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))) (forall ((B2 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))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))) (forall ((B2 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))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_complex A2) B) (@ _let_1 (@ (@ tptp.plus_plus_complex A) B)))))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))) (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_real I2) K) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J) L2)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))) (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))))) (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))))) (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))))) (forall ((X tptp.extended_enat)) (= (= tptp.one_on7984719198319812577d_enat X) (= X tptp.one_on7984719198319812577d_enat))) (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))) (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))) (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))) (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))) (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))) (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))) (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))) (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)))) (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)))) (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)))) (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (exists ((C2 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A4) C2))))) (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)))) (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)))) (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)))) (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))))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))) (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))) (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))) (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))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat C) D) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) (@ (@ tptp.plus_p3455044024723400733d_enat B) D))))) (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))))) (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))))) (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))))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))) (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))))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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)))) (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)))) (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))))) (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))))) (forall ((A tptp.complex) (E tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) E)) C))) (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))) (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))) (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))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))) (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)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))) (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))))) (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))))) (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))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))) (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)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))) (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))))) (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))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))) (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)))) (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)))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.one_on7984719198319812577d_enat) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))) (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))))) (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))))) (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))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B) A)) (@ (@ tptp.times_times_complex C) A)))) (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)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))) (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))))) (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))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))) (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))))) (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))))) (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))))) (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex C) B) A) (= C (@ (@ tptp.minus_minus_complex A) B)))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 C)) B)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))) (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))) (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))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))) (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))) (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))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C)))) (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)))) (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)))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.minus_minus_complex C) B)) (= (@ (@ tptp.plus_plus_complex A) B) C))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.minus_minus_complex A) B) C) (= A (@ (@ tptp.plus_plus_complex C) B)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))) (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_complex A2) B) (@ _let_1 (@ (@ tptp.minus_minus_complex A) B)))))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger X))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer Y) Z)) (@ (@ tptp.ord_max_Code_integer (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z)) (@ (@ tptp.plus_plus_real Y) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Z)) (@ (@ tptp.plus_p5714425477246183910nteger Y) Z)))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Z)) (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z)) (@ (@ tptp.minus_minus_real Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))) (forall ((M tptp.real) (N2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_real M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))) (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M) N2)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat B) tptp.one_on7984719198319812577d_enat)))) (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)))) (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)))) (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)))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))) (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))))))) (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))) (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)))) (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)))) (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)))) (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)))))) (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))))) (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)))) (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)))) (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N2) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))) (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))) (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N2) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))) (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))) (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N2) K)))) (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N2) K)))) (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N2) K)))) (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))) (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))) (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)))) (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)))) (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))) (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))) (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))) (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))) (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))) (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)))) (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)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) (@ (@ tptp.times_times_complex Y) Y)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))) (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) A)) E)) D)))) (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)))) (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)))) (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) E)) C) D))) (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))) (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))) (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)))) (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)))) (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))) (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))) (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)))) (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)))) (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))) (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))) (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))) (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))) (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))) (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)))) (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)))) (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)))) (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)))) (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))) (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))) (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))))) (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))))) (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))) (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))) (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)) (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)) (forall ((L2 tptp.num) (R tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L2) (@ (@ tptp.product_Pair_nat_nat Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R))))))))) (forall ((L2 tptp.num) (R tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L2) (@ (@ tptp.product_Pair_int_int Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_int L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R))))))))) (forall ((L2 tptp.num) (R tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L2) (@ (@ tptp.produc1086072967326762835nteger Q2) R)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R))))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _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) X) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ 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.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))) (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)))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= X Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 Ma))) Deg) TreeList2) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_3) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT) (Summary tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high X) _let_4))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_6 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_4) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_3) _let_4)) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) _let_1))) (let ((_let_3 (@ tptp.nth_VEBT_VEBT _let_2))) (let ((_let_4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_5 (@ (@ tptp.divide_divide_nat Deg) _let_4))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_4) _let_5))) (let ((_let_7 (@ tptp.if_nat (= X Ma)))) (let ((_let_8 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_5))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_4) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_5) L2) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_1)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 _let_11)))))) Ma)))) Deg) _let_2) _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 H2))))) Ma)))) Deg) _let_2) Summary)))))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (= X Mi))) (let ((_let_9 (@ tptp.if_nat _let_8))) (let ((_let_10 (@ (@ _let_9 _let_7) X))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_high _let_10) _let_3))) (let ((_let_12 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_11)) (@ (@ tptp.vEBT_VEBT_low _let_10) _let_3)))) (let ((_let_13 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_11) _let_12))) (let ((_let_14 (@ tptp.nth_VEBT_VEBT _let_13))) (let ((_let_15 (@ tptp.if_nat (and (=> _let_8 (= _let_7 Ma)) (=> (not _let_8) (= X Ma)))))) (let ((_let_16 (@ (@ _let_9 _let_10) Mi))) (let ((_let_17 (@ tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (@ (@ tptp.vEBT_vebt_delete Summary) _let_11))) (let ((_let_19 (@ tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (@ tptp.the_nat _let_19))) (=> (and (@ (@ tptp.ord_less_eq_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_11) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_12)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ (@ tptp.if_nat (= _let_19 tptp.none_nat)) _let_16) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_20)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_20)))))) Ma)))) Deg) _let_13) _let_18)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_11) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_11))))) Ma)))) Deg) _let_13) Summary))) _let_1)))))))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H2)) L2))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT _let_3))) (let ((_let_5 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_6 (@ (@ tptp.divide_divide_nat Deg) _let_5))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_5) _let_6))) (let ((_let_8 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_9 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_10 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ tptp.the_nat _let_11))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_6))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_5) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_1 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_6) L2) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ (@ tptp.if_nat (= _let_11 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_12)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 _let_12)))))) Ma)))) Deg) _let_3) _let_10)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 H2))))) Ma)))) Deg) _let_3) Summary))))))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_3))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_12 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_3) L2) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_high Xn) _let_4))) (let ((_let_8 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_7 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_5)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_8))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_4) L2) (=> (@ (@ tptp.ord_less_nat _let_7) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn)))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_8)) (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3)))) (let ((_let_10 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_8) _let_9))) (let ((_let_11 (@ tptp.nth_VEBT_VEBT _let_10))) (let ((_let_12 (@ tptp.if_nat (= _let_7 Ma)))) (let ((_let_13 (@ tptp.product_Pair_nat_nat _let_7))) (let ((_let_14 (@ (@ tptp.vEBT_vebt_delete Summary) _let_8))) (let ((_let_15 (@ tptp.vEBT_vebt_maxt _let_14))) (let ((_let_16 (@ tptp.the_nat _let_15))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ (@ tptp.if_nat (= _let_15 tptp.none_nat)) _let_7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_16)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_16)))))) Ma)))) Deg) _let_10) _let_14)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_8))))) Ma)))) Deg) _let_10) Summary))) _let_1)))))))))))))))))))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _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) X) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_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)))))))))))))) (forall ((C tptp.complex)) (= (lambda ((X2 tptp.complex)) (@ (@ tptp.times_times_complex X2) C)) (@ tptp.times_times_complex C))) (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))) (forall ((C tptp.nat)) (= (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C)) (@ tptp.times_times_nat C))) (forall ((C tptp.int)) (= (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int X2) C)) (@ tptp.times_times_int C))) (= (lambda ((X2 tptp.extended_enat)) X2) (@ tptp.times_7803423173614009249d_enat tptp.one_on7984719198319812577d_enat)) (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)) (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)) (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)) (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)) (forall ((X tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A3 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) (@ tptp.some_P7363390416028606310at_nat B3)))))))))) (forall ((X tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) (@ tptp.some_nat B3)))))))))) (forall ((X tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A3 tptp.num) (B3 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) (@ tptp.some_num B3)))))))))) (forall ((X tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X5 tptp.product_prod_nat_nat) (Y5 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X5)) (@ tptp.some_P7363390416028606310at_nat Y5)))))))))) (forall ((X tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X5 tptp.nat) (Y5 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X5)) (@ tptp.some_nat Y5)))))))))) (forall ((X tptp.produc7036089656553540234on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num Bool)) (X5 tptp.num) (Y5 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X5)) (@ tptp.some_num Y5)))))))))) (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))) (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))))) (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))))) (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))))) (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))))) (forall ((X3 tptp.real)) (exists ((Y5 tptp.real)) (@ (@ tptp.ord_less_real Y5) X3))) (forall ((X3 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X3) X_1))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) W)))) (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex Y) W)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W)) (@ (@ tptp.times_times_real Y) Z)))) (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W)) (@ (@ tptp.times_times_complex Y) Z)))) (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))))) (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))))) (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)))) (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)))) (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)))) (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)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))) (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat X) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))) (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.member_nat Y3) Xs) (@ (@ tptp.ord_less_nat Y3) X2) (forall ((Z5 tptp.nat)) (=> (@ (@ tptp.member_nat Z5) Xs) (=> (@ (@ tptp.ord_less_nat Z5) X2) (@ (@ tptp.ord_less_eq_nat Z5) Y3))))))) (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.member_nat Y3) Xs) (@ (@ tptp.ord_less_nat X2) Y3) (forall ((Z5 tptp.nat)) (=> (@ (@ tptp.member_nat Z5) Xs) (=> (@ (@ tptp.ord_less_nat X2) Z5) (@ (@ tptp.ord_less_eq_nat Y3) Z5))))))) (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) __flatten_var_0))) (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))) (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))) (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)))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (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.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= X Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= X Ma))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (@ (@ tptp.vEBT_vebt_delete _let_2) X))) (let ((_let_24 (and _let_9 _let_16))) (let ((_let_25 (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)))) (and (=> _let_25 (= _let_23 _let_2)) (=> (not _let_25) (and (=> _let_24 (= _let_23 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary))) (=> (not _let_24) (= _let_23 (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma)))) _let_1) _let_14) Summary))) _let_2)))))))))))))))))))))))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y3 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat X) Y3)))) tptp.bot_bot_set_nat)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y3 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat Y3) X)))) tptp.bot_bot_set_nat)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))) (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S3)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))) (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 Bool)) (=> (exists ((Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (exists ((Va2 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va2)))) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc 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 TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))) (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))) (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))) (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A4 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B4))))) (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))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= N2 tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3)))))) (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))) (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))) (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y222 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2)) (= N2 tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.zero_z5237406670263579293d_enat) (or (= A tptp.zero_z5237406670263579293d_enat) (= B tptp.zero_z5237406670263579293d_enat)))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.zero_z5237406670263579293d_enat) A) tptp.zero_z5237406670263579293d_enat)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.zero_z5237406670263579293d_enat) A) A)) (forall ((A 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tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))) (forall ((A tptp.complex) (B 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tptp.divide6298287555418463151nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (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)))) (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)))) (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))))) (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))))) (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)))) (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)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)) (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M 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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)))) (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))) (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))) (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))) (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))) (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))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ 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tptp.zero_zero_real))) (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))) (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))) (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)))) (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)))) (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))) (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))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ 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(@ tptp.ord_less_eq_int B) A))) (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))) (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))) (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ 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tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) A) B))) (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)))))))) (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)))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))) (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)))) (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)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger A) B)))) (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))))) (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))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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)))))))) (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)))))))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)) (= (@ _let_112 tptp.one_one_complex) tptp.zero_zero_complex) (= (@ _let_114 tptp.one_one_real) tptp.zero_zero_real) (= (@ _let_113 tptp.one_one_int) tptp.zero_zero_int) (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger A) A) tptp.one_one_Code_integer))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (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)))) (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)))) (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)))))) (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)))))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (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)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (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)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.suc N2)) tptp.zero_z5237406670263579293d_enat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)) (forall ((K tptp.num)) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numeral_numeral_nat K)) tptp.zero_z5237406670263579293d_enat)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)) (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.zero_z3403309356797280102nteger) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (= M _let_1) (= N2 _let_1))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (@ _let_1 M) (@ _let_1 N2))))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))) (forall ((X tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M) _let_1) (or (= M tptp.zero_zero_nat) (= X _let_1))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (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) N2)))))))) (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))) (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)))) (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))))))) (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))))))) (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))))))) (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))))))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))) (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))))) (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))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (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))))) (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))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (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))))) (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))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (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))))) (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))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M)) N2) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N2)) N2) M))) (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)))) (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)))) (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)))) (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)))) (forall ((B tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))) (forall ((B tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))) (forall ((B tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))) (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))) (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))) (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))) (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))) (forall ((A tptp.real) (B tptp.real) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (@ (@ tptp.ord_less_eq_real A) B))))))) (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.ord_less_eq_nat A) B))))))) (forall ((A tptp.int) (B tptp.int) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.ord_less_eq_int A) B))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))) _let_156 _let_155 _let_154 _let_156 _let_155 _let_154 (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))) (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))) (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))) (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)))) (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)))) (forall ((B tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))) (forall ((B tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))) (forall ((B tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))) (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))) (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B))) (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)) (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux))) (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))) (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))) (@ tptp.vEBT_VEBT_minNull _let_131) (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))) (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X5)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2)) X5)))))))) (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 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Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))) (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X223))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) Deg3))))))) (forall ((X tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))) (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)) (forall ((X tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) X)) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (@ _let_150 tptp.zero_z5237406670263579293d_enat) (@ _let_81 tptp.zero_zero_real) (@ _let_147 tptp.zero_zero_nat) (@ _let_98 tptp.zero_zero_int) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))) (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.extended_enat)) (=> (not (= N2 tptp.zero_z5237406670263579293d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (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 (@ (@ 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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))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (not (= A tptp.zero_z5237406670263579293d_enat)) (=> (not (= B tptp.zero_z5237406670263579293d_enat)) (not (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.zero_z5237406670263579293d_enat))))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= (@ (@ tptp.times_7803423173614009249d_enat A) B) tptp.zero_z5237406670263579293d_enat) (or (= A tptp.zero_z5237406670263579293d_enat) (= B tptp.zero_z5237406670263579293d_enat)))) (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)))) (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)))) (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)))) (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B 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N4)))) (@ P N2)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (@ (@ P X5) tptp.zero_zero_nat)) (=> (forall ((Y5 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y5))) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ P X5) Y5) (@ (@ P (@ tptp.suc X5)) (@ tptp.suc Y5)))) (@ (@ P M) N2))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N4 tptp.nat)) (=> (@ P (@ tptp.suc N4)) (@ P N4))) (@ P tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (not (@ P N4)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N4) (not (@ P M2))))))) (@ P N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (= M N2))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((A Bool) (B Bool) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) (@ tptp.suc (@ tptp.suc N2))) _let_1))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))) (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (= A B))))))) (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (= A B))))))) (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (= A B))))))) (= (lambda ((H tptp.extended_enat)) tptp.zero_z5237406670263579293d_enat) (@ tptp.times_7803423173614009249d_enat tptp.zero_z5237406670263579293d_enat)) (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)) (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)) (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)) (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X) (or (= X Mi) (= X Ma)))) (forall ((A tptp.real) (B tptp.real) (N2 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) N2) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))) (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))) (forall ((A tptp.int) (B tptp.int) (N2 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) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc N4)))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5)))))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5)))))))))) (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))) (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))))))) (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))))))) (forall ((A Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))) (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))) (forall ((B Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))))) (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)))))) (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)))))) (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)))) (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)))) (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)))) (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)))))) (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)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B) C))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A)) (@ _let_1 B)))))) (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)))))) (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)))))) (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)))))) (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))))) (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))))) (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)))))) (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)))))) (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))))) (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))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B) D)))))))) (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)))))))) (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)))))))) (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)))))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) (@ (@ tptp.times_7803423173614009249d_enat B) D)))))))) (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)))))))) (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)))))))) (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)))))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) tptp.zero_z5237406670263579293d_enat) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat X) Y) tptp.zero_z5237406670263579293d_enat) (and (= X tptp.zero_z5237406670263579293d_enat) (= Y tptp.zero_z5237406670263579293d_enat))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) tptp.zero_z5237406670263579293d_enat)))) (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)))) (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)))) (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)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B)))))) (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)))))) (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)))))) (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)))))) (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat B))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))) (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)))))) (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)))))) (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)))))) (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) B)))) (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)))) (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)))) (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)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat B))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))) (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)))))) (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)))))) (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)))))) (forall ((A tptp.extended_enat) (C tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) C)) B)))) (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)))) (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)))) (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)))) (not (@ _let_153 tptp.zero_z5237406670263579293d_enat)) (not (@ _let_105 tptp.zero_zero_real)) (not (@ _let_152 tptp.zero_zero_nat)) (not (@ _let_104 tptp.zero_zero_int)) _let_151 _let_149 _let_148 _let_146 _let_151 _let_149 _let_148 _let_146 (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)))))) (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)))))) (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)))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))) (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)))) (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)))) (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)))))) (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)))))) (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)))))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))))) (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)))))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))) (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))))) (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))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat B))) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) C)))))) (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)))))) (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)))))) (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)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (not (forall ((C3 tptp.extended_enat)) (=> (= B (@ (@ tptp.plus_p3455044024723400733d_enat A) C3)) (= C3 tptp.zero_z5237406670263579293d_enat)))))) (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)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B)))))) (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)))))) (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)))))) (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)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) tptp.zero_z5237406670263579293d_enat)))) (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)))) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))) (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))) (not (@ _let_145 tptp.zero_z5237406670263579293d_enat)) (not (@ _let_103 tptp.zero_zero_real)) (not (@ _let_144 tptp.zero_zero_nat)) (not (@ _let_102 tptp.zero_zero_int)) _let_143 _let_142 _let_141 _let_140 _let_143 _let_142 _let_141 _let_140 (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A4) B4)) tptp.zero_zero_real))) (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A4) B4)) tptp.zero_zero_int))) (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))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (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)))))) (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))))) (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)))))) (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A4) B4)) tptp.zero_zero_real))) (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A4) B4)) tptp.zero_zero_int))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))) (forall ((A tptp.real) (B tptp.real) (N2 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) N2)) (@ (@ tptp.power_power_real B) N2))))) (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2)) (@ (@ tptp.power_power_nat B) N2))))) (forall ((A tptp.int) (B tptp.int) (N2 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) N2)) (@ (@ tptp.power_power_int B) N2))))) (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))))) (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))))) (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)))))) (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))))) (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)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))) (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)))) (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)))) (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))))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X) Z) (@ (@ tptp.times_times_real W) Y)))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X) Z) (@ (@ tptp.times_times_complex W) Y)))))) (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)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.power_8040749407984259932d_enat A) tptp.zero_zero_nat) tptp.one_on7984719198319812577d_enat)) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (or (@ P tptp.zero_zero_nat) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N2) (@ P (@ tptp.suc I5))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M6 tptp.nat)) (= N2 (@ tptp.suc M6))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (and (@ P tptp.zero_zero_nat) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N2) (@ P (@ tptp.suc I5))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J))))) (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) _let_45) (= (@ tptp.size_size_option_nat tptp.none_nat) _let_45) (= (@ tptp.size_size_option_num tptp.none_num) _let_45) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) M))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat)))) (= tptp.one_one_nat _let_45) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2)) X5)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2)) X5)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S2)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (Uw2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B3 Bool) (Va2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) (@ tptp.suc (@ tptp.suc Va2)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ 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 (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve)) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5)))))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B3 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B3)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N4))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X (@ (@ 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 (= X (@ (@ 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 (= X (@ (@ 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) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X5))))))))))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S3))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))) (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))))))) (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))) (forall ((Uv Bool) (Uw Bool) (N2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N2)) tptp.none_nat)) (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))))))) (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))))))) (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))))))) (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))))))) (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))))))) (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))))))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))))))) (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)))))))) (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)))))))) (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)))) (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)))) (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)))) (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)))))) (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)))))) (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))))))) (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))))))) (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))))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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))))) (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))))) (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))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) B) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B)))))) (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)))))) (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)))))) (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)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) tptp.zero_z5237406670263579293d_enat)))) (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)))) (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)))) (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)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat A) B)))))) (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)))))) (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)))))) (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)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) tptp.zero_z5237406670263579293d_enat)))) (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)))) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger A) B)))))) (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)))))) (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)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger)))) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))) (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))))) (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))) (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))) (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))) (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.one_on7984719198319812577d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) B)) tptp.one_on7984719198319812577d_enat))))) (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))))) (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))))) (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))))) (forall ((C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) tptp.one_on7984719198319812577d_enat) (=> (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.times_7803423173614009249d_enat A) C)) A)))) (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)))) (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)))) (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)))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))) (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))) (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))) (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))))) (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))))) (@ _let_139 _let_138) (@ _let_82 _let_137) (@ _let_132 _let_136) (@ _let_94 _let_134) (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))))))) (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)))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z)))) (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)))) (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))))) (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))))) (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)))) (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))))))))))) (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))))))))))) (forall ((A tptp.real) (N2 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) N2)) tptp.one_one_real)))) (forall ((A tptp.nat) (N2 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) N2)) tptp.one_one_nat)))) (forall ((A tptp.int) (N2 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) N2)) tptp.one_one_int)))) (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))))))) (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))))))) (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))))))) (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))))))) (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)))))) (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))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))) (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))))))) (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))))))) (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))))))) (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))))))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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))))) (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)))) (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)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))) (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)))) (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)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))) (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))))))) (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))))))) (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))) (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TrLst2) Smry2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))) (= _let_133 _let_45) (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)))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M) N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))) (forall ((N2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I2))) N2))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N2) K)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ P N4) (@ P (@ tptp.suc N4))))) (@ P N2))))) (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))) (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))) (forall ((X tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs2)))) (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))) (forall ((X Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))) (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))) (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))) (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N2))))) (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)))))))) (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)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 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) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.divide_divide_nat M) N2))))) (forall ((Q2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N2) Q2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))) (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B3 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A3) B3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Mi2)))))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z4) (=> (@ (@ tptp.ord_less_real Z4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z4) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))) (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))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X) Y))))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z)))) (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)))) (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))))) (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))))) (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)))) (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))))))) (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))))))))))) (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)))))))))) (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))))) (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)))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))) (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)))))))))))) (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)))))))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ 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))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ 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))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ 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))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))) (forall ((A tptp.real) (N2 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 N2))) A)))) (forall ((A tptp.nat) (N2 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 N2))) A)))) (forall ((A tptp.int) (N2 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 N2))) A)))) (forall ((A tptp.real) (N2 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 N2))) tptp.one_one_real)))) (forall ((A tptp.nat) (N2 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 N2))) tptp.one_one_nat)))) (forall ((A tptp.int) (N2 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 N2))) tptp.one_one_int)))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N3)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N3)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N3)) (@ _let_1 N2))))))) (= (@ (@ tptp.power_8040749407984259932d_enat tptp.zero_z5237406670263579293d_enat) _let_2) tptp.zero_z5237406670263579293d_enat) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_2) tptp.zero_zero_nat) (= (@ _let_77 _let_2) tptp.zero_zero_real) (= (@ _let_76 _let_2) tptp.zero_zero_int) (= (@ _let_75 _let_2) tptp.zero_zero_complex) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N3)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N3) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N3)) (@ _let_1 N2))))))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_nat A) N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_int A) N2)))))) (= _let_2 _let_46) (@ _let_132 _let_2) (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2))))))) (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= N2 (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((Q2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N2) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2))))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I5)) J3)) (@ P I5))))))))) (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))) (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))) (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)) (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)) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))) (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)))))))))))) (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))))))))))) (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))) (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)))) (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))))))) (forall ((U tptp.real) (V tptp.real) (R tptp.real) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_eq_real R) S3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R) (@ (@ tptp.minus_minus_real V) U))) S3))) V))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))) (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))))) (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))))) (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))) (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))) (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))) (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_int))))) (forall ((A tptp.nat) (N2 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 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))) (forall ((A tptp.int) (N2 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 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ (@ tptp.plus_plus_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N2))))) (= tptp.power_8040749407984259932d_enat (lambda ((P4 tptp.extended_enat) (M6 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M6 tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat P4) (@ (@ tptp.power_8040749407984259932d_enat P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_complex (lambda ((P4 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P4) (@ (@ tptp.power_power_complex P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_real (lambda ((P4 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P4) (@ (@ tptp.power_power_real P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_nat (lambda ((P4 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P4) (@ (@ tptp.power_power_nat P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_int (lambda ((P4 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P4) (@ (@ tptp.power_power_int P4) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))) (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)) (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)) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))) (forall ((A tptp.real) (N2 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))) N2)))) (forall ((A tptp.int) (N2 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))) N2)))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ P N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (= Y (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))) (forall ((A tptp.real) (N2 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))) N2)))) (@ _let_1 A)))) (forall ((A tptp.int) (N2 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))) N2)))) (@ _let_1 A)))) (forall ((A tptp.real) (N2 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))) N2)))) tptp.zero_zero_real))) (forall ((A tptp.int) (N2 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))) N2)))) tptp.zero_zero_int))) (forall ((X tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N2)) (@ _let_1 M)))))))) (forall ((X tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N2)) (@ _let_1 N2)))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))) (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))) (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A4 Bool) (B4 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B4))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N) _let_1)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N 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 N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N) _let_3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))) (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A3 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B3))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 N4) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 (@ tptp.suc N4)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 N4) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 (@ tptp.suc N4)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2)))))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.vEBT_Leaf false) B3)))))) (=> (forall ((A3 Bool)) (=> (exists ((B3 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.vEBT_Leaf A3) false)))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (exists ((N4 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc N4)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (not (= Y _let_1))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa2 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi2))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (not (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))))))))))))))))))))))))))))))))))))))) (forall ((Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))) (= (@ (@ 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(exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N4 tptp.nat)) (= Xa2 (@ tptp.suc N4))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ 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) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc 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 TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ 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))) N2)) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N2)) tptp.bot_bot_set_nat)) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))) (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)))))) (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)))))) (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)) (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)) (forall ((X tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.bot_bo4199563552545308370d_enat) X) X)) (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)) (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)) (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)) (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)) (forall ((X tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) tptp.bot_bo4199563552545308370d_enat) X)) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B3))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.suc N4))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low 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))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))) (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B2) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B2))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B2) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B2) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B2))) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))) (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)) (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)) (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)) (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X))) (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X))) (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real A) A)) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)) (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)) (forall ((X tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real X) X)) (forall ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) X)) (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)) (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_real A2) B2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_nat A2) B2)))) (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_int A2) B2))) (forall ((A2 tptp.set_complex) (B2 tptp.set_complex)) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le211207098394363844omplex A2) B2))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_real A2) B2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_nat A2) B2))) (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))) (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat)) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N2) tptp.zero_z5237406670263579293d_enat) N2)) (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))) (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)))) (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))) (= tptp.bot_bot_nat tptp.zero_zero_nat) (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))))) (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))) (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))) (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((N2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N2)) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X2))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X2))))) (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) _let_131) (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real Y) X) (= (@ (@ tptp.ord_less_eq_set_real X) Y) (= X Y)))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.set_real) (B tptp.set_real) (F (-> tptp.set_real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.set_real) (Y5 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))) (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))) (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))) (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))) (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B tptp.int) (C tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))) (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C tptp.int)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))) (forall ((A tptp.num) (F (-> tptp.set_real tptp.num)) (B tptp.set_real) (C tptp.set_real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (=> (forall ((X5 tptp.set_real) (Y5 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))) (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_real X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))) (forall ((A tptp.set_real) (B tptp.set_real) (F (-> tptp.set_real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.set_real) (Y5 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.int tptp.nat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.set_real) (F (-> tptp.num tptp.set_real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_set_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (= (lambda ((Y4 tptp.set_real) (Z2 tptp.set_real)) (= Y4 Z2)) (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A4) B4) (@ (@ tptp.ord_less_eq_set_real B4) A4)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A4)))) (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (@ (@ tptp.ord_less_eq_num B4) A4)))) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ tptp.ord_less_eq_nat B4) A4)))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ tptp.ord_less_eq_int B4) A4)))) (forall ((A tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ (@ tptp.ord_less_eq_set_real B) A) (= A B)))) (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)))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))) (forall ((B tptp.set_real) (A tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real C))) (=> (@ (@ tptp.ord_less_eq_set_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (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))))) (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))))) (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))))) (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))))) (forall ((B tptp.set_real) (A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real B) A) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (= A B)))) (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)))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))) (= (lambda ((Y4 tptp.set_real) (Z2 tptp.set_real)) (= Y4 Z2)) (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real B4) A4) (@ (@ tptp.ord_less_eq_set_real A4) B4)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A4) (@ (@ tptp.ord_less_eq_set_nat A4) B4)))) (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (@ (@ tptp.ord_less_eq_num A4) B4)))) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (@ (@ tptp.ord_less_eq_nat A4) B4)))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (@ (@ tptp.ord_less_eq_int A4) B4)))) (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))) (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))) (forall ((X tptp.set_real) (Y tptp.set_real) (Z tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_real Y) Z) (@ _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))) (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (@ _let_1 C))))) (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))))) (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))))) (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))))) (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))))) (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (=> (@ (@ tptp.ord_less_eq_set_real Y) X) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ 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(@ (@ tptp.ord_less_eq_set_nat B) C) (@ (@ tptp.ord_less_eq_set_nat A) C)))) (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)))) (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)))) (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)))) (= (lambda ((Y4 tptp.set_real) (Z2 tptp.set_real)) (= Y4 Z2)) (lambda ((X2 tptp.set_real) (Y3 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real X2) Y3) (@ (@ tptp.ord_less_eq_set_real Y3) X2)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (@ (@ tptp.ord_less_eq_set_nat Y3) X2)))) (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((X2 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y3) (@ (@ tptp.ord_less_eq_num Y3) X2)))) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2)))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (@ (@ tptp.ord_less_eq_int Y3) X2)))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (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)))))))))))))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (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)))))))))))))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (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)))))))))))))))))) (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))))) (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))))) (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))))) (forall ((X tptp.real)) (exists ((Y5 tptp.real)) (@ (@ tptp.ord_less_real Y5) X))) (forall ((X tptp.int)) (exists ((Y5 tptp.int)) (@ (@ tptp.ord_less_int Y5) X))) (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))) (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))) (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real X) Z4) (@ (@ tptp.ord_less_real Z4) Y))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (not (@ (@ tptp.ord_le72135733267957522d_enat B) A)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (= A B) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (@ (@ tptp.ord_le72135733267957522d_enat A) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (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))))) (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))))) (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))))) (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))))) (forall ((P (-> tptp.extended_enat Bool)) (A tptp.extended_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (forall ((Y2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y2) X5) (@ P Y2))) (@ P X5))) (@ P A))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y2) X5) (@ P Y2))) (@ P X5))) (@ P A))) (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= X Y)))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat A) B)))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))) (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) A))) 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(=> (forall ((A3 tptp.extended_enat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))) (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.real)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.real) (B3 tptp.real)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))) (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.num)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) 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tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.extended_enat) (F (-> tptp.num tptp.extended_enat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.real) (F (-> tptp.extended_enat tptp.real)) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B)) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))) (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (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 ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (P Bool)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) X) P))) (forall ((X tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P))) (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))) (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))) (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (= X Y) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))) (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))) (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (= Y X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (not (@ (@ tptp.ord_le72135733267957522d_enat Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))) (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (or (@ (@ tptp.ord_less_set_real A5) B5) (= A5 B5)))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B5) (= A5 B5)))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C4 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.ord_less_set_real B2) C4) (@ (@ tptp.ord_less_set_real A2) C4)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_set_nat B2) C4) (@ (@ tptp.ord_less_set_nat A2) C4)))) (= tptp.ord_less_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A5) B5) (not (@ (@ tptp.ord_less_eq_set_real B5) A5))))) (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (@ (@ tptp.ord_less_eq_set_nat B5) A5))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_set_real A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (@ _let_1 C4))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C4) (@ _let_1 C4))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B2) (@ (@ tptp.ord_less_eq_set_real A2) B2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X2 tptp.complex)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)) (forall ((X2 tptp.list_nat)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X2 tptp.real)) (=> (@ P X2) (@ Q X2))))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X2 tptp.nat)) (=> (@ P X2) (@ Q X2))))) (= (lambda ((Y4 tptp.set_real) (Z2 tptp.set_real)) (= Y4 Z2)) (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A5) B5) (@ (@ tptp.ord_less_eq_set_real B5) A5)))) (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (@ (@ tptp.ord_less_eq_set_nat B5) A5)))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (@ _let_1 C4))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C4) (@ _let_1 C4))))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)))) (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)))) (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))) (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real A2) A2)) (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) A2)) (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (forall ((T2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A5) B5) (not (= A5 B5))))) (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (= A5 B5))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_real B2) A2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat B2) A2))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_real A2) B2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2))) (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (not (@ (@ tptp.ord_less_eq_set_real B2) A2)))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (not (@ (@ tptp.ord_less_eq_set_nat B2) A2)))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B2) (not (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ (@ tptp.ord_less_eq_set_real B2) A2))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.ord_less_eq_set_nat B2) A2))))) (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_int) (B2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (C4 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (= (@ (@ tptp.minus_minus_set_real B2) (@ (@ tptp.minus_minus_set_real C4) A2)) A2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C4) (= (@ (@ tptp.minus_minus_set_nat B2) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) B2)) A2)) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B2)) A2)) (forall ((A2 tptp.set_real) (C4 tptp.set_real) (D4 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real D4) B2) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_set_real C4) D4))))) (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D4 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_set_nat C4) D4))))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int))) (forall ((A tptp.real) (N2 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 N2)) A))))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N4)) Y))))) (= (@ tptp.vEBT_vebt_buildup _let_45) _let_131) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ 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) N2) A)))))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N2) A) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.power_power_real Y2) N2) A)) (= Y2 X5)))))))) (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))))) (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))))) (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A5))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B5))))) (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A5))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B5))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A5))) (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) B5))))) (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A5))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B5))))) (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A5))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B5))))) (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) A2)) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X2) A2) (@ P X2))))) A2)) (forall ((A2 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) A2)) (forall ((A2 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X2) A2) (@ P X2))))) A2)) (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) A2)) (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) A2)) (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)))))))) (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X) (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))) (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real Y) X) (not (@ (@ tptp.ord_less_set_real X) Y)))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le2932123472753598470d_enat Y) X))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat A) B)) (or (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B)) (= A B)))) (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)))) (forall ((A tptp.set_real) (B tptp.set_real)) (= (not (@ (@ tptp.ord_less_set_real A) B)) (or (not (@ (@ tptp.ord_less_eq_set_real A) B)) (= A B)))) (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)))) (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)))) (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)))) (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)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))) (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (not (@ (@ tptp.ord_less_set_real X) Y)) (= (@ (@ tptp.ord_less_eq_set_real X) Y) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))) (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (= (not (@ (@ tptp.ord_less_set_real X) Y)) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))) (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (@ (@ tptp.ord_less_eq_real Y) X5))) (@ (@ tptp.ord_less_eq_real Y) Z))) (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y) (@ (@ tptp.ord_less_eq_real X5) Z))) (@ (@ tptp.ord_less_eq_real Y) Z))) (= tptp.ord_le72135733267957522d_enat (lambda ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat X2) Y3) (not (@ (@ tptp.ord_le2932123472753598470d_enat Y3) X2))))) (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y3) (not (@ (@ tptp.ord_less_eq_real Y3) X2))))) (= tptp.ord_less_set_real (lambda ((X2 tptp.set_real) (Y3 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real X2) Y3) (not (@ (@ tptp.ord_less_eq_set_real Y3) X2))))) (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (not (@ (@ tptp.ord_less_eq_set_nat Y3) X2))))) (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y3) (not (@ (@ tptp.ord_less_eq_num Y3) X2))))) (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (not (@ (@ tptp.ord_less_eq_nat Y3) X2))))) (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (not (@ (@ tptp.ord_less_eq_int Y3) X2))))) (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (not (@ (@ tptp.ord_le2932123472753598470d_enat Y) X)) (@ (@ tptp.ord_le72135733267957522d_enat X) Y))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))) (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat A4) B4) (= A4 B4)))) (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B4) (= A4 B4)))) (= tptp.ord_less_eq_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (or (@ (@ tptp.ord_less_set_real A4) B4) (= A4 B4)))) (= tptp.ord_less_eq_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A4) B4) (= A4 B4)))) (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B4) (= A4 B4)))) (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B4) (= A4 B4)))) (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B4) (= A4 B4)))) (= tptp.ord_le72135733267957522d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4) (not (= A4 B4))))) (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (= A4 B4))))) (= tptp.ord_less_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A4) B4) (not (= A4 B4))))) (= tptp.ord_less_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B4) (not (= A4 B4))))) (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (= A4 B4))))) (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (= A4 B4))))) (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (= A4 B4))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (@ (@ tptp.ord_le72135733267957522d_enat A) C)))) (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)))) (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (@ (@ tptp.ord_less_set_real B) C) (@ (@ tptp.ord_less_set_real A) C)))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) C) (@ _let_1 C))))) (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))))) (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_set_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_real B) C) (@ _let_1 C))))) (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))))) (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))))) (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))))) (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))))) (= tptp.ord_le72135733267957522d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4) (not (@ (@ tptp.ord_le2932123472753598470d_enat B4) A4))))) (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (@ (@ tptp.ord_less_eq_real B4) A4))))) (= tptp.ord_less_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real A4) B4) (not (@ (@ tptp.ord_less_eq_set_real B4) A4))))) (= tptp.ord_less_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A4) B4) (not (@ (@ tptp.ord_less_eq_set_nat B4) A4))))) (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (@ (@ tptp.ord_less_eq_num B4) A4))))) (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (@ (@ tptp.ord_less_eq_nat B4) A4))))) (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (@ (@ tptp.ord_less_eq_int B4) A4))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))) (= tptp.ord_le2932123472753598470d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat B4) A4) (= A4 B4)))) (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A4) (= A4 B4)))) (= tptp.ord_less_eq_set_real (lambda ((B4 tptp.set_real) (A4 tptp.set_real)) (or (@ (@ tptp.ord_less_set_real B4) A4) (= A4 B4)))) (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B4) A4) (= A4 B4)))) (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B4) A4) (= A4 B4)))) (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B4) A4) (= A4 B4)))) (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A4) (= A4 B4)))) (= tptp.ord_le72135733267957522d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat B4) A4) (not (= A4 B4))))) (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (= A4 B4))))) (= tptp.ord_less_set_real (lambda ((B4 tptp.set_real) (A4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real B4) A4) (not (= A4 B4))))) (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A4) (not (= A4 B4))))) (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (= A4 B4))))) (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (= A4 B4))))) (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (= A4 B4))))) (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (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))))) (forall ((B tptp.set_real) (A tptp.set_real) (C tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_set_real C))) (=> (@ (@ tptp.ord_less_eq_set_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (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))))) (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))))) (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))))) (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))))) (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) B) (@ (@ tptp.ord_le72135733267957522d_enat C) A)))) (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)))) (forall ((B tptp.set_real) (A tptp.set_real) (C tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real B) A) (=> (@ (@ tptp.ord_less_eq_set_real C) B) (@ (@ tptp.ord_less_set_real C) A)))) (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)))) (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)))) (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)))) (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)))) (= tptp.ord_le72135733267957522d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat B4) A4) (not (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4))))) (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (@ (@ tptp.ord_less_eq_real A4) B4))))) (= tptp.ord_less_set_real (lambda ((B4 tptp.set_real) (A4 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real B4) A4) (not (@ (@ tptp.ord_less_eq_set_real A4) B4))))) (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A4 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B4) A4) (not (@ (@ tptp.ord_less_eq_set_nat A4) B4))))) (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (@ (@ tptp.ord_less_eq_num A4) B4))))) (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (@ (@ tptp.ord_less_eq_nat A4) B4))))) (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (@ (@ tptp.ord_less_eq_int A4) B4))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (@ (@ tptp.ord_le2932123472753598470d_enat A) B))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))) (forall ((A tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A) B) (@ (@ tptp.ord_less_eq_set_real A) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))) (forall ((B tptp.set_real) (A tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real B) A) (@ (@ tptp.ord_less_eq_set_real B) A))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))) (= tptp.ord_le2932123472753598470d_enat (lambda ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (or (@ (@ tptp.ord_le72135733267957522d_enat X2) Y3) (= X2 Y3)))) (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y3) (= X2 Y3)))) (= tptp.ord_less_eq_set_real (lambda ((X2 tptp.set_real) (Y3 tptp.set_real)) (or (@ (@ tptp.ord_less_set_real X2) Y3) (= X2 Y3)))) (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X2) Y3) (= X2 Y3)))) (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y3) (= X2 Y3)))) (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y3) (= X2 Y3)))) (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y3) (= X2 Y3)))) (= tptp.ord_le72135733267957522d_enat (lambda ((X2 tptp.extended_enat) (Y3 tptp.extended_enat)) (and (@ (@ tptp.ord_le2932123472753598470d_enat X2) Y3) (not (= X2 Y3))))) (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y3) (not (= X2 Y3))))) (= tptp.ord_less_set_real (lambda ((X2 tptp.set_real) (Y3 tptp.set_real)) (and (@ (@ tptp.ord_less_eq_set_real X2) Y3) (not (= X2 Y3))))) (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (not (= X2 Y3))))) (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y3) (not (= X2 Y3))))) (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (not (= X2 Y3))))) (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (not (= X2 Y3))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le2932123472753598470d_enat X) Y)) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))) (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))) (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (not (@ (@ tptp.ord_le72135733267957522d_enat X) Y)) (@ (@ tptp.ord_le2932123472753598470d_enat Y) X))) (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))) (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (@ (@ tptp.ord_le2932123472753598470d_enat X) Y))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real X) Y) (@ (@ tptp.ord_less_eq_set_real X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (=> (not (= A B)) (@ (@ tptp.ord_le72135733267957522d_enat A) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.set_real) (B tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_real A) B)))) (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)))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (@ (@ tptp.ord_le72135733267957522d_enat A) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.set_real) (B tptp.set_real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_real A) B) (@ (@ tptp.ord_less_set_real A) B)))) (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)))) (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (=> (@ (@ tptp.ord_le72135733267957522d_enat Y) Z) (@ (@ tptp.ord_le72135733267957522d_enat X) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X) Z)))) (forall ((X tptp.set_real) (Y tptp.set_real) (Z tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (=> (@ (@ tptp.ord_less_set_real Y) Z) (@ (@ tptp.ord_less_set_real X) Z)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z) (@ (@ tptp.ord_less_set_nat X) Z)))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))) (forall ((X tptp.set_real) (Y tptp.set_real) (Z tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_set_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_real Y) Z) (@ _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))) (forall ((A tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.extended_enat tptp.real)) (B tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.extended_enat) (F (-> tptp.real tptp.extended_enat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.extended_enat) (F (-> tptp.num tptp.extended_enat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.extended_enat) (F (-> tptp.int tptp.extended_enat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat A) (@ F C)))))) (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))) (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))) (forall ((A tptp.extended_enat) (F (-> tptp.num tptp.extended_enat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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 ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.extended_enat) (F (-> tptp.nat tptp.extended_enat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (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_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y5)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (F (-> tptp.extended_enat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.extended_enat) (Y5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.extended_enat)) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ F A)) C))))) (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y5) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (or (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (@ (@ tptp.ord_le72135733267957522d_enat Y) X))) (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))) (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (or (@ (@ tptp.ord_le72135733267957522d_enat X) Y) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))) (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (or (@ (@ tptp.ord_less_set_real X) Y) (= X Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))) (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))) (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))) (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))) (forall ((A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A)) (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)) (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)) (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))) (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))) (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))) (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))) (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))) (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))) (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))) (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))) (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y) Y))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= (@ (@ tptp.ord_max_Code_integer X) Y) Y))) (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (= (@ (@ tptp.ord_max_set_real X) Y) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_max_set_nat X) Y) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (@ (@ tptp.ord_max_num X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))) (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y) X))) (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) X) (= (@ (@ tptp.ord_max_Code_integer X) Y) X))) (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real Y) X) (= (@ (@ tptp.ord_max_set_real X) Y) X))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_max_set_nat X) Y) X))) (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_max_num X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))) (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4)) B4) A4))) (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le3102999989581377725nteger A4) B4)) B4) A4))) (= tptp.ord_max_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (@ (@ (@ tptp.if_set_real (@ (@ tptp.ord_less_eq_set_real A4) B4)) B4) A4))) (= tptp.ord_max_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A4) B4)) B4) A4))) (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))) (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))) (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (=> (= Xa2 _let_1) (=> (and (=> B3 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B3) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B3)) _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))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X _let_1) (=> (= Y 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) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.vEBT_Leaf false) B3)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A3))) (let ((_let_3 (@ _let_2 B3))) (=> (= X _let_3) (=> (= Xa2 _let_1) (=> (= Y (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A3 Bool) (B3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B3)) (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N4)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= Xa2 _let_1) (=> (= Y _let_2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa2 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi2))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (=> (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _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) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S2))) (=> (= X _let_1) (=> (= Y _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) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (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) (TreeList3 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) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))) (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)) (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) (@ _let_1 K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))) _let_130 (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat) (forall ((K tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N2) K))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (=> (not Y) (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))) (=> (= X _let_1) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.set_or5403411693681687835d_enat A) B) tptp.bot_bo7653980558646680370d_enat))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))) (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real) (D tptp.set_real)) (= (@ (@ tptp.ord_le3558479182127378552t_real (@ (@ tptp.set_or7743017856606604397t_real A) B)) (@ (@ tptp.set_or7743017856606604397t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_set_real A) B)) (and (@ (@ tptp.ord_less_eq_set_real C) A) (@ (@ tptp.ord_less_eq_set_real B) D))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.set_real) (B tptp.set_real)) (= (= (@ (@ tptp.set_or7743017856606604397t_real A) B) tptp.bot_bot_set_set_real) (not (@ (@ tptp.ord_less_eq_set_real A) B)))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.set_real) (B tptp.set_real)) (= (= tptp.bot_bot_set_set_real (@ (@ tptp.set_or7743017856606604397t_real A) B)) (not (@ (@ tptp.ord_less_eq_set_real A) B)))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((L2 tptp.set_real) (H2 tptp.set_real) (L3 tptp.set_real) (H3 tptp.set_real)) (= (= (@ (@ tptp.set_or7743017856606604397t_real L2) H2) (@ (@ tptp.set_or7743017856606604397t_real L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_real L2) H2)) (not (@ (@ tptp.ord_less_eq_set_real L3) H3)))))) (forall ((L2 tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L2) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))) (forall ((L2 tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L2) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L2) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))) (forall ((L2 tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L2) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))) (forall ((L2 tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L2) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L2) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))) (forall ((L2 tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L2) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L2) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))) (forall ((I2 tptp.set_real) (L2 tptp.set_real) (U tptp.set_real)) (= (@ (@ tptp.member_set_real I2) (@ (@ tptp.set_or7743017856606604397t_real L2) U)) (and (@ (@ tptp.ord_less_eq_set_real L2) I2) (@ (@ tptp.ord_less_eq_set_real I2) U)))) (forall ((I2 tptp.set_nat) (L2 tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ (@ tptp.set_or4548717258645045905et_nat L2) U)) (and (@ (@ tptp.ord_less_eq_set_nat L2) I2) (@ (@ tptp.ord_less_eq_set_nat I2) U)))) (forall ((I2 tptp.num) (L2 tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L2) U)) (and (@ (@ tptp.ord_less_eq_num L2) I2) (@ (@ tptp.ord_less_eq_num I2) U)))) (forall ((I2 tptp.nat) (L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (and (@ (@ tptp.ord_less_eq_nat L2) I2) (@ (@ tptp.ord_less_eq_nat I2) U)))) (forall ((I2 tptp.int) (L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (and (@ (@ tptp.ord_less_eq_int L2) I2) (@ (@ tptp.ord_less_eq_int I2) U)))) (forall ((I2 tptp.real) (L2 tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L2) U)) (and (@ (@ tptp.ord_less_eq_real L2) I2) (@ (@ tptp.ord_less_eq_real I2) U)))) (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M7 tptp.nat)) (=> (@ P X) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M5)))))))))) (forall ((X tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A3 tptp.nat) (B3 tptp.nat) (Acc tptp.num)) (not (= X (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A3) (@ (@ tptp.product_Pair_nat_num B3) Acc)))))))) (forall ((X tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B3 tptp.nat) (Acc tptp.nat)) (not (= X (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A3) (@ (@ tptp.product_Pair_nat_nat B3) Acc)))))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat) (D tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (= (@ (@ tptp.ord_le2529575680413868914d_enat (@ (@ tptp.set_or5403411693681687835d_enat A) B)) (@ (@ tptp.set_or5403411693681687835d_enat C) D)) (and (or (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_le2932123472753598470d_enat B) D) (or (@ (@ tptp.ord_le72135733267957522d_enat C) A) (@ (@ tptp.ord_le72135733267957522d_enat B) D)))) (@ _let_1 D))))) (forall ((A tptp.set_real) (B tptp.set_real) (C tptp.set_real) (D tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real C))) (= (@ (@ tptp.ord_le7926960851185191020t_real (@ (@ tptp.set_or7743017856606604397t_real A) B)) (@ (@ tptp.set_or7743017856606604397t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_real B) D) (or (@ (@ tptp.ord_less_set_real C) A) (@ (@ tptp.ord_less_set_real B) D)))) (@ _let_1 D))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))) (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))))) (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))))) (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A3 tptp.real) (B3 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (=> (@ (@ P B3) C3) (=> (@ (@ tptp.ord_less_eq_real A3) B3) (=> (@ (@ tptp.ord_less_eq_real B3) C3) (@ _let_1 C3))))))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A3 tptp.real) (B3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A3) X5) (@ (@ tptp.ord_less_eq_real X5) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B3) A3)) D5)) (@ (@ P A3) B3)))))))) (@ (@ P A) B))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X) Y)))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))) (forall ((Q2 tptp.nat) (R tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R)) (= R tptp.zero_zero_nat))) (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R)) (= R tptp.zero_zero_int))) (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (= (@ (@ tptp.modulo_modulo_int _let_1) B) _let_1))) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))) (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) (@ _let_1 K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))) (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)) (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))) (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))) (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))) (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))) (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))) (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))) (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))) (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))) (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((N2 tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((K tptp.nat) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N2)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N2) K)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) _let_129 _let_128 _let_129 _let_128 (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)))) (forall ((K tptp.num) (N2 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) N2))) _let_1) tptp.one_one_nat)))) (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)))) (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)))) (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)))) (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)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))) (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)) (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)))) (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)))) (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)))) (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))) (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))) (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))))) (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))))) (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))) (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))) (forall ((A tptp.nat) (C tptp.nat) (A6 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A6) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A6) B6)) C))))) (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A6) B6)) C))))) (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))) (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))) (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)))) (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)))) (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))) (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))) (forall ((A tptp.nat) (C tptp.nat) (A6 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A6) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A6) B6)) C))))) (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A6) B6)) C))))) (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))) (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))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))) (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A6) B6)) C))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N2)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N2)) B))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N2)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N2)) B))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) K)) (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))) (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))) (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))) (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))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))) (forall ((M tptp.num) (N2 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 N2)) _let_1)))) (forall ((M tptp.num) (N2 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 N2)) _let_1)))) (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)))))))) (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)))) (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)))) (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)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (let ((_let_3 (= _let_1 N2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (P5 tptp.nat) (M tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) P5) (=> (@ (@ tptp.ord_less_nat M) P5) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) P5) (=> (@ P N4) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N4)) P5))))) (@ P M)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)) (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q3))))) (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N)) N)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))) (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)))) (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)))) (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)))) (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)))) (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))) (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)) (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)) (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))) (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)))) (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)))) (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)))) (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))) (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))) (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))) (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))) (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))) (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))) (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))))) (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))))) (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))))) (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))) (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))) (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))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (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))) (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))) (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))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q3 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q3))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (forall ((S2 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S2))))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (forall ((S2 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q2) S2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N2)) Q2))) (@ _let_1 N2)))))) (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N)) N)))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N2)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I5)) J3)) (@ P J3))))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (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))))))) (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))))))) (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))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N2))) M) tptp.one_one_nat))) (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))))))) (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))))))) (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)))) (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)))) (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)))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))) (forall ((A tptp.nat) (N2 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 N2))) (= (@ (@ 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 N2) M)))) _let_2))))) (forall ((A tptp.int) (N2 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 N2))) (= (@ (@ 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 N2) M)))) _let_2))))) (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)))))))) (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)))))))) (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)))))))) (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))) (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))) (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)))))))) (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)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (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))))))))) (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))))))))) (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))))))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X) Y)))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B2) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B2) N2))))) (forall ((A2 tptp.nat) (N2 tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A2) N2)))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B2) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ tptp.divide_divide_nat B2) N2))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs2) Ys)) N2) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs2) Ys)) N2) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) N2) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) N2) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs2) Ys)) N2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) N2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs2) Ys)) N2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((X tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A2) Z) (=> (@ tptp.finite_finite_nat B2) (=> (= A2 B2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A2) X) X_1))))))) (forall ((Z tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X) X_1)))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))) (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (@ (@ tptp.ord_less_nat X3) A))))))) (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (@ (@ tptp.ord_less_nat A) X3))))))) (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y22)) (= X22 Y22))) (forall ((A tptp.code_integer) (B Bool) (A6 tptp.code_integer) (B6 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A6) B6)) (and (= A A6) (= B B6)))) (forall ((A tptp.num) (B tptp.num) (A6 tptp.num) (B6 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A6) B6)) (and (= A A6) (= B B6)))) (forall ((A tptp.nat) (B tptp.num) (A6 tptp.nat) (B6 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A6) B6)) (and (= A A6) (= B B6)))) (forall ((A tptp.nat) (B tptp.nat) (A6 tptp.nat) (B6 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A6) B6)) (and (= A A6) (= B B6)))) (forall ((A tptp.int) (B tptp.int) (A6 tptp.int) (B6 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A6) B6)) (and (= A A6) (= B B6)))) (forall ((X1 tptp.code_integer) (X22 Bool) (Y1 tptp.code_integer) (Y22 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o X1) X22) (@ (@ tptp.produc6677183202524767010eger_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.num) (X22 tptp.num) (Y1 tptp.num) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X22) (@ (@ tptp.product_Pair_num_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.nat) (X22 tptp.num) (Y1 tptp.nat) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num X1) X22) (@ (@ tptp.product_Pair_nat_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))) (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))) (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))) (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) (@ _let_1 K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))) (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))) (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))))) (forall ((N3 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N3) (@ (@ tptp.ord_less_nat X5) N2))) (@ tptp.finite_finite_nat N3))) (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_nat X2) M6)))))) (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_eq_nat X2) M6)))))) (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))) (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))) (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))) (forall ((P (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I2)))))) (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) (@ F N4))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) U)))))) (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs) N2))))))) (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N2))))))) (forall ((A2 tptp.set_o) (N2 tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (= (@ tptp.size_size_list_o Xs) N2))))))) (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (= (@ tptp.size_size_list_int Xs) N2))))))) (forall ((A2 tptp.set_real) (N2 tptp.nat)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite306553202115118035t_real (@ tptp.collect_list_real (lambda ((Xs tptp.list_real)) (and (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (= (@ tptp.size_size_list_real Xs) N2))))))) (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (= (@ tptp.size_size_list_nat Xs) N2))))))) (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2))))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L2)) L2))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))) (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N2))))))) (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N2))))))) (forall ((A2 tptp.set_o) (N2 tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N2))))))) (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N2))))))) (forall ((A2 tptp.set_real) (N2 tptp.nat)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite306553202115118035t_real (@ tptp.collect_list_real (lambda ((Xs tptp.list_real)) (and (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_real Xs)) N2))))))) (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N2))))))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L2)))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L2)) tptp.zero_zero_int))) (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)))) (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)))) (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)))) (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real A) A)) (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)) (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)) (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) A))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))) (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))) (forall ((A tptp.code_integer) (B Bool) (A6 tptp.code_integer) (B6 Bool)) (=> (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A6) B6)) (not (=> (= A A6) (= B (not B6)))))) (forall ((A tptp.num) (B tptp.num) (A6 tptp.num) (B6 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A6) B6)) (not (=> (= A A6) (not (= B B6)))))) (forall ((A tptp.nat) (B tptp.num) (A6 tptp.nat) (B6 tptp.num)) (=> (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A6) B6)) (not (=> (= A A6) (not (= B B6)))))) (forall ((A tptp.nat) (B tptp.nat) (A6 tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A6) B6)) (not (=> (= A A6) (not (= B B6)))))) (forall ((A tptp.int) (B tptp.int) (A6 tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A6) B6)) (not (=> (= A A6) (not (= B B6)))))) (forall ((P (-> tptp.produc6271795597528267376eger_o Bool)) (P5 tptp.produc6271795597528267376eger_o)) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (@ P (@ (@ tptp.produc6677183202524767010eger_o A3) B3))) (@ P P5))) (forall ((P (-> tptp.product_prod_num_num Bool)) (P5 tptp.product_prod_num_num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A3) B3))) (@ P P5))) (forall ((P (-> tptp.product_prod_nat_num Bool)) (P5 tptp.product_prod_nat_num)) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (@ P (@ (@ tptp.product_Pair_nat_num A3) B3))) (@ P P5))) (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P5 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B3))) (@ P P5))) (forall ((P (-> tptp.product_prod_int_int Bool)) (P5 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A3) B3))) (@ P P5))) (forall ((P5 tptp.produc6271795597528267376eger_o)) (exists ((X5 tptp.code_integer) (Y5 Bool)) (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)))) (forall ((P5 tptp.product_prod_num_num)) (exists ((X5 tptp.num) (Y5 tptp.num)) (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)))) (forall ((P5 tptp.product_prod_nat_num)) (exists ((X5 tptp.nat) (Y5 tptp.num)) (= P5 (@ (@ tptp.product_Pair_nat_num X5) Y5)))) (forall ((P5 tptp.product_prod_nat_nat)) (exists ((X5 tptp.nat) (Y5 tptp.nat)) (= P5 (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (forall ((P5 tptp.product_prod_int_int)) (exists ((X5 tptp.int) (Y5 tptp.int)) (= P5 (@ (@ tptp.product_Pair_int_int X5) Y5)))) (forall ((Y tptp.produc6271795597528267376eger_o)) (not (forall ((A3 tptp.code_integer) (B3 Bool)) (not (= Y (@ (@ tptp.produc6677183202524767010eger_o A3) B3)))))) (forall ((Y tptp.product_prod_num_num)) (not (forall ((A3 tptp.num) (B3 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_num_num A3) B3)))))) (forall ((Y tptp.product_prod_nat_num)) (not (forall ((A3 tptp.nat) (B3 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_nat_num A3) B3)))))) (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B3 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A3) B3)))))) (forall ((Y tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A3) B3)))))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L2) _let_1))))) (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))))))) (forall ((B6 tptp.extended_enat) (A6 tptp.extended_enat)) (= (not (@ (@ tptp.ord_le2932123472753598470d_enat B6) A6)) (@ (@ tptp.ord_le72135733267957522d_enat A6) B6))) (forall ((B6 tptp.real) (A6 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B6) A6)) (@ (@ tptp.ord_less_real A6) B6))) (forall ((B6 tptp.num) (A6 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B6) A6)) (@ (@ tptp.ord_less_num A6) B6))) (forall ((B6 tptp.nat) (A6 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B6) A6)) (@ (@ tptp.ord_less_nat A6) B6))) (forall ((B6 tptp.int) (A6 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B6) A6)) (@ (@ tptp.ord_less_int A6) B6))) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))) (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)))))))) (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))))) (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4)) B4) A4))) (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le3102999989581377725nteger A4) B4)) B4) A4))) (= tptp.ord_max_set_real (lambda ((A4 tptp.set_real) (B4 tptp.set_real)) (@ (@ (@ tptp.if_set_real (@ (@ tptp.ord_less_eq_set_real A4) B4)) B4) A4))) (= tptp.ord_max_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A4) B4)) B4) A4))) (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))) (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))) (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K))))) (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B5 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B5) A2)))))) (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite9007344921179782393t_real (@ tptp.collect_set_real (lambda ((B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real B5) A2)))))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B5) A2)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z5 tptp.real)) (= (@ (@ tptp.power_power_real Z5) N2) tptp.one_one_real)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.extended_enat)) (Y (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_on7984719198319812577d_enat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_on7984719198319812577d_enat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_7803423173614009249d_enat (@ X I5)) (@ Y I5)) tptp.one_on7984719198319812577d_enat))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.extended_enat)) (Y (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_on7984719198319812577d_enat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_on7984719198319812577d_enat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_7803423173614009249d_enat (@ X I5)) (@ Y I5)) tptp.one_on7984719198319812577d_enat))))))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.extended_enat)) (Y (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_on7984719198319812577d_enat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_on7984719198319812577d_enat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_7803423173614009249d_enat (@ X I5)) (@ Y I5)) tptp.one_on7984719198319812577d_enat))))))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.extended_enat)) (Y (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.one_on7984719198319812577d_enat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.one_on7984719198319812577d_enat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.times_7803423173614009249d_enat (@ X I5)) (@ Y I5)) tptp.one_on7984719198319812577d_enat))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.extended_enat)) (Y (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_z5237406670263579293d_enat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_z5237406670263579293d_enat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ X I5)) (@ Y I5)) tptp.zero_z5237406670263579293d_enat))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.extended_enat)) (Y (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_z5237406670263579293d_enat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_z5237406670263579293d_enat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ X I5)) (@ Y I5)) tptp.zero_z5237406670263579293d_enat))))))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.extended_enat)) (Y (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_z5237406670263579293d_enat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_z5237406670263579293d_enat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ X I5)) (@ Y I5)) tptp.zero_z5237406670263579293d_enat))))))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.extended_enat)) (Y (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.zero_z5237406670263579293d_enat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.zero_z5237406670263579293d_enat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ X I5)) (@ Y I5)) tptp.zero_z5237406670263579293d_enat))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R)) (@ (@ (@ 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 R)) tptp.one_one_int)))))))) (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N4 tptp.nat)) (forall ((X3 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X3)) N4)))))) (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N4 tptp.nat)) (forall ((X3 tptp.list_o)) (=> (@ (@ tptp.member_list_o X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X3)) N4)))))) (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N4 tptp.nat)) (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X3)) N4)))))) (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N4 tptp.nat)) (forall ((X3 tptp.list_int)) (=> (@ (@ tptp.member_list_int X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X3)) N4)))))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real A) X5) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_real) (A tptp.set_real)) (=> (@ tptp.finite9007344921179782393t_real A2) (=> (@ (@ tptp.member_set_real A) A2) (exists ((X5 tptp.set_real)) (and (@ (@ tptp.member_set_real X5) A2) (@ (@ tptp.ord_less_eq_set_real A) X5) (forall ((Xa tptp.set_real)) (=> (@ (@ tptp.member_set_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_real X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat A) X5) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A2) (@ (@ tptp.ord_less_eq_num A) X5) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat A) X5) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int A) X5) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real X5) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_real) (A tptp.set_real)) (=> (@ tptp.finite9007344921179782393t_real A2) (=> (@ (@ tptp.member_set_real A) A2) (exists ((X5 tptp.set_real)) (and (@ (@ tptp.member_set_real X5) A2) (@ (@ tptp.ord_less_eq_set_real X5) A) (forall ((Xa tptp.set_real)) (=> (@ (@ tptp.member_set_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_real Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat X5) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A2) (@ (@ tptp.ord_less_eq_num X5) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat X5) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_int X5) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ tptp.finite3207457112153483333omplex B2) (@ tptp.finite3207457112153483333omplex A2)))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ tptp.finite_finite_real B2) (@ tptp.finite_finite_real A2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ tptp.finite_finite_nat B2) (@ tptp.finite_finite_nat A2)))) (forall ((S tptp.set_complex) (T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (not (@ tptp.finite3207457112153483333omplex S)) (not (@ tptp.finite3207457112153483333omplex T3))))) (forall ((S tptp.set_real) (T3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (not (@ tptp.finite_finite_real S)) (not (@ tptp.finite_finite_real T3))))) (forall ((S tptp.set_nat) (T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T3) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T3))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (@ tptp.finite3207457112153483333omplex A2)))) (forall ((B2 tptp.set_real) (A2 tptp.set_real)) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ tptp.finite_finite_real A2)))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ tptp.finite_finite_nat A2)))) (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_real)) (=> (@ tptp.finite9007344921179782393t_real A2) (=> (not (= A2 tptp.bot_bot_set_set_real)) (exists ((X5 tptp.set_real)) (and (@ (@ tptp.member_set_real X5) A2) (forall ((Xa tptp.set_real)) (=> (@ (@ tptp.member_set_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_real X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X5) Xa) (= X5 Xa))))))))) (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_real)) (=> (@ tptp.finite9007344921179782393t_real A2) (=> (not (= A2 tptp.bot_bot_set_set_real)) (exists ((X5 tptp.set_real)) (and (@ (@ tptp.member_set_real X5) A2) (forall ((Xa tptp.set_real)) (=> (@ (@ tptp.member_set_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_real Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X5) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X5) (= X5 Xa))))))))) (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X5) (= X5 Xa))))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R)))))))))) (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real) (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ (@ P N4) (@ (@ tptp.modulo_modulo_nat M5) N4)) (@ (@ P M5) N4)))) (@ (@ P M) N2)))) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N2)) K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N2) (@ (@ tptp.divide_divide_int K) _let_1)) L2)))))) (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) _let_56) (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) _let_28) (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) _let_47) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))) (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))) (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)))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex A) B)) (@ _let_1 B)))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) A)) (@ _let_1 B)))) (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)))) (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)))) (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)))) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))) (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (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)))))) (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)))))) (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)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N2))))) (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)) (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int) (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))))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B)) (@ _let_1 B)))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (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))) (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))) (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))) (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))))))) (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))))))) (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))))))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (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)))) (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)))) (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)))) (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))))))) (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))))))) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N2) K) L2)) (@ _let_1 L2)))) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N2) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))) (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N2)) (not (@ _let_1 N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N2))) (@ _let_1 N2)))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.dvd_dvd_nat A) B)))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.dvd_dvd_int A) B)))) (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))))) (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))))) (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))))) (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))))))) (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))))))) (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))))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N2) _let_1)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1))))) (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)))))))) (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)))))))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)))))) (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)))))))) (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)))))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (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)))) (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)))) (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)))) (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)))))))) (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)))))))) (forall ((N2 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) N2)) tptp.one_one_Code_integer)) (= N2 tptp.zero_zero_nat)))) (forall ((N2 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) N2)) tptp.one_one_nat)) (= N2 tptp.zero_zero_nat)))) (forall ((N2 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) N2)) tptp.one_one_int)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))) (forall ((P5 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P5) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= P5 (@ (@ tptp.times_times_nat X5) Y5)) (=> (@ (@ tptp.dvd_dvd_nat X5) A) (not (@ (@ tptp.dvd_dvd_nat Y5) B)))))))) (forall ((P5 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P5) (@ (@ tptp.times_times_int A) B)) (not (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.times_times_int X5) Y5)) (=> (@ (@ tptp.dvd_dvd_int X5) A) (not (@ (@ tptp.dvd_dvd_int Y5) B)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B7 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B7) C5)) (@ (@ tptp.dvd_dvd_nat B7) B) (@ (@ tptp.dvd_dvd_nat C5) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B7 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B7) C5)) (@ (@ tptp.dvd_dvd_int B7) B) (@ (@ tptp.dvd_dvd_int C5) C))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (not (forall ((K2 tptp.complex)) (not (= A (@ (@ tptp.times_times_complex B) K2))))))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K2 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K2))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))) (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))) (forall ((A tptp.complex) (B tptp.complex) (K tptp.complex)) (=> (= A (@ (@ tptp.times_times_complex B) K)) (@ (@ tptp.dvd_dvd_complex B) A))) (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))) (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))) (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))) (= tptp.dvd_dvd_Code_integer (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A4 (@ (@ tptp.times_3573771949741848930nteger B4) K3))))) (= tptp.dvd_dvd_complex (lambda ((B4 tptp.complex) (A4 tptp.complex)) (exists ((K3 tptp.complex)) (= A4 (@ (@ tptp.times_times_complex B4) K3))))) (= tptp.dvd_dvd_real (lambda ((B4 tptp.real) (A4 tptp.real)) (exists ((K3 tptp.real)) (= A4 (@ (@ tptp.times_times_real B4) K3))))) (= tptp.dvd_dvd_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (exists ((K3 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B4) K3))))) (= tptp.dvd_dvd_int (lambda ((B4 tptp.int) (A4 tptp.int)) (exists ((K3 tptp.int)) (= A4 (@ (@ tptp.times_times_int B4) K3))))) (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))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (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))))) (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))))) (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))))) (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))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex A) C))) (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))) (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))) (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))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex A) B))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))) (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))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex A) B) (=> (@ (@ tptp.dvd_dvd_complex C) D) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) D))))) (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))))) (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))))) (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))))) (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))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex B) C))) (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))) (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))) (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))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex B) A))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))) (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)))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)))))) (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)))))) (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)))))) (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)))))) (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))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ _let_1 B))))) (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))))) (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))))) (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))))) (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))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ _let_1 C))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))) (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)) (forall ((A tptp.extended_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat tptp.one_on7984719198319812577d_enat) A)) (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)) (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)) (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int C) B)) (@ _let_1 (@ (@ tptp.minus_minus_int B) C))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)))) (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)))) (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)))) (forall ((K tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N2)))))) (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N2)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C) (@ _let_1 C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C) (@ _let_1 C))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C) (@ _let_1 C))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (@ _let_1 M))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y5 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 X5) (@ (@ tptp.plus_plus_nat (@ _let_2 Y5)) D3)) (= (@ _let_2 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y5)) D3))))))))) (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X5 tptp.nat) (Y5 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 X5) (@ (@ tptp.plus_plus_nat (@ _let_3 Y5)) D)) (= (@ _let_3 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y5)) D)))))))))))))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y5 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 X5)) (@ _let_2 Y5)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X5)) (@ _let_1 Y5)) D3)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B)))) (@ (@ tptp.dvd_dvd_complex A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (@ (@ tptp.dvd_dvd_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) A)))) (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) B)))) (@ (@ tptp.dvd_dvd_real A) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (@ (@ tptp.dvd_dvd_nat A) B))) (forall ((N2 tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 L2)) R)))) (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)) (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)) (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))) (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)))) (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)))) (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)))))) (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)))))) (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)))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (forall ((B tptp.nat) (A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))) (forall ((B tptp.int) (A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N2) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N2) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) M))))) (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) M))))) (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) M))))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) M))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))) (forall ((A tptp.complex) (N2 tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N2))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer C) (@ (@ tptp.minus_8373710615458151222nteger A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (@ (@ tptp.dvd_dvd_int C) (@ (@ tptp.minus_minus_int A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y5)) D3))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (or (@ (@ tptp.ord_less_nat N2) M) (@ _let_1 N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 M)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))))) (= tptp.neg_nu7009210354673126013omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex X2) X2))) (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))) (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))) (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)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y)) (= X Y)))))) (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)))))))) (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)))))))) (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)))))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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))))) (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))))) (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))))) (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)))))))) (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)))))))) (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)))))))) (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)))) (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)))) (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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)))))) (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)))))) (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)))))) (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)))) (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)))) (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)))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N2 tptp.zero_zero_nat)))) (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))) (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))) (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))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat K) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M)))) (forall ((N2 tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N2))))) (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M5 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M5)))))) (@ _let_127 tptp.zero_z3403309356797280102nteger) (@ _let_126 tptp.zero_zero_nat) (@ _let_125 tptp.zero_zero_int) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3))))))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3))))))) (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3))))))) (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B3) tptp.one_one_nat) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_nat A) B3) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B3)))))))))))))) (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B3) tptp.one_one_int) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_int A) B3) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B3)))))))))))))) (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B3 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B3 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B3) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B3) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B3)))))))))))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (not (@ _let_127 tptp.one_one_Code_integer)) (not (@ _let_126 tptp.one_one_nat)) (not (@ _let_125 tptp.one_one_int)) (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide_divide_nat A4) _let_1) (@ (@ tptp.divide_divide_nat B4) _let_1))))))) (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A4 tptp.int) (B4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide_divide_int A4) _let_1) (@ (@ tptp.divide_divide_int B4) _let_1))))))) (= (lambda ((Y4 tptp.code_integer) (Z2 tptp.code_integer)) (= Y4 Z2)) (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide6298287555418463151nteger A4) _let_1) (@ (@ tptp.divide6298287555418463151nteger B4) _let_1))))))) (forall ((X tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N2)))))) (forall ((X tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N2)))))) (forall ((X tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N2)))))) (forall ((N2 tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N2)))) (forall ((N2 tptp.nat) (X tptp.extended_enat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.dvd_dv3785147216227455552d_enat X) (@ (@ tptp.power_8040749407984259932d_enat X) N2)))) (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N2)))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N2)))) (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N2)))) (forall ((N2 tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N2)) M) (= N2 tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M)) M) (= N2 tptp.one_one_nat)))) (forall ((Q2 tptp.nat) (N2 tptp.nat) (R tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((R tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R) N2) (=> (@ (@ tptp.ord_less_eq_nat R) M) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M) R)) (= (@ (@ tptp.modulo_modulo_nat M) N2) R))))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))) (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))) (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_integer))))))) (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))) (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))) (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))))))) (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))))))) (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))))))) (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))))))))) (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))))))))) (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))))))))) (forall ((A tptp.real) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((N2 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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (@ _let_1 A))))) (forall ((N2 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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N2)))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N2)))) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N4 tptp.nat)) (not (= X (@ tptp.suc N4))))))) (forall ((A tptp.real) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P A3) B3) (@ (@ P B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P A) B))))) (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))) (forall ((M tptp.nat) (N2 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 N2))) (= (@ (@ 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) N2))))))) (forall ((M tptp.nat) (N2 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 N2))) (= (@ (@ 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) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ 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) N2))))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))) (forall ((A tptp.int) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))) (forall ((X8 tptp.set_Extended_enat)) (=> (not (= X8 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X5) X8) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) X8) (@ (@ tptp.ord_le72135733267957522d_enat X5) Xa))))) (not (@ tptp.finite4001608067531595151d_enat X8))))) (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X5) Xa))))) (not (@ tptp.finite_finite_real X8))))) (forall ((X8 tptp.set_num)) (=> (not (= X8 tptp.bot_bot_set_num)) (=> (forall ((X5 tptp.num)) (=> (@ (@ tptp.member_num X5) X8) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X8) (@ (@ tptp.ord_less_num X5) Xa))))) (not (@ tptp.finite_finite_num X8))))) (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X5) Xa))))) (not (@ tptp.finite_finite_nat X8))))) (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X5) Xa))))) (not (@ tptp.finite_finite_int X8))))) (forall ((S tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (not (= S tptp.bot_bo7653980558646680370d_enat)) (exists ((X5 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X5) S) (not (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) S) (@ (@ tptp.ord_le72135733267957522d_enat Xa) X5))))))))) (forall ((S tptp.set_real)) (=> (@ tptp.finite_finite_real S) (=> (not (= S tptp.bot_bot_set_real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) S) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S) (@ (@ tptp.ord_less_real Xa) X5))))))))) (forall ((S tptp.set_num)) (=> (@ tptp.finite_finite_num S) (=> (not (= S tptp.bot_bot_set_num)) (exists ((X5 tptp.num)) (and (@ (@ tptp.member_num X5) S) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S) (@ (@ tptp.ord_less_num Xa) X5))))))))) (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) S) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S) (@ (@ tptp.ord_less_nat Xa) X5))))))))) (forall ((S tptp.set_int)) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) S) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S) (@ (@ tptp.ord_less_int Xa) X5))))))))) (forall ((N2 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 N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) _let_3)) _let_2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N2) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))) (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)))))))) (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X3 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X3) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K4) D4))) T)))))))) (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)))))))) (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)))))))) (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))))))) (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X3 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X3) T)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K4) D4))) T))))))) (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))))))) (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))))))) (forall ((P (-> tptp.code_integer Bool)) (L2 tptp.code_integer)) (= (exists ((X2 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L2) X2))) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L2) (@ (@ tptp.plus_p5714425477246183910nteger X2) tptp.zero_z3403309356797280102nteger)) (@ P X2))))) (forall ((P (-> tptp.extended_enat Bool)) (L2 tptp.extended_enat)) (= (exists ((X2 tptp.extended_enat)) (@ P (@ (@ tptp.times_7803423173614009249d_enat L2) X2))) (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.dvd_dv3785147216227455552d_enat L2) (@ (@ tptp.plus_p3455044024723400733d_enat X2) tptp.zero_z5237406670263579293d_enat)) (@ P X2))))) (forall ((P (-> tptp.complex Bool)) (L2 tptp.complex)) (= (exists ((X2 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L2) X2))) (exists ((X2 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L2) (@ (@ tptp.plus_plus_complex X2) tptp.zero_zero_complex)) (@ P X2))))) (forall ((P (-> tptp.real Bool)) (L2 tptp.real)) (= (exists ((X2 tptp.real)) (@ P (@ (@ tptp.times_times_real L2) X2))) (exists ((X2 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L2) (@ (@ tptp.plus_plus_real X2) tptp.zero_zero_real)) (@ P X2))))) (forall ((P (-> tptp.nat Bool)) (L2 tptp.nat)) (= (exists ((X2 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L2) X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L2) (@ (@ tptp.plus_plus_nat X2) tptp.zero_zero_nat)) (@ P X2))))) (forall ((P (-> tptp.int Bool)) (L2 tptp.int)) (= (exists ((X2 tptp.int)) (@ P (@ (@ tptp.times_times_int L2) X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L2) (@ (@ tptp.plus_plus_int X2) tptp.zero_zero_int)) (@ P X2))))) (= tptp.nat_triangle (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ 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))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))) (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)))))) (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)))))) (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)))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I2))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I2))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I2))))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.zero_n1046097342994218471d_enat P)) (@ tptp.zero_n1046097342994218471d_enat Q)) (and (not P) Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))) (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))) (= (@ tptp.zero_n1046097342994218471d_enat true) tptp.one_on7984719198319812577d_enat) (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex) (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real) (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat) (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int) (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer) (forall ((P Bool)) (= (= (@ tptp.zero_n1046097342994218471d_enat P) tptp.one_on7984719198319812577d_enat) P)) (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)) (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)) (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)) (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)) (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)) (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M N2) (=> (not (= M tptp.zero_zero_nat)) (= X Y))))) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) N2)) (forall ((N2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N2) X)) N2)) (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N2) X)) N2)) (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X)) N2)) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))) (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)) (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)) (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)) (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)) (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))) (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))) (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))) (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))) (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))) (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))) (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))) (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N2) (@ tptp.zero_n2687167440665602831ol_nat (not (= N2 _let_1)))))) (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.product_prod_nat_nat) (N2 tptp.nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I2) X))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I2) X))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I2) X))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N2)) _let_1)))) (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P5))) P5)) (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P5))) P5)) (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P5))) P5)) (forall ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)) (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1201886186963655149omplex (and P Q)) (@ (@ tptp.times_times_complex (@ tptp.zero_n1201886186963655149omplex P)) (@ tptp.zero_n1201886186963655149omplex Q)))) (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)))) (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)))) (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)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))) (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)) (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)) (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)) (= tptp.zero_n1046097342994218471d_enat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_Extended_enat P4) tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat))) (= tptp.zero_n1201886186963655149omplex (lambda ((P4 Bool)) (@ (@ (@ tptp.if_complex P4) tptp.one_one_complex) tptp.zero_zero_complex))) (= tptp.zero_n3304061248610475627l_real (lambda ((P4 Bool)) (@ (@ (@ tptp.if_real P4) tptp.one_one_real) tptp.zero_zero_real))) (= tptp.zero_n2687167440665602831ol_nat (lambda ((P4 Bool)) (@ (@ (@ tptp.if_nat P4) tptp.one_one_nat) tptp.zero_zero_nat))) (= tptp.zero_n2684676970156552555ol_int (lambda ((P4 Bool)) (@ (@ (@ tptp.if_int P4) tptp.one_one_int) tptp.zero_zero_int))) (= tptp.zero_n356916108424825756nteger (lambda ((P4 Bool)) (@ (@ (@ tptp.if_Code_integer P4) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (forall ((P (-> tptp.extended_enat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1046097342994218471d_enat P5)) (and (=> P5 (@ P tptp.one_on7984719198319812577d_enat)) (=> (not P5) (@ P tptp.zero_z5237406670263579293d_enat))))) (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (and (=> P5 (@ P tptp.one_one_complex)) (=> (not P5) (@ P tptp.zero_zero_complex))))) (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (and (=> P5 (@ P tptp.one_one_real)) (=> (not P5) (@ P tptp.zero_zero_real))))) (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (and (=> P5 (@ P tptp.one_one_nat)) (=> (not P5) (@ P tptp.zero_zero_nat))))) (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (and (=> P5 (@ P tptp.one_one_int)) (=> (not P5) (@ P tptp.zero_zero_int))))) (forall ((P (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P5)) (and (=> P5 (@ P tptp.one_one_Code_integer)) (=> (not P5) (@ P tptp.zero_z3403309356797280102nteger))))) (forall ((P (-> tptp.extended_enat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1046097342994218471d_enat P5)) (not (or (and P5 (not (@ P tptp.one_on7984719198319812577d_enat))) (and (not P5) (not (@ P tptp.zero_z5237406670263579293d_enat))))))) (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (not (or (and P5 (not (@ P tptp.one_one_complex))) (and (not P5) (not (@ P tptp.zero_zero_complex))))))) (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (not (or (and P5 (not (@ P tptp.one_one_real))) (and (not P5) (not (@ P tptp.zero_zero_real))))))) (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (not (or (and P5 (not (@ P tptp.one_one_nat))) (and (not P5) (not (@ P tptp.zero_zero_nat))))))) (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (not (or (and P5 (not (@ P tptp.one_one_int))) (and (not P5) (not (@ P tptp.zero_zero_int))))))) (forall ((P (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P5)) (not (or (and P5 (not (@ P tptp.one_one_Code_integer))) (and (not P5) (not (@ P tptp.zero_z3403309356797280102nteger))))))) (forall ((Xs2 tptp.list_real) (N2 tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N2) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) (@ tptp.set_real2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_real N2) X))))) (forall ((Xs2 tptp.list_complex) (N2 tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N2) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) (@ tptp.set_complex2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_complex N2) X))))) (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (N2 tptp.nat) (X tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs2) N2) (=> (forall ((Y5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y5) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replic4235873036481779905at_nat N2) X))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2) (=> (forall ((Y5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y5) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N2) X))))) (forall ((Xs2 tptp.list_o) (N2 tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N2) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) (@ tptp.set_o2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_o N2) X))))) (forall ((Xs2 tptp.list_nat) (N2 tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N2) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) (@ tptp.set_nat2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_nat N2) X))))) (forall ((Xs2 tptp.list_int) (N2 tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N2) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) (@ tptp.set_int2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_int N2) X))))) (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X5 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X) Xs2))) (forall ((Xs2 tptp.list_o) (X Bool)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs2)) (= X5 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X) Xs2))) (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs2)) (= X5 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X) Xs2))) (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs2)) (= X5 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X) Xs2))) (forall ((P (-> tptp.extended_enat Bool)) (P6 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q5 (-> tptp.extended_enat Bool))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q5 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q5 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q5 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q5 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.extended_enat Bool)) (P6 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q5 (-> tptp.extended_enat Bool))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q5 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q5 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q5 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q5 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q5 X3))))))))) (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (not (= X3 T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (not (= X3 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (not (= X3 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (not (= X3 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (not (= X3 T)))))) (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (not (= X3 T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (not (= X3 T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (not (= X3 T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (not (= X3 T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (not (= X3 T)))))) (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (not (@ (@ tptp.ord_le72135733267957522d_enat X3) T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (not (@ (@ tptp.ord_less_real X3) T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (not (@ (@ tptp.ord_less_num X3) T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (not (@ (@ tptp.ord_less_nat X3) T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ 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(Q5 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q5 X3))))))))) (forall ((P (-> tptp.extended_enat Bool)) (P6 (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool)) (Q5 (-> tptp.extended_enat Bool))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.extended_enat)) (forall ((X5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X5) Z3) (= (@ Q X5) (@ Q5 X5))))) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (= (or (@ P X3) (@ Q X3)) (or (@ P6 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tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X3))) (=> (@ _let_1 Z4) (@ _let_1 T)))))) (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (not (@ (@ tptp.ord_le72135733267957522d_enat T) X3)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (not (@ (@ tptp.ord_less_real T) X3)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (not (@ (@ tptp.ord_less_num T) X3)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (not (@ (@ tptp.ord_less_nat T) X3)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (not (@ (@ tptp.ord_less_int T) X3)))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ 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(@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B3)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))) (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (not (@ (@ tptp.ord_le2932123472753598470d_enat X3) T)))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (not (@ (@ tptp.ord_less_eq_real X3) T)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (not (@ (@ tptp.ord_less_eq_num X3) T)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (not (@ (@ tptp.ord_less_eq_nat X3) T)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (not (@ (@ tptp.ord_less_eq_int X3) T)))))) (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (@ (@ tptp.ord_le2932123472753598470d_enat T) X3))))) (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (@ (@ tptp.ord_less_eq_real T) X3))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (@ (@ tptp.ord_less_eq_num T) X3))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (@ (@ tptp.ord_less_eq_nat T) X3))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (@ (@ tptp.ord_less_eq_int T) X3))))) (forall ((T tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ 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X3) Z4) (not (@ (@ tptp.ord_less_eq_real T) X3)))))) (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (not (@ (@ tptp.ord_less_eq_num T) X3)))))) (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (not (@ (@ tptp.ord_less_eq_nat T) X3)))))) (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (not (@ (@ tptp.ord_less_eq_int T) X3)))))) (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N2))) _let_2))))) (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N2))) _let_2))))) (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N2))) _let_2))))) (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex) (K2 tptp.complex)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K2) D4))))) (=> (forall ((X5 tptp.complex) (K2 tptp.complex)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K2) D4))))) (forall ((X3 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K4) D4)))) (= (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) 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)))))))) (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) 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)))))))) (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex) (K2 tptp.complex)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K2) D4))))) (=> (forall ((X5 tptp.complex) (K2 tptp.complex)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K2) D4))))) (forall ((X3 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K4) D4)))) (= (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1)))))))) (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) 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)))))))) (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) 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)))))))) (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))) (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))))))))))))))) (forall ((D tptp.code_integer) (S3 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S3)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.extended_enat) (S3 tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X3) S3)))) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S3 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S3)))) (=> (@ (@ tptp.ord_less_real Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S3 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S3)))) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S3 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S3)))) (=> (@ (@ tptp.ord_less_int Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S3 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S3))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.extended_enat) (S3 tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (not (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X3) S3))))) (=> (@ (@ tptp.ord_le72135733267957522d_enat Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S3 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S3))))) (=> (@ (@ tptp.ord_less_real Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S3 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S3))))) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S3 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S3))))) (=> (@ (@ tptp.ord_less_int Z4) X3) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S3 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S3)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.extended_enat) (S3 tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X3) S3)))) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S3 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S3)))) (=> (@ (@ tptp.ord_less_real X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S3 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S3)))) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S3 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S3)))) (=> (@ (@ tptp.ord_less_int X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S3 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S3))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.extended_enat) (S3 tptp.extended_enat)) (exists ((Z4 tptp.extended_enat)) (forall ((X3 tptp.extended_enat)) (let ((_let_1 (not (@ (@ tptp.dvd_dv3785147216227455552d_enat D) (@ (@ tptp.plus_p3455044024723400733d_enat X3) S3))))) (=> (@ (@ tptp.ord_le72135733267957522d_enat X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S3 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S3))))) (=> (@ (@ tptp.ord_less_real X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S3 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S3))))) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S3 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S3))))) (=> (@ (@ tptp.ord_less_int X3) Z4) (= _let_1 _let_1)))))) (forall ((X tptp.nat) (Y 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 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((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))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _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)))))))))))))))))))))) (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X (-> tptp.nat tptp.nat)) (X22 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))) (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))) (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))) (forall ((R tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R))) (=> (not (= R 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)))))))) (forall ((R tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (=> (not (= R 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)))))))) (forall ((R tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R))) (=> (not (= R 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)))))))) (forall ((R tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R))) (=> (not (= R 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)))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)) (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (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)))) (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)))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))) (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))) (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))) (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))) (forall ((W tptp.complex) (Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.times_times_complex W))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.real) (Y tptp.real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_complex (@ _let_2 D)) (@ _let_1 C)))))))) (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)))))))) (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)))))))) (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)))))))) (forall ((N2 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 N2)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N2))))))) (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))) (= tptp.nat_set_decode (lambda ((X2 tptp.nat)) (@ tptp.collect_nat (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat _let_1) N))))))))) (= tptp.bit_ri6519982836138164636nteger (lambda ((N tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A4) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N 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 N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))))))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A4) _let_1))) (@ (@ (@ tptp.if_int (= N 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 N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))))))))) (= tptp.artanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))) (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))) (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))) (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))) (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A4) _let_1)))))) (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A4) _let_1)))))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A4) _let_1)))))) (forall ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.pow K) L2)))) (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L2)))) (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L2)))) (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L2)))) (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L2)))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real B2)) (@ tptp.uminus612125837232591019t_real A2)))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat B2)) (@ tptp.uminus5710092332889474511et_nat A2)))) (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real A2)) (@ tptp.uminus612125837232591019t_real B2)) (@ (@ tptp.ord_less_eq_set_real B2) A2))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ tptp.uminus5710092332889474511et_nat B2)) (@ (@ tptp.ord_less_eq_set_nat B2) A2))) (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))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))) (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))) (forall ((X tptp.set_real) (Y tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real X)) (@ tptp.uminus612125837232591019t_real Y)) (@ (@ tptp.ord_less_eq_set_real Y) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X))) (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))) (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))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= M N2))) (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))))) (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))))) (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))))) (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))))) (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))) (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))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))) (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)))) (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)))) (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)))) (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)))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)) (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))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_real X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ tptp.ln_ln_real X) (@ tptp.ln_ln_real Y)) (= X Y)))))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (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))) (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc6842872674320459806at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))) (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))) (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))) (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))) (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))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))) (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))) (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))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))) (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))) (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)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))) (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)))) (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))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))) (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))) (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))) (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))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (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))) (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))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (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)))) (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)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (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)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (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)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (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)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (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)))))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))) (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))) (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))) (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))) (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))) (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))) (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int B) A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (= (@ _let_1 (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (= (@ tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) tptp.one_one_nat) tptp.one_one_nat)) (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) tptp.one_one_int) tptp.one_one_int)) (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) tptp.one_one_nat) tptp.one_one_nat)) (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N2) _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) _let_1) _let_1))) (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))))) (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))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))) (= (@ _let_124 _let_26) tptp.zero_zero_real) (= (@ _let_123 _let_88) tptp.zero_zero_int) (= (@ _let_53 _let_54) tptp.zero_zero_complex) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_87) tptp.zero_z3403309356797280102nteger) (= (@ _let_122 tptp.one_one_real) tptp.zero_zero_real) (= (@ _let_121 tptp.one_one_int) tptp.zero_zero_int) (= (@ _let_120 tptp.one_one_complex) tptp.zero_zero_complex) (= (@ _let_119 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= (@ _let_118 _let_26) tptp.zero_zero_real) (= (@ _let_117 _let_88) tptp.zero_zero_int) (= (@ _let_116 _let_54) tptp.zero_zero_complex) (= (@ _let_115 _let_87) tptp.zero_z3403309356797280102nteger) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= N2 tptp.one))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))) (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))) (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2))))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_eq_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_eq_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_num N2) M))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (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)))) (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))) (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)))) (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))))) (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)))) (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))))))) (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))))))) (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))))))) (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))))))) (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)))) (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)))) (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))) (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))))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (= (@ _let_122 _let_26) _let_109) (= (@ _let_121 _let_88) _let_108) (= (@ _let_120 _let_54) _let_107) (= (@ _let_119 _let_87) _let_106) (= (@ _let_118 tptp.one_one_real) _let_109) (= (@ _let_117 tptp.one_one_int) _let_108) (= (@ _let_116 tptp.one_one_complex) _let_107) (= (@ _let_115 tptp.one_one_Code_integer) _let_106) (= (@ _let_114 _let_26) _let_28) (= (@ _let_113 _let_88) _let_47) (= (@ _let_112 _let_54) _let_56) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) _let_87) _let_41) (= (@ (@ tptp.divide_divide_int _let_88) _let_47) _let_88) (= (@ (@ tptp.divide6298287555418463151nteger _let_87) _let_41) _let_87) _let_111 _let_110 _let_111 _let_110 (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.power_power_real A) N2)))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.power_power_int A) N2)))) (forall ((N2 tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.power_power_complex A) N2)))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N2))))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N2))))) (forall ((N2 tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N2))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N2))))) (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))) (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))) (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))) (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))))) (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))))) (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))))) (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))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ tptp.neg_numeral_dbl_real _let_26) _let_109) (= (@ tptp.neg_numeral_dbl_int _let_88) _let_108) (= (@ tptp.neg_nu7009210354673126013omplex _let_54) _let_107) (= (@ tptp.neg_nu8804712462038260780nteger _let_87) _let_106) (forall ((N2 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))) N2)) tptp.one_one_real)) (forall ((N2 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))) N2)) tptp.one_one_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_complex)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_Code_integer)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2) tptp.one_one_real))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2) tptp.one_one_int))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2) tptp.one_one_complex))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2) tptp.one_one_Code_integer))) (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_real _let_1) N2) _let_1)))) (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_int _let_1) N2) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex _let_1) N2) _let_1)))) (forall ((N2 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))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N2) _let_1)))) (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))))) (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))))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))) (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)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N2) M))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N2) M))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N2) M))) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N2))) _let_1)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))) (forall ((N2 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 N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))) (forall ((N2 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 N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)) (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q2)))) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))) (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)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))) (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)))) (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))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))) (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))) (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)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (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)))) (forall ((X tptp.set_real) (Y tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real X) Y) (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real Y)) (@ tptp.uminus612125837232591019t_real X)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X)))) (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real Y) (@ tptp.uminus612125837232591019t_real X)) (@ (@ tptp.ord_less_eq_set_real X) (@ tptp.uminus612125837232591019t_real Y)))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))) (forall ((Y tptp.set_real) (X tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real Y)) X) (@ (@ tptp.ord_less_eq_set_real (@ tptp.uminus612125837232591019t_real X)) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y))) (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))) (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))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))) (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)))) (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)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))) (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)))) (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)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)))) (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)))) (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)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))) (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))))) (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))))) (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))))) (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))))) (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)))) (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)))) (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)))) (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)))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))) (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))) (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))) (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)))) (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)))) (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)))) (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)))) (not (= tptp.one_one_real _let_26)) (not (= tptp.one_one_int _let_88)) (not (= tptp.one_one_complex _let_54)) (not (= tptp.one_one_Code_integer _let_87)) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)))) (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))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))) (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))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))) (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))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))) (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))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))) (forall ((F (-> tptp.nat tptp.nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))) (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc6842872674320459806at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))) (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))) (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))) (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))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))) (forall ((A tptp.int) (B tptp.int) (A6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A6) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A6)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (A6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A6) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A6)) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B))) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B))) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))) (forall ((N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N2))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) B)) (@ _let_1 B)))) (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int) (R tptp.int) (S3 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ tptp.bit_concat_bit N2))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R) S3)) (and (= (@ _let_1 K) (@ _let_1 R)) (= L2 S3)))))) (forall ((F (-> tptp.nat tptp.nat Bool)) (G (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (= (@ tptp.produc6081775807080527818_nat_o F) G))) (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (G (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (= (@ tptp.produc6842872674320459806at_nat F) G))) (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 ((X5 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (= (@ tptp.produc27273713700761075at_nat F) G))) (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 ((X5 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y5)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))) (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X5 tptp.int) (Y5 tptp.int)) (= (@ (@ F X5) Y5) (@ G (@ (@ tptp.product_Pair_int_int X5) Y5)))) (= (@ tptp.produc4245557441103728435nt_int F) G))) (forall ((F (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y3)))) F)) (forall ((F (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ tptp.produc6842872674320459806at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y3)))) F)) (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y3)) __flatten_var_0))) F)) (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y3)) __flatten_var_0))) F)) (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y3)))) F)) (forall ((Q (-> Bool Bool)) (P (-> tptp.nat tptp.nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc6081775807080527818_nat_o P) Z)) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))) (forall ((Q (-> tptp.nat Bool)) (P (-> tptp.nat tptp.nat tptp.nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc6842872674320459806at_nat P) Z)) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))) (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 ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))) (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 ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))) (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 ((X5 tptp.int) (Y5 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X5) Y5)) (not (@ Q (@ (@ P X5) Y5)))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) X))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N2))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))) (forall ((N2 tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ _let_1 tptp.zero_zero_int)))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N2) M)) _let_2) _let_1) A))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))) (not (@ _let_105 _let_26)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) _let_87)) (not (@ _let_104 _let_88)) (@ _let_101 tptp.one_one_real) (@ _let_100 tptp.one_one_Code_integer) (@ _let_99 tptp.one_one_int) (not (= tptp.zero_zero_real _let_26)) (not (= tptp.zero_zero_int _let_88)) (not (= tptp.zero_zero_complex _let_54)) (not (= tptp.zero_z3403309356797280102nteger _let_87)) (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))) (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))) (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))) (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))) (not (@ _let_103 _let_26)) (not (@ _let_102 _let_88)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) _let_87)) (@ _let_97 tptp.one_one_real) (@ _let_96 tptp.one_one_int) (@ _let_95 tptp.one_one_Code_integer) (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)))) (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)))) (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)))))) (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)))))) (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real N2) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((N2 tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((B2 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B2 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))) (forall ((B2 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B2 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))) (forall ((B2 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B2 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))) (forall ((B2 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B2 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))) (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))) (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))) (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))) (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B4)))) (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))) (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))) (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))) (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B4)))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (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 N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (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)))))) (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)))))) (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)))))) (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)))))) (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))))) (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))))) (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))))) (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))))) (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))) (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))) (forall ((U tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X) X))) (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y3 tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y3)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X))) (@ tptp.uminus_uminus_real X))))) (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) X))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X)) (=> (@ _let_1 X) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N2)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) A)) (@ _let_1 A))))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)) (@ _let_101 tptp.zero_zero_real) (@ _let_100 tptp.zero_z3403309356797280102nteger) (@ _let_99 tptp.zero_zero_int) (not (@ _let_81 _let_26)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_87)) (not (@ _let_98 _let_88)) (@ _let_97 tptp.zero_zero_real) (@ _let_96 tptp.zero_zero_int) (@ _let_95 tptp.zero_z3403309356797280102nteger) (not (@ _let_82 _let_26)) (not (@ _let_94 _let_88)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) _let_87)) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)) (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)) (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)) (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))) (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))) (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))) (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (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))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))) (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))))) (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))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))) (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)) (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)) (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)) (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))))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))) (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))) (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))) (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))) (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))) (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))))) (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))))) (= (@ tptp.uminus_uminus_real _let_59) _let_26) (= (@ tptp.uminus_uminus_int _let_93) _let_88) (= (@ tptp.uminus1482373934393186551omplex _let_58) _let_54) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_87) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.power_power_real A) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int A) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ (@ tptp.power_power_complex A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger A) N2)))) (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ (@ tptp.power_power_real X) _let_1)))) (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ (@ tptp.power_power_int X) _let_1)))) (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ (@ tptp.power_power_complex X) _let_1)))) (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ 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)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ 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)))) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (= (@ tptp.ln_ln_real X) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))) (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))))) (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))))) (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))))) (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))))) (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)))))))))))) (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)))))))))))) (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))))))) (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))))))) (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))))))) (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))))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (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))))))) (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))))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (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))))))) (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))))))) (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))))))) (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))))))) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1482373934393186551omplex Y)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y)))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A4 tptp.int)) (@ (@ tptp.modulo_modulo_int A4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y)) Y)))))) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (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))))) (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))))) (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))))) (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))))) (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))))))))))) (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)))))))))))) (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)))))))))))) (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)))))))))))) (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))) (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))))) (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))))) (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))))) (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))))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((U tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X) _let_1)))) (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))) (forall ((N2 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))) N2))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) K))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N2) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) A))) (forall ((N2 tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) A))) (forall ((N2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) A))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (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)))))))))))) (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))))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (= (@ (@ 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))) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (= (@ (@ 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))) N2))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (= (@ (@ 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))) N2))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K))))) (forall ((N2 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))) N2)) _let_1))) (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L2)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L2) (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) 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))) N2))))) (forall ((K tptp.int) (N2 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))) N2)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K)))) (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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))) N2)) 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)))))) (forall ((N2 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))) N2))) _let_1))) (forall ((N2 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))) N2))) _let_1))) (forall ((N2 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))) N2))) _let_1))) (forall ((N2 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))) N2))) _let_1))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))) (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))) (forall ((K tptp.int) (N2 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))) N2))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N2) 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) N2)) tptp.one_one_Code_integer))))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N2) 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) N2)) tptp.one_one_int))))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N2) 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) N2)) tptp.one_one_nat))))))))) (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)))))) (forall ((K tptp.int) (N2 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 N2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))) (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real _let_28)) tptp.one_one_real) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))))))) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R4)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R4 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R4)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))) (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ 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))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N2)) (= M N2))) (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)))) (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)))) (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)))) (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)))) (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)))) (forall ((P5 tptp.produc6271795597528267376eger_o) (C (-> tptp.code_integer Bool Bool))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc7828578312038201481er_o_o C) P5))) (forall ((P5 tptp.product_prod_num_num) (C (-> tptp.num tptp.num Bool))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc5703948589228662326_num_o C) P5))) (forall ((P5 tptp.product_prod_nat_num) (C (-> tptp.nat tptp.num Bool))) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc4927758841916487424_num_o C) P5))) (forall ((P5 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc4947309494688390418_int_o C) P5))) (forall ((P5 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat Bool))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= P5 (@ (@ tptp.product_Pair_nat_nat A3) B3)) (@ (@ C A3) B3))) (@ (@ tptp.produc6081775807080527818_nat_o C) P5))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc4130284055270567454et_nat C) (@ (@ tptp.product_Pair_nat_num A) B)))))) (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)))))) (forall ((P5 tptp.produc6271795597528267376eger_o) (Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P5)))) (forall ((P5 tptp.produc6271795597528267376eger_o) (Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ tptp.member_real Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P5)))) (forall ((P5 tptp.produc6271795597528267376eger_o) (Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ tptp.member_int Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P5)))) (forall ((P5 tptp.produc6271795597528267376eger_o) (Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o A3) B3)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P5)))) (forall ((P5 tptp.product_prod_num_num) (Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P5)))) (forall ((P5 tptp.product_prod_num_num) (Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ tptp.member_real Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P5)))) (forall ((P5 tptp.product_prod_num_num) (Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ tptp.member_int Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P5)))) (forall ((P5 tptp.product_prod_num_num) (Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num A3) B3)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P5)))) (forall ((P5 tptp.product_prod_nat_num) (Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat))) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num A3) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4130284055270567454et_nat C) P5)))) (forall ((P5 tptp.product_prod_nat_num) (Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real))) (=> (forall ((A3 tptp.nat) (B3 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num A3) B3)) (@ (@ tptp.member_real Z) (@ (@ C A3) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P5)))) (forall ((P5 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A3) B3) P5) (@ (@ (@ C A3) B3) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P5) X))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N2)))) (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))) (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit1 N2)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (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)))) (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)))) (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))) (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))) (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_92 _let_91 (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (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))) (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))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))) (= (@ tptp.abs_abs_real _let_26) tptp.one_one_real) (= (@ tptp.abs_abs_int _let_88) tptp.one_one_int) (= (@ tptp.abs_abs_Code_integer _let_87) tptp.one_one_Code_integer) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N2)) (@ tptp.bit0 (@ _let_1 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))) (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))))) (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)))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))) (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)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) tptp.one)))) (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))) (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.bit1 N2))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) (or (not (= A tptp.zero_zero_real)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2)) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))) (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))) (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))) (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)))) (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)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N2) M)))) (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))) (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))) (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))))) (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))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))) (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)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))) (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)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))) (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))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R4 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))) (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))) (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))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))) (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)))) (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)))) _let_92 _let_91 (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))) (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P5)) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P5)) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P5)) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ tptp.member_int Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (P5 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P5)) (not (forall ((X5 tptp.code_integer) (Y5 Bool)) (=> (= P5 (@ (@ tptp.produc6677183202524767010eger_o X5) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P5)) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P5)) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P5)) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ tptp.member_int Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (P5 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P5)) (not (forall ((X5 tptp.num) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_num_num X5) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.nat) (C (-> tptp.nat tptp.num tptp.set_nat)) (P5 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4130284055270567454et_nat C) P5)) (not (forall ((X5 tptp.nat) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num X5) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X5) Y5)))))))) (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (P5 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P5)) (not (forall ((X5 tptp.nat) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num X5) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y5)))))))) (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))) (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))) (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))) (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))) (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ 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(@ (@ tptp.produc4927758841916487424_num_o C) P5) (not (forall ((X5 tptp.nat) (Y5 tptp.num)) (=> (= P5 (@ (@ tptp.product_Pair_nat_num X5) Y5)) (not (@ (@ C X5) Y5))))))) (forall ((C (-> tptp.int tptp.int Bool)) (P5 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P5) (not (forall ((X5 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int X5) Y5)) (not (@ (@ C X5) Y5))))))) (forall ((C (-> tptp.nat tptp.nat Bool)) (P5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o C) P5) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= P5 (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ (@ C X5) Y5))))))) (forall ((R2 (-> 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 R2) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R2 A) B) C))) (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P5 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P5) Z) (not (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= P5 (@ (@ tptp.product_Pair_nat_nat X5) Y5)) (not (@ (@ (@ C X5) Y5) Z))))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))) (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))) (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)))) (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)))) (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))))))) (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))))))) (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)))) (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)))) (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)))) (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)))) (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)))) (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)))) (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))))) (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)))) (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)))) (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)))) (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))) (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))) (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))) (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)))) (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)))) (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)))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))) (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)))) (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)))) (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)))) (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))) (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N4))))) (=> (forall ((N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N4))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N4))))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N4))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N4))))) (not (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N4))))))))))))))) (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y (@ tptp.bit1 X33)))))))) (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) U)) Y))) V)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.one_one_real)) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X))) (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E2))) (= X tptp.zero_zero_real))) (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)))))) (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)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)) (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)) (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))) (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))) (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))) (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))) (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))) (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))) (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))) (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))))) (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))))) (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)))) (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)))) (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R))))) (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R))))) (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R))))) (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R))))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))))) (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X) _let_1))))) (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X) _let_1))))) (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X) _let_1))))) (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1))))) (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y2))) D3) (and (@ (@ tptp.ord_less_real A) Y2) (@ (@ tptp.ord_less_real Y2) B))))))))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (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))))) (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))))) (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))))) (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))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))) (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger N2))) (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))) (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))) (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))) (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))) (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))) (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))) (= (@ tptp.numeral_numeral_nat _let_64) (@ tptp.suc _let_46)) (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))) (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y2))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y2) (@ (@ tptp.ord_less_eq_real Y2) B))))))))) (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))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X) tptp.one_one_real))) (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))) (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)))) (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2) (@ (@ tptp.power_power_real A) N2)))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2) (@ (@ tptp.power_power_int A) N2)))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))) (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ P X5) (@ (@ tptp.power_power_real X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X5) (@ (@ P X5) (@ (@ tptp.power_power_int X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))) (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))) (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))) (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))) (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))) (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))) (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))) (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_real B) N2))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_int B) N2))))) (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N)) (@ (@ tptp.modulo_modulo_nat M6) N)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X) Z)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ 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 N2) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))) (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N)))))) (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N)))))) (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N)))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (= (@ tptp.neg_nu6075765906172075777c_real _let_26) (@ tptp.uminus_uminus_real _let_65)) (= (@ tptp.neg_nu3811975205180677377ec_int _let_88) (@ tptp.uminus_uminus_int _let_89)) (= (@ tptp.neg_nu6511756317524482435omplex _let_54) (@ tptp.uminus1482373934393186551omplex _let_90)) (= (@ tptp.neg_nu7757733837767384882nteger _let_87) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger _let_64))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex) (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real) (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int) (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat) (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))) (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K)))) (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) (@ tptp.pred_numeral K))))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N2)))) (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) _let_26) (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) _let_88) (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) _let_54) (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) _let_87) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))) (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))))) (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))))) (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))))) (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))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))) (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)))) (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)))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X5 tptp.num)) (=> (@ P X5) (@ P (@ tptp.inc X5)))) (@ P X)))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))) (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))) (= (@ tptp.inc tptp.one) _let_1) (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))) (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))) (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))) (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L2))) (@ tptp.abs_abs_int L2)))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))) (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))) (forall ((X tptp.num)) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.inc X)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat X)) tptp.one_on7984719198319812577d_enat))) (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))) (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X)) tptp.one_one_real))) (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))) (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L2))) (@ _let_2 (@ _let_1 L2)))))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_nat I4) N2)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K)))))))) (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))) (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))) (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K))))))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K))))))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))) (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) _let_90) (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) _let_65) (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) _let_89) (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))) (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))) (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K3) _let_1))))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K3) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))) (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))) (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))) (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))))) (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))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))) (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))))) (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))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))) (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))) (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N2)) (= Z (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N2)) (= Z (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))) (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))) (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))) (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))) (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))) (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex) (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int) (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real) (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))) (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))) (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))) (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))) (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)))) (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)))) (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))) (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)))) (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)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X (@ (@ tptp.power_power_int B) W)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X (@ (@ tptp.power_power_int B) W)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X (@ (@ tptp.power_power_int B) W)))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B) W) X))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B) W) X))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B) W) X))) (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N2))) (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N2))) (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N2))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))) (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real) (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int) (= (@ tptp.neg_nu8295874005876285629c_real _let_26) _let_26) (= (@ tptp.neg_nu5851722552734809277nc_int _let_88) _let_88) (= (@ tptp.neg_nu8557863876264182079omplex _let_54) _let_54) (= (@ tptp.neg_nu5831290666863070958nteger _let_87) _let_87) (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))) (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))) (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))) (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))) (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))) (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)))) (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))) (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)))) (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))) (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))) (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))) (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))) (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))) (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))) (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))) (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)))) (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))) (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))) (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))) (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)))) (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))) (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))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))) (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))) (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (forall ((X tptp.int) (Y tptp.complex)) (let ((_let_1 (@ tptp.ring_17405671764205052669omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))) (forall ((X tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_real (@ tptp.ring_1_of_int_real X)) (@ tptp.ring_1_of_int_real Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_int (@ tptp.ring_1_of_int_int X)) (@ tptp.ring_1_of_int_int Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.ord_max_int X) Y)) (@ (@ tptp.ord_max_Code_integer (@ tptp.ring_18347121197199848620nteger X)) (@ tptp.ring_18347121197199848620nteger Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X) Y))) (= (@ tptp.bitM tptp.one) tptp.one) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))) (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 N2)))) (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N2)) (@ tptp.bit1 (@ tptp.bitM N2)))) (forall ((N2 tptp.num)) (= (@ tptp.inc (@ tptp.bitM N2)) (@ tptp.bit0 N2))) (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.inc N2)) (@ tptp.bit1 N2))) (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X)))) (forall ((D tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N2) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real D))))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N2)) tptp.one) (@ tptp.bit0 N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N2)) (@ tptp.bit0 N2))) (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)))) (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))))) (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))) (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))) (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)))) (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))))) (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))) (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))) (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)))) (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))) (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))) (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))) (= tptp.ord_less_eq_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))) (= tptp.ord_less_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))) (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))) (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))) (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))) (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D))) _let_1))))) (forall ((N2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2))) tptp.one_one_complex))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N2))) tptp.one_one_real))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) tptp.one_one_int))) (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))) (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))) (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))) (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X))))) (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X)))) tptp.one_one_real)) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y)))))))) (forall ((X tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y2)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y2) tptp.one_one_int)))) (= Y2 X5)))))) (forall ((X tptp.real)) (exists ((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)))))) (forall ((N2 tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N2)) (@ (@ 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 N2)))))) (forall ((N2 tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N2)) (@ (@ 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 N2)))))) (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))) (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 tptp.zero_zero_int) (= L tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L) (@ (@ (@ tptp.if_int (= L _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))) (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 _let_2) (= L _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B))) (= (@ (@ tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) B) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) A) A)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ _let_1 N2)))) (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.zero_zero_int) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.zero_zero_int) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.zero_zero_nat) A) A)) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 A)) (@ _let_1 B))))) (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)) (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)) (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) X)) (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger _let_1) X) _let_1))) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) X) _let_1))) (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger X) _let_1) _let_1))) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int X) _let_1) _let_1))) (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N2) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))) (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int) (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))) (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) (and (@ _let_1 K) (@ _let_1 L2))))) (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)) (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))) (= (@ tptp.bit_se2002935070580805687sk_nat _let_45) tptp.one_one_nat) (= (@ tptp.bit_se2000444600071755411sk_int _let_45) tptp.one_one_int) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N2))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X))) (forall ((X tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int)) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int) tptp.one_one_int)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.zero_zero_int)) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L2)))) (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ tptp.bit_se2000444600071755411sk_int N)))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A4) (@ tptp.bit_se2002935070580805687sk_nat N)))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Z)) X) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y) X)) (@ (@ tptp.bit_se1409905431419307370or_int Z) X)))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y) Z)) X) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) X)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int X))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int Y) Z)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int Y) Z)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int B))) (let ((_let_2 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int B))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat B))) (let ((_let_2 (@ tptp.bit_se1412395901928357646or_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.bit_se725231765392027082nd_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B4) A4))) (= tptp.bit_se727722235901077358nd_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B4) A4))) (= tptp.bit_se1409905431419307370or_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int B4) A4))) (= tptp.bit_se1412395901928357646or_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat B4) A4))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int A))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat A))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat B) C))))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) (@ (@ tptp.plus_plus_int X) Y))) (forall ((X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int X) tptp.zero_zero_int) X)) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.bit_se1409905431419307370or_int A) B) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.bit_se1412395901928357646or_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((A2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A2))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))) (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.exp_real A2))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))) (forall ((A tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ tptp.bit_se1080825931792720795nteger A))) (let ((_let_3 (@ tptp.bit_se3949692690581998587nteger A))) (=> (= (@ _let_3 X) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 Y) _let_1) (= X Y))))))))) (forall ((A tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_3 (@ tptp.bit_se725231765392027082nd_int A))) (=> (= (@ _let_3 X) tptp.zero_zero_int) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y) tptp.zero_zero_int) (=> (= (@ _let_2 Y) _let_1) (= X Y))))))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))) (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))))) (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))))) (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.zero_zero_real))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (= (@ tptp.exp_real X5) Y)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))) (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y)))))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L2)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y))))) (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Y))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ (@ tptp.times_times_complex Y) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y) (@ (@ tptp.times_times_real Y) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N2)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_se2002935070580805687sk_nat N2)))) (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N2)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_se2000444600071755411sk_int N2)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))) (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) K))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))) (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))) tptp.one_one_real)) (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)) (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N2)) (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2))))) (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N2)) (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N2))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2)))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X)))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ (@ tptp.minus_minus_real Y) tptp.one_one_real)) (= (@ tptp.exp_real X5) Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))) (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))))) (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))))) (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))))) (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))))) (@ (@ tptp.ord_less_eq_real _let_86) _let_65) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N2)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))) (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ tptp.exp_real X2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))) (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))) (let ((_let_2 (@ tptp.exp_complex X2))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))) (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real _let_72)) _let_28) (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))))) (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))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N2)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N2)) (= N2 tptp.zero_zero_nat))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))) (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K3)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))) (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N4 tptp.nat)) (and (not (@ P N4)) (@ P (@ tptp.suc N4))))))) (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z4)))) (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z4)) X))) (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z4)))) (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X))))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X))))) (forall ((X tptp.real) (Y 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 Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y)))))) (forall ((X tptp.real) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X) N2))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) X))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))) (forall ((X tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) A2)) B2) (and (@ (@ tptp.member_int X) B2) (@ (@ tptp.ord_less_eq_set_int A2) B2)))) (forall ((X tptp.complex) (A2 tptp.set_complex) (B2 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.insert_complex X) A2)) B2) (and (@ (@ tptp.member_complex X) B2) (@ (@ tptp.ord_le211207098394363844omplex A2) B2)))) (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A2)) B2) (and (@ (@ tptp.member8440522571783428010at_nat X) B2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2)))) (forall ((X tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) A2)) B2) (and (@ (@ tptp.member_real X) B2) (@ (@ tptp.ord_less_eq_set_real A2) B2)))) (forall ((X tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) A2)) B2) (and (@ (@ tptp.member_nat X) B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2)))) (forall ((A tptp.int) (A2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))) (forall ((A tptp.real) (A2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= (@ (@ tptp.insert_real A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))) (forall ((A tptp.nat) (A2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))) (forall ((B tptp.int) (A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))) (forall ((B tptp.real) (A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= _let_1 (@ (@ tptp.insert_real A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))) (forall ((B tptp.nat) (A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))) (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_int N2))) (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))) (forall ((A2 tptp.set_complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex A2) (@ tptp.uminus8566677241136511917omplex (@ (@ tptp.insert_complex B) tptp.bot_bot_set_complex))) (not (@ (@ tptp.member_complex B) A2)))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A2) (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (not (@ (@ tptp.member8440522571783428010at_nat B) A2)))) (forall ((A2 tptp.set_int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B) A2)))) (forall ((A2 tptp.set_real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B) A2)))) (forall ((A2 tptp.set_nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B) A2)))) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)) (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))) (forall ((N2 tptp.nat) (X tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (forall ((N2 tptp.nat) (X tptp.int)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))) (forall ((A2 tptp.set_int) (B2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_int B) B2))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_real B) B2))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_nat B) B2))))) (forall ((B2 tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B2) (@ (@ tptp.insert_int A) B2))) (forall ((B2 tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B2) (@ (@ tptp.insert_real A) B2))) (forall ((B2 tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.insert_nat A) B2))) (forall ((X tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B2)) (@ _let_1 B2))))) (forall ((X tptp.complex) (A2 tptp.set_complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) B2)) (@ _let_1 B2))))) (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B2)) (@ _let_1 B2))))) (forall ((X tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B2)) (@ _let_1 B2))))) (forall ((X tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B2)) (@ _let_1 B2))))) (forall ((C4 tptp.set_int) (D4 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C4) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C4)) (@ _let_1 D4))))) (forall ((C4 tptp.set_real) (D4 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C4) D4) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C4)) (@ _let_1 D4))))) (forall ((C4 tptp.set_nat) (D4 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C4) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C4)) (@ _let_1 D4))))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one) (forall ((X8 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X8) _let_1) (or (= X8 tptp.bot_bot_set_int) (= X8 _let_1))))) (forall ((X8 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (= (@ (@ tptp.ord_less_eq_set_real X8) _let_1) (or (= X8 tptp.bot_bot_set_real) (= X8 _let_1))))) (forall ((X8 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X8) _let_1) (or (= X8 tptp.bot_bot_set_nat) (= X8 _let_1))))) (forall ((A2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A2) _let_1) (or (= A2 tptp.bot_bot_set_int) (= A2 _let_1))))) (forall ((A2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A2) _let_1) (or (= A2 tptp.bot_bot_set_real) (= A2 _let_1))))) (forall ((A2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (or (= A2 tptp.bot_bot_set_nat) (= A2 _let_1))))) (forall ((A2 tptp.set_int) (B2 tptp.set_int) (X tptp.int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_int X) A2))))))) (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (X tptp.complex) (C4 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex B2))) (let ((_let_2 (@ tptp.ord_le211207098394363844omplex A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_complex X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_complex X) A2))))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B2))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member8440522571783428010at_nat X) A2))))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (X tptp.real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_real X) A2))))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (X tptp.nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_nat X) A2))))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) tptp.one) (@ tptp.bit0 tptp.one))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) tptp.one) tptp.one)) (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))) (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S4) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S))))) (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S4) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S))))) (forall ((S tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) S4) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S))))) (forall ((S tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y2 tptp.real)) (=> (@ (@ tptp.member_real Y2) S4) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S))))) (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S))))) (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S))))) (forall ((S tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X5 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X5) S4)))))) (@ P S))))) (forall ((S tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real S) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X5 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y2 tptp.real)) (=> (@ (@ tptp.member_real Y2) S4) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X5) S4)))))) (@ P S))))) (forall ((S tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X5 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S4) (@ (@ tptp.ord_less_eq_int (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X5) S4)))))) (@ P S))))) (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X5 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S4) (@ (@ tptp.ord_less_eq_int (@ F Y2)) (@ F X5)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X5) S4)))))) (@ P S))))) (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B3 tptp.extended_enat) (A7 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A7) (=> (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A7) (@ (@ tptp.ord_le72135733267957522d_enat X3) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_Extended_enat B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B3 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) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B3 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) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B3 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) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B3 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) B3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B3 tptp.extended_enat) (A7 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A7) (=> (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A7) (@ (@ tptp.ord_le72135733267957522d_enat B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_Extended_enat B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B3 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A7) (@ (@ tptp.ord_less_real B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B3 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) A7) (@ (@ tptp.ord_less_num B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B3 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A7) (@ (@ tptp.ord_less_nat B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B3) A7)))))) (@ P A2))))) (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B3 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A7) (@ (@ tptp.ord_less_int B3) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B3) A7)))))) (@ P A2))))) (forall ((F3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F3) A2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A3 tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A3))) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat A3) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A3 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A3))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le211207098394363844omplex F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A3) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A3 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A3))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_int F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A3) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A3 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A3))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_real F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A3) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A3) F4))))))))) (@ P F3)))))) (forall ((F3 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F3) A2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A3 tptp.product_prod_nat_nat) (F4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A3))) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert8211810215607154385at_nat A3) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A3 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A3))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A3) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F3) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A3 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A3))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A3) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F3) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A3 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A3))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A3) F4)))))))) (@ P F3)))))) (forall ((F3 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F3) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A3) F4)))))))) (@ P F3)))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (let ((_let_2 (@ (@ tptp.member_complex X) A2))) (let ((_let_3 (@ tptp.insert_complex X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X) A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))) (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X) A2))) (let ((_let_3 (@ tptp.insert_int X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))) (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X) A2))) (let ((_let_3 (@ tptp.insert_real X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X) A2))) (let ((_let_3 (@ tptp.insert_nat X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))) (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B2) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) B2) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B2) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B2))))) (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I2) X))) (@ (@ tptp.insert_int X) (@ tptp.set_int2 Xs2)))) (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X))) (@ (@ tptp.insert_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)))) (forall ((Xs2 tptp.list_real) (I2 tptp.nat) (X tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I2) X))) (@ (@ tptp.insert_real X) (@ tptp.set_real2 Xs2)))) (forall ((Xs2 tptp.list_nat) (I2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I2) X))) (@ (@ tptp.insert_nat X) (@ tptp.set_nat2 Xs2)))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))) (forall ((P (-> tptp.set_Pr1261947904930325089at_nat Bool)) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (=> (not (@ tptp.finite6177210948735845034at_nat B2)) _let_1) (=> (forall ((A7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A7) (=> (not (= A7 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A7) B2) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A7) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A7) (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))) (@ P A7)))))) _let_1))))) (forall ((P (-> tptp.set_complex Bool)) (B2 tptp.set_complex)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_complex) (=> (=> (not (@ tptp.finite3207457112153483333omplex B2)) _let_1) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (not (= A7 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A7) B2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X3) tptp.bot_bot_set_complex))))) (@ P A7)))))) _let_1))))) (forall ((P (-> tptp.set_int Bool)) (B2 tptp.set_int)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B2)) _let_1) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (not (= A7 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) B2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))) (@ P A7)))))) _let_1))))) (forall ((P (-> tptp.set_real Bool)) (B2 tptp.set_real)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_real) (=> (=> (not (@ tptp.finite_finite_real B2)) _let_1) (=> (forall ((A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (not (= A7 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A7) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))) (@ P A7)))))) _let_1))))) (forall ((P (-> tptp.set_nat Bool)) (B2 tptp.set_nat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B2)) _let_1) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (not (= A7 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) B2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))) (@ P A7)))))) _let_1))))) (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A7) (=> (not (= A7 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A7) B2) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A7) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A7) (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))) (@ P A7)))))) (@ P B2))))) (forall ((B2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (not (= A7 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A7) B2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X3) tptp.bot_bot_set_complex))))) (@ P A7)))))) (@ P B2))))) (forall ((B2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (not (= A7 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) B2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))) (@ P A7)))))) (@ P B2))))) (forall ((B2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (not (= A7 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A7) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))) (@ P A7)))))) (@ P B2))))) (forall ((B2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (not (= A7 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) B2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))) (@ P A7)))))) (@ P B2))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_complex X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_complex A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A2) B2)))))))))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2)))))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B2)))))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B2)))))))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B2)))))))))))) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N2)) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))) (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N2)) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N2)) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N2)) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))) (forall ((N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))) (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bit1 M5)))))) (=> (=> _let_3 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N4 tptp.num)) (= X (@ tptp.bit0 N4))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit0 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit0 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (=> (=> (exists ((N4 tptp.num)) (= X (@ tptp.bit1 N4))) _let_2) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit1 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (not (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit1 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))))))))))))))))) (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)))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))) (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L2))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L2) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L2)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.log _let_1) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X)))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))))))) (= tptp.arctan (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X2) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 X) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X)))))) (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y)) (= X Y))) (= (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) tptp.bot_bot_nat_o) (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o) (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X) Y))) (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real) (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))) (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)) (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (= (@ tptp.sqrt _let_68) _let_28) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X) (= (@ _let_2 (@ (@ tptp.log A) X)) (@ _let_1 X))))))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_real A) X)))))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) A))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y)))))))) (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)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N2))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real A) X))))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) A))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N2))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N2)))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))) (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))) (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X))) (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _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)))) (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N2) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N2) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.nat_set_encode A2)))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N4)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N4)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N4)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N4)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2))))) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (forall ((M tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (= _let_1 _let_1))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))) (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))) (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int A) B)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))) (forall ((K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) N2)))) (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (= M N2))))) (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (= M N2))))) (forall ((K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) N2)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N2)))) (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N2) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N2) (= N2 tptp.zero_zero_nat))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((A tptp.int) (B tptp.int)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N4)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N4)))) (= (@ (@ tptp.plus_plus_int A) B) (@ (@ tptp.bit_se1409905431419307370or_int A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N4)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N4)))) (= (@ (@ tptp.plus_plus_nat A) B) (@ (@ tptp.bit_se1412395901928357646or_nat A) B)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))) (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))) (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))) (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N2) (and B (= N2 tptp.zero_zero_nat)))) (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N2) (and B (= N2 tptp.zero_zero_nat)))) (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N2) (and B (= N2 tptp.zero_zero_nat)))) (= tptp.log (lambda ((A4 tptp.real) (X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real A4)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) A) (@ (@ tptp.bit_se2923211474154528505it_int N2) A)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real X) _let_1) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y))))))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (= tptp.ln_ln_real (@ tptp.log _let_86)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N2) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))) (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (A4 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A4) N)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N) A4))) (= tptp.bit_se2161824704523386999it_nat (lambda ((N tptp.nat) (A4 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A4) N)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N) A4))) (@ (@ tptp.ord_less_real _let_52) _let_28) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 B))))))) (forall ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))) (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) (@ (@ tptp.minus_minus_nat N2) M)))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))) (forall ((N2 tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc N2)) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N2))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))) (forall ((A tptp.code_integer)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N4) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (forall ((A tptp.int)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N4) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (forall ((A tptp.nat)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N4) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y)))))))))) (forall ((K tptp.int)) (not (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N4) M2) (= (@ _let_1 M2) (@ _let_1 N4))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (not (@ _let_1 N4)))))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y)))))))))) (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A4) (@ (@ tptp.power_8256067586552552935nteger _let_1) N))))))) (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A4) (@ (@ tptp.power_power_int _let_1) N))))))) (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A4) (@ (@ tptp.power_power_nat _let_1) N))))))) (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))) (forall ((Y tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y)))))) (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))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X) (= Y tptp.zero_zero_real)))) (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))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.log A) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X)))))))))) (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N2) (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N2) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) Z)) (@ (@ tptp.insert_nat N2) _let_1))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X) Y))))))) (forall ((N2 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) N2) (= (@ tptp.sqrt (@ _let_3 N2)) (@ _let_3 (@ (@ tptp.divide_divide_nat N2) _let_2)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.sqrt X)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N2))))))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N2))))))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N2))))))))) (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A4) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A4) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A4) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N2) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N2) _let_1))))))) (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))) (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A12)))) (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))) (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))) (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.arcosh_real X) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))) (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I4 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J2) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)) (@ (@ P I4) J2)))) (@ (@ P A0) A12)))) (= tptp.arsinh_real (lambda ((X2 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))) (forall ((M tptp.nat) (N2 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)) N2)) (=> (@ (@ 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 N2)))))) (= _let_69 (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_68) (@ tptp.arctan (@ _let_57 _let_85)))) (@ tptp.arctan (@ _let_57 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_84)))))))))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_85) (@ tptp.arctan (@ _let_57 (@ tptp.numeral_numeral_real _let_84))))) (@ _let_49 (@ tptp.arctan (@ _let_78 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_23))))))))) _let_69) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) (@ tptp.semiri4939895301339042750nteger N2)) (= M N2))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (= (@ tptp.semiri4216267220026989637d_enat tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat) (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ tptp.semiri4939895301339042750nteger tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger) (forall ((N2 tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.semiri4216267220026989637d_enat N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.semiri4939895301339042750nteger N2)) (= tptp.zero_zero_nat N2))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat M) tptp.zero_z5237406670263579293d_enat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))) (forall ((N2 tptp.num)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((N2 tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6690914467698888265omplex N2))) (forall ((N2 tptp.num)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6620942414471956472nteger N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat N2) tptp.one_on7984719198319812577d_enat) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N2) tptp.one_one_Code_integer) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.semiri4216267220026989637d_enat N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (= N2 tptp.one_one_nat))) (= (@ tptp.semiri4216267220026989637d_enat tptp.one_one_nat) tptp.one_on7984719198319812577d_enat) (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real) _let_80 (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex) (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger M)) N2))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X)) (= (@ (@ tptp.power_power_nat B) W) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X)) (= (@ (@ tptp.power_power_nat B) W) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X)) (= (@ (@ tptp.power_power_nat B) W) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X)) (= (@ (@ tptp.power_power_nat B) W) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W) (@ tptp.semiri4939895301339042750nteger X)) (= (@ (@ tptp.power_power_nat B) W) X))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger X) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))) (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))) (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))) (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))) (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.semiri4216267220026989637d_enat M)) tptp.zero_z5237406670263579293d_enat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc M)) (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.semiri4216267220026989637d_enat M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X)) N2) (@ tptp.semiri4216267220026989637d_enat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2) (@ tptp.semiri4939895301339042750nteger Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat Y) (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))) (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N2))) (forall ((N2 tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat W)))) (forall ((N2 tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) M))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))) (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))))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))) (forall ((X tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N4)))) (forall ((X tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N4)))) (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger X))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.semiri4939895301339042750nteger M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))) (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))) (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))) (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.ring_18347121197199848620nteger X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.semiri4216267220026989637d_enat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) tptp.zero_z5237406670263579293d_enat))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.suc N2)) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc N2)) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (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)))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (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)))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (@ tptp.divide6298287555418463151nteger A))) (= (@ _let_3 (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_3 _let_2)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.semiri4216267220026989637d_enat M)) (@ tptp.semiri4216267220026989637d_enat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger I2)) (@ tptp.semiri4939895301339042750nteger J)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.dvd_dvd_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat M) N2))) (@ _let_82 tptp.pi) (not (@ _let_83 tptp.zero_zero_real)) (@ _let_81 tptp.pi) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X)) (@ tptp.semiri4216267220026989637d_enat Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_Code_integer (@ tptp.semiri4939895301339042750nteger X)) (@ tptp.semiri4939895301339042750nteger Y)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se1412395901928357646or_nat M) N2)) (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se1412395901928357646or_nat M) N2)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se1412395901928357646or_nat M) N2)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ tptp.bit_se2119862282449309892nteger N2))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ tptp.bit_se2000444600071755411sk_int N2))) (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) X))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2))))) (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N2))) (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N2))) (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N2))) (forall ((N2 tptp.nat) (X tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) X)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N2))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y2 tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) X)))))) (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X)))) (forall ((D tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real D))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N2))) (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)))))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N2))) (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)))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N2))) (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)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri8010041392384452111omplex N2)))) (@ _let_83 _let_68) (= tptp.ord_less_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))) (@ (@ tptp.ord_less_eq_real _let_28) tptp.pi) (= tptp.ord_less_eq_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))) (not (= _let_30 _let_28)) (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log B) _let_1)))))) (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))) (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D))) _let_1))))) (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N4 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) E)))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N2)))) N2) (@ tptp.exp_real X)))) (forall ((N2 tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N2)))) N2) (@ tptp.exp_complex X)))) (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M5)) X)) C))) (= X tptp.zero_zero_real)))))) (not (= _let_30 tptp.zero_zero_real)) (@ (@ tptp.ord_less_real _let_30) _let_28) (@ (@ tptp.ord_less_eq_real _let_30) _let_28) (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X))))) (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X)))) tptp.one_one_real)) (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))) (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N2)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) (@ tptp.semiri5074537144036343181t_real N2))))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ln_ln_real X))))) (forall ((X tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_1 X)))))) (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (@ _let_82 _let_30) (@ _let_81 _let_30) (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N2)))) (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ 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 N2))))))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_50)) tptp.pi) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N2))))) (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.arctan tptp.one_one_real) _let_69) (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ 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 N2))))))) (@ (@ tptp.ord_less_real _let_40) tptp.zero_zero_real) (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))) (forall ((Y 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 Y))) (forall ((N2 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)) N2)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (forall ((N2 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)) N2)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ 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 N2)))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N2))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real X)))))) (= tptp.semiri4216267220026989637d_enat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= N tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.produc2676513652042109336d_enat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ tptp.semiri4216267220026989637d_enat M6)))) (@ (@ (@ tptp.if_Extended_enat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M6)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M6)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (= N tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M6)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri4939895301339042750nteger (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1830744345554046123nteger (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.semiri4939895301339042750nteger M6)))) (@ (@ (@ tptp.if_Code_integer (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M6)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))) (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)))) (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) N2)) (@ _let_4 N2))) 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)))))))))))) (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (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) N2)) (@ _let_3 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))) (forall ((N2 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)) N2)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N))))))))) (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M))) (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))) (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))) (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) tptp.zero_zero_real)) (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)) (forall ((N2 tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)) (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ F tptp.zero_zero_nat))) (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ F tptp.zero_zero_nat))) (= (@ tptp.sin_real _let_50) tptp.zero_zero_real) (= (@ tptp.sin_real _let_30) tptp.one_one_real) (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X))) (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.zero_zero_real)) (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))) (forall ((N2 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 N2))) tptp.zero_zero_real)) (= (@ tptp.sin_real _let_79) _let_26) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) X))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))) (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((Z tptp.int)) (=> (forall ((N4 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N4)))) (not (forall ((N4 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))) (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N4))) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))) (@ P Z)))) (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))) (forall ((B tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B) A))) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex A))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2))) Z))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))) (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)))) (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)))) _let_80 (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)))) (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))) (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) (@ tptp.sin_real X)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)) (forall ((M tptp.int)) (=> (forall ((N4 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N4)))) (not (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))))))))) (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))) (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))) (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X)))) (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.pi) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) tptp.pi))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= K (@ tptp.semiri1314217659103216013at_int N4)))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N4)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4))))))) (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N4 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N4)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4)))) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4)))))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N4 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X)))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4))))))) (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X))))) (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2)))))) (= (@ tptp.sin_real _let_69) _let_73) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))) (= (@ tptp.sin_real _let_67) _let_72) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y)) (= X Y))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))) (= (@ tptp.sin_real _let_70) _let_71) (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)))) (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)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X) Y))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_eq_real X5) _let_1) (= (@ tptp.sin_real X5) Y) (forall ((Y2 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)) Y2) (@ (@ tptp.ord_less_eq_real Y2) _let_1) (= (@ tptp.sin_real Y2) Y)) (= Y2 X5)))))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))) (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (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))))))) (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))))))) (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))) (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))) (= _let_69 (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))) (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)))) (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)))) (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)))) (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)))) (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))))) (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)))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))) (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real) (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))) (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))) (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))) (forall ((X tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real))) (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))) (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)))) (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)))) (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N2))) (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N2))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y)))) (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))))) (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))))) (forall ((W tptp.real) (N2 tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N2) (@ (@ tptp.power_power_real Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))) (forall ((W tptp.complex) (N2 tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N2) (@ (@ tptp.power_power_complex Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))) (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S3) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real R) S3))))) (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S3) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real R) S3))))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))) (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S3) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real R) S3))))) (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S3) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real R) S3))))) (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N2))) (forall ((X tptp.complex) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N2))) (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)))) (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)))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((A tptp.real) (R tptp.real) (B tptp.real) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R) S3))))) (forall ((A tptp.complex) (R tptp.real) (B tptp.complex) (S3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R) S3))))) (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))) (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))) E))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))) E))) (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))) (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))))) (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)))) (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)))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))) (forall ((W tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N2) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))) (forall ((W tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N2) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))) (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))))) (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))))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))) (forall ((X tptp.real)) (=> (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X) tptp.one_one_real))) (forall ((X tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X) tptp.one_one_real))) (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))))))) (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))))))) (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))))) (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))))) (forall ((B tptp.nat) (K tptp.nat) (N2 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 N2)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))) (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))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T4)) (not (= Y (@ tptp.sin_real T4))))))))))) (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)) X) (exists ((N tptp.int)) (= X (@ tptp.ring_1_of_int_real N))))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ tptp.summable_real F))) (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real) (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))) (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))) (forall ((X tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) Z))) (= (@ tptp.cos_real tptp.pi) _let_26) (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))) (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))) (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)))) (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))) (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))) (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))) (forall ((X tptp.num) (N2 tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (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))) (forall ((C tptp.complex)) (= (@ tptp.summable_complex (@ tptp.power_power_complex C)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))) (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))))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))) (= (@ tptp.cos_real _let_30) tptp.zero_zero_real) (= (@ tptp.cos_real _let_50) tptp.one_one_real) (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X))) (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.cos_real X))) (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (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))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) tptp.one_one_complex))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) tptp.one_one_complex))) (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.one_one_real)) (forall ((N2 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 N2))) tptp.one_one_real)) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))) (= (@ tptp.cos_real _let_79) tptp.zero_zero_real) (forall ((N2 tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))) (forall ((G (-> tptp.nat tptp.real)) (N3 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N4))) (@ G N4)))) (@ tptp.summable_real F)))) (forall ((G (-> tptp.nat tptp.real)) (N3 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N4))) (@ G N4)))) (@ tptp.summable_complex F)))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N))))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N))))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N))))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N))))))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))))) (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ tptp.summable_real F))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ G N4))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ G N4))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ G N4))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))) (@ tptp.summable_real _let_77) (@ tptp.summable_int _let_76) (@ tptp.summable_complex _let_75) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex F)) C) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C)))))) (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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C)))))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) (@ tptp.suminf_complex F))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (= (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex F)) (@ tptp.suminf_complex G)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N)))))))) (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))))))) (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))))))) (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))) (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))) (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))) (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_real)))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_nat)))))) (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_int)))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N4))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))) (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N4))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)) (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))) (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))) (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F N)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N))))) (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))) (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))))) (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))) (forall ((X tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X (@ _let_1 (@ tptp.cos_real A3))) (= Y (@ _let_1 (@ tptp.sin_real A3))))))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I5))))))) (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I5))))))) (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I5))))))) (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_real F))))))) (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_nat F))))))) (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_int F))))))) (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))) (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.sin_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.sin_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))) (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)))) (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex C)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X)))) (forall ((X tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X)))) (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))) (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z)))) (forall ((X tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) A))) (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y)) (= X Y)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ _let_1 X))))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N))))))) (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))) (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))) (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))) (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) (@ (@ tptp.plus_plus_real R) tptp.one_one_real))) (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) tptp.one_one_real)) R)) (not (= _let_74 tptp.zero_zero_real)) (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))))) (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X)))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))) (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)))) (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X)) tptp.one_one_real))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))) (@ F tptp.zero_zero_nat))))) (forall ((R tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (=> (@ tptp.summable_real F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N9)))))) R))))))) (forall ((R tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (=> (@ tptp.summable_complex F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N9)))))) R))))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I4)) tptp.one_one_real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ (@ tptp.power_power_real Z) I5))))))))) (forall ((R tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_real R) R0) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N4))) (@ (@ tptp.power_power_real R0) N4))) M7)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N))) (@ (@ tptp.power_power_real R) N)))))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X))) (@ tptp.cos_complex X))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X))) (@ tptp.cos_real X))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1)))) (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.archim7802044766580827645g_real X) Z))))) (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1))))) (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I5 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I5))) (=> (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 I5)))))) (forall ((C tptp.real) (N3 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N4)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N4)))))) (@ tptp.summable_real F)))) (forall ((C tptp.real) (N3 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N4)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N4)))))) (@ tptp.summable_complex F)))) (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))))))) (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))) (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))) (@ (@ tptp.ord_less_real _let_74) tptp.zero_zero_real) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X5) tptp.zero_zero_real) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y2) tptp.zero_zero_real)) (= Y2 X5))))) (@ (@ tptp.ord_less_eq_real _let_74) tptp.zero_zero_real) (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) tptp.pi) (= (@ tptp.cos_real X5) Y) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (= (@ tptp.cos_real Y2) Y)) (= Y2 X5)))))))) (forall ((X tptp.real)) (exists ((Y5 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y5) (@ (@ tptp.ord_less_eq_real Y5) tptp.pi) (= (@ tptp.sin_real Y5) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y5) (@ tptp.cos_real X))))) (forall ((Q2 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real P5) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P5) Q2)))) Q2)))) (= (@ tptp.cos_real _let_69) _let_73) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))))) tptp.one_one_real)) (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))))) (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))))) (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)))))) (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)))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1))))) (forall ((Q2 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P5) Q2)))) tptp.one_one_real)) Q2)) P5))) (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X))) tptp.one_one_real))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X)))))) (= (@ tptp.cos_real _let_70) _let_72) (= (@ tptp.cos_real _let_67) _let_71) (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))) (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))))) (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))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.cos_real X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_2)))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_2)))))) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X)))))) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X)))))) (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X2 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X2 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))) (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)))))))) (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)))))))) (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.pi) (= X (@ tptp.cos_real T4)) (= Y (@ tptp.sin_real T4)))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))) (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))) (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T4)) (= Y (@ tptp.sin_real T4)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T4)) (= Y (@ tptp.sin_real T4))))))) (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ 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 N2)) tptp.one_one_int))))))) (forall ((N2 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) N2) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) (@ tptp.numeral_numeral_nat _let_1))))))))) (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)))))))))) (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))) (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((X tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) A)) (not (= X tptp.zero_zero_real)))) (forall ((A tptp.real) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))) (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))) (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))) (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))) (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N2))))) (forall ((A tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y)) Y)))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X)) X)))))) (forall ((N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)) (forall ((X tptp.real) (N2 tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N2)) tptp.pi))) (@ tptp.tan_real X))) (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi))) (@ tptp.tan_real X))) (forall ((X tptp.real) (I2 tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))) (@ tptp.tan_real X))) (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)) (forall ((X tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N2))))) (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X)))) (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))) (forall ((A tptp.real) (X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real A) B))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))) (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.numera6690914467698888265omplex W)) (and (= A (@ tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A)))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X) Y)))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) tptp.one_one_real)))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) B))))))) (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X) A)))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))) (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)))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) B)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X))))) (forall ((X tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X)))))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))) (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))) (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))))) (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))))))) (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))) (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) N2)))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X))))) (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)))))) (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) A))))) (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X))))) (= (@ tptp.tan_real _let_69) tptp.one_one_real) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y)))))))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X))))))))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X))))))))) (= (@ tptp.tan_real _let_70) _let_66) (= tptp.powr_real (lambda ((X2 tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= X2 tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X2)))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y) (@ tptp.tan_real X5)))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))) (forall ((Y tptp.real)) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) Y) (forall ((Y2 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)) Y2) (@ (@ tptp.ord_less_real Y2) _let_1) (= (@ tptp.tan_real Y2) Y)) (= Y2 X5)))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y))) (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 Y) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))) (forall ((Y tptp.real)) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) Y))))) (= (@ tptp.tan_real (@ tptp.uminus_uminus_real _let_69)) _let_26) (forall ((Y tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y)))) (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X)))) (forall ((X tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N2)))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X5) Y))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X))) tptp.one_one_real))) (= (@ tptp.tan_real _let_67) (@ _let_57 _let_66)) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y) (= (@ tptp.arctan Y) X)))))) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X)) X))))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arctan Y))) (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) Y))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.plus_plus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) 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))))))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) 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))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) 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))))))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) 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))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z4 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)) Z4) (@ (@ tptp.ord_less_real Z4) _let_1) (= (@ tptp.tan_real Z4) X)))))) (= tptp.tan_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))) (= tptp.tan_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))) (= tptp.arcosh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ 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))))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) 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 N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real) (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex) (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.one_one_real) (= X tptp.one_one_real))) (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.one_one_complex) (= X tptp.one_one_real))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))) (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))) (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X)) N2))) (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X)) N2))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))) (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A2))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A2))))))) (= (@ tptp.arccos _let_26) tptp.pi) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A2))) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))) (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cos_real _let_62) _let_26) (= (@ tptp.cos_complex _let_55) _let_54) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y)))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y)) Y)))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups7108830773950497114d_enat 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_z5237406670263579293d_enat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))) (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5)))) A2) tptp.zero_zero_complex))))) (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5)))) A2) tptp.zero_zero_real))))) (forall ((X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((X tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((X tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) _let_1))))) (forall ((X tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real B))))) (= (@ tptp.arccos tptp.zero_zero_real) _let_30) (= (@ tptp.arcsin tptp.one_one_real) _let_30) (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5))) (@ D I5)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5))) (@ D I5)))) A2) tptp.zero_zero_complex))))) (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5))) (@ D I5)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5))) (@ D I5)))) A2) tptp.zero_zero_real))))) (= (@ tptp.cos_real _let_63) tptp.zero_zero_real) (= (@ tptp.cos_complex _let_61) tptp.zero_zero_complex) (= (@ tptp.sin_real _let_63) tptp.one_one_real) (= (@ tptp.sin_complex _let_61) tptp.one_one_complex) (= (@ tptp.arcsin _let_26) _let_40) (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I5)))) A2))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I5)))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I5)))) A2))) (forall ((S tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S))) (@ (@ tptp.groups8097168146408367636l_real G) S)))) (forall ((S tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S))) (@ (@ tptp.groups8778361861064173332t_real G) S)))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.complex)) (G (-> tptp.product_prod_nat_nat tptp.real))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6381953495645901045omplex F) S))) (@ (@ tptp.groups4567486121110086003t_real G) S)))) (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S))) (@ (@ tptp.groups6591440286371151544t_real G) S)))) (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S))) (@ (@ tptp.groups5808333547571424918x_real G) S)))) (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S))) (@ (@ tptp.groups6591440286371151544t_real G) S)))) (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))) (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))) (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))) (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))) (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))) (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))) (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) K5)) (@ (@ tptp.groups3542108847815614940at_nat G) K5)))) (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) K5)) (@ (@ tptp.groups6591440286371151544t_real G) K5)))) (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4538972089207619220nt_int F) K5)) (@ (@ tptp.groups4538972089207619220nt_int G) K5)))) (forall ((K5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat)) (G (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups977919841031483927at_nat F) K5)) (@ (@ tptp.groups977919841031483927at_nat G) K5)))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I5)) (@ G J3)))) B2))) A2))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I5)) (@ G J3)))) B2))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B2 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ G J3)))) B2))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B2 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I5)) (@ G J3)))) B2))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F N)) R))) A2))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.times_times_complex (@ F N)) R))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) R))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int (@ F N)) R))) A2))) (forall ((R tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat R) (@ F N)))) A2))) (forall ((R tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.times_times_complex R) (@ F N)))) A2))) (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R) (@ F N)))) A2))) (forall ((R tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int R) (@ F N)))) A2))) (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))) (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))) (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))) (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) R))) A2))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) R))) A2))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))) (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups7108830773950497114d_enat F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2800946370649118462d_enat F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups4225252721152677374d_enat F) A2)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups1752964319039525884d_enat F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A2)))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) A2)))) (forall ((A2 tptp.set_real) (F (-> tptp.real 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tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups2800946370649118462d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) tptp.zero_z5237406670263579293d_enat))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups4225252721152677374d_enat F) A2)) tptp.zero_z5237406670263579293d_enat))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ 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tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) tptp.zero_zero_real))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) tptp.zero_zero_nat))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) tptp.zero_zero_nat))) (forall ((F (-> tptp.real tptp.nat)) (I6 tptp.set_real) (G (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I6) (@ (@ tptp.groups1935376822645274424al_nat G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I2) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.int tptp.nat)) (I6 tptp.set_int) (G (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I6) (@ (@ tptp.groups4541462559716669496nt_nat G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I2) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.complex tptp.nat)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I6) (@ (@ tptp.groups5693394587270226106ex_nat G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.real tptp.int)) (I6 tptp.set_real) (G (-> tptp.real tptp.int)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I6) (@ (@ tptp.groups1932886352136224148al_int G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I2) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I6) (@ (@ tptp.groups3539618377306564664at_int G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.complex tptp.int)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.int)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) I6) (@ (@ tptp.groups5690904116761175830ex_int G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.nat tptp.nat)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) I6) (@ (@ tptp.groups3542108847815614940at_nat G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.nat tptp.real)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.real)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real F) I6) (@ (@ tptp.groups6591440286371151544t_real G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.int tptp.int)) (I6 tptp.set_int) (G (-> tptp.int tptp.int)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4538972089207619220nt_int F) I6) (@ (@ tptp.groups4538972089207619220nt_int G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I2) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I2) (@ G I2))))))) (forall ((F (-> tptp.product_prod_nat_nat tptp.nat)) (I6 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (I2 tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.groups977919841031483927at_nat F) I6) (@ (@ tptp.groups977919841031483927at_nat G) I6)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member8440522571783428010at_nat I2) I6) (=> (@ tptp.finite6177210948735845034at_nat I6) (= (@ F I2) (@ G I2))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.suc X5))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.suc X5))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A2) (@ (@ tptp.groups6591440286371151544t_real G) A2))))) (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y))))) (forall ((X tptp.real) (Y tptp.real) (R tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R)) (@ (@ tptp.times_times_real Y) R)))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((S3 tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I2 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S3)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))) (forall ((S3 tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I2 (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups7108830773950497114d_enat F) S3)) (@ (@ tptp.groups1752964319039525884d_enat G) T))))))) (forall ((S3 tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.extended_enat)) (I2 (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.groups1752964319039525884d_enat F) S3)) (@ (@ tptp.groups7108830773950497114d_enat G) T))))))) (forall ((S3 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) T) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ G X5)))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F X5)) (@ G 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tptp.member_complex X5) S3) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X5) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) S3)) (@ (@ tptp.groups5690904116761175830ex_int G) T))))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups2800946370649118462d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups4225252721152677374d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups7108830773950497114d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (= (= (@ (@ tptp.groups1752964319039525884d_enat F) A2) tptp.zero_z5237406670263579293d_enat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_z5237406670263579293d_enat))))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_real))))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) 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X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ G X5)))) (=> (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ 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A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))) (forall ((R2 (-> tptp.extended_enat tptp.extended_enat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.extended_enat)) (G (-> tptp.nat tptp.extended_enat))) (=> (@ (@ R2 tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat) (=> (forall ((X15 tptp.extended_enat) (Y15 tptp.extended_enat) (X23 tptp.extended_enat) (Y23 tptp.extended_enat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_p3455044024723400733d_enat X15) Y15)) (@ (@ tptp.plus_p3455044024723400733d_enat X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups7108830773950497114d_enat H2) S)) (@ (@ tptp.groups7108830773950497114d_enat G) S))))))) (forall ((R2 (-> tptp.extended_enat tptp.extended_enat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ (@ R2 tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat) (=> (forall ((X15 tptp.extended_enat) (Y15 tptp.extended_enat) (X23 tptp.extended_enat) (Y23 tptp.extended_enat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_p3455044024723400733d_enat X15) Y15)) (@ (@ tptp.plus_p3455044024723400733d_enat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups1752964319039525884d_enat H2) S)) (@ (@ tptp.groups1752964319039525884d_enat G) S))))))) (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups2073611262835488442omplex H2) S)) (@ (@ tptp.groups2073611262835488442omplex G) S))))))) (forall ((R2 (-> tptp.real tptp.real Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups5808333547571424918x_real H2) S)) (@ (@ tptp.groups5808333547571424918x_real G) S))))))) (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R2 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups5693394587270226106ex_nat H2) S)) (@ (@ tptp.groups5693394587270226106ex_nat G) S))))))) (forall ((R2 (-> tptp.int tptp.int Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R2 tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_int X15) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups3539618377306564664at_int H2) S)) (@ (@ tptp.groups3539618377306564664at_int G) S))))))) (forall ((R2 (-> tptp.int tptp.int Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ (@ R2 tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_int X15) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups5690904116761175830ex_int H2) S)) (@ (@ tptp.groups5690904116761175830ex_int G) S))))))) (forall ((R2 (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ (@ R2 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups3542108847815614940at_nat H2) S)) (@ (@ tptp.groups3542108847815614940at_nat G) S))))))) (forall ((R2 (-> tptp.complex tptp.complex Bool)) (S tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ (@ R2 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups7754918857620584856omplex H2) S)) (@ (@ tptp.groups7754918857620584856omplex G) S))))))) (forall ((R2 (-> tptp.real tptp.real Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R2 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R2 X15) X23) (@ (@ R2 Y15) Y23)) (@ (@ R2 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S) (@ (@ R2 (@ H2 X5)) (@ G X5)))) (@ (@ R2 (@ (@ tptp.groups6591440286371151544t_real H2) S)) (@ (@ tptp.groups6591440286371151544t_real G) S))))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups1752964319039525884d_enat F) A2)) (@ (@ tptp.groups1752964319039525884d_enat G) A2)))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (G (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_le72135733267957522d_enat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.groups7108830773950497114d_enat F) A2)) (@ (@ tptp.groups7108830773950497114d_enat G) A2)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ 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tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))) (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))) (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2)))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_complex (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_complex (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_complex (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y))))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y))))) (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (B2 tptp.extended_enat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2800946370649118462d_enat F) S3) B2) (=> (@ (@ tptp.member_real I2) S3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) B2)))))) (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (B2 tptp.extended_enat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups4225252721152677374d_enat F) S3) B2) (=> (@ (@ tptp.member_int I2) S3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) B2)))))) (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (B2 tptp.extended_enat) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups7108830773950497114d_enat F) S3) B2) (=> (@ (@ tptp.member_nat I2) S3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) B2)))))) (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (B2 tptp.extended_enat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups1752964319039525884d_enat F) S3) B2) (=> (@ (@ tptp.member_complex I2) S3) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) B2)))))) (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S3) B2) (=> (@ (@ tptp.member_real I2) S3) (@ (@ tptp.ord_less_eq_real (@ F I2)) B2)))))) (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.real)) (B2 tptp.real) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S3) B2) (=> (@ (@ tptp.member_int I2) S3) (@ (@ tptp.ord_less_eq_real (@ F I2)) B2)))))) (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (B2 tptp.real) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S3) B2) (=> (@ (@ tptp.member_complex I2) S3) (@ (@ tptp.ord_less_eq_real (@ F I2)) B2)))))) (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.nat)) (B2 tptp.nat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S3) B2) (=> (@ (@ tptp.member_real I2) S3) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B2)))))) (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.nat)) (B2 tptp.nat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S3) B2) (=> (@ (@ tptp.member_int I2) S3) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B2)))))) (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B2 tptp.nat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S3) B2) (=> (@ (@ tptp.member_complex I2) S3) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B2)))))) (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.extended_enat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups2800946370649118462d_enat F) S3) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_real I2) S3) (= (@ F I2) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.extended_enat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups4225252721152677374d_enat F) S3) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_int I2) S3) (= (@ F I2) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat)) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups7108830773950497114d_enat F) S3) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_nat I2) S3) (= (@ F I2) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (=> (= (@ (@ tptp.groups1752964319039525884d_enat F) S3) tptp.zero_z5237406670263579293d_enat) (=> (@ (@ tptp.member_complex I2) S3) (= (@ F I2) tptp.zero_z5237406670263579293d_enat)))))) (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.real)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S3) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I2) S3) (= (@ F I2) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.real)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S3) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I2) S3) (= (@ F I2) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S3) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I2) S3) (= (@ F I2) tptp.zero_zero_real)))))) (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S3) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S3) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I2) S3) (= (@ F I2) tptp.zero_zero_nat)))))) (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S3) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S3) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I2) S3) (= (@ F I2) tptp.zero_zero_nat)))))) (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S3) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I2) S3) (= (@ F I2) tptp.zero_zero_nat)))))) (forall ((X tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))) (forall ((X tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))) (forall ((X tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))) (forall ((X tptp.real) (Y tptp.real) (R tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X) R)) Y))) (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R) X)) Y))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X))))) (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2800946370649118462d_enat F) I6)))))))) (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4225252721152677374d_enat F) I6)))))))) (forall ((I6 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups7108830773950497114d_enat F) I6)))))))) (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1752964319039525884d_enat F) I6)))))))) (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))) (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))) (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))) (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))) (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))))) (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X)))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups1752964319039525884d_enat F) I6)))))) (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups7108830773950497114d_enat F) I6)))))) (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups4225252721152677374d_enat F) I6)))))) (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ F I4)))) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ (@ tptp.groups2800946370649118462d_enat F) I6)))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I6)))))) (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I6)))))) (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I6)))))) (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))) (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))) (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y)) (= X Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X) Y))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))) (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4225252721152677374d_enat G) T3) (@ (@ tptp.groups4225252721152677374d_enat H2) S))))))) (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1752964319039525884d_enat G) T3) (@ (@ tptp.groups1752964319039525884d_enat H2) S))))))) (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3049146728041665814omplex G) T3) (@ (@ tptp.groups3049146728041665814omplex H2) S))))))) (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) T3) (@ (@ tptp.groups8778361861064173332t_real H2) S))))))) (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T3) (@ (@ tptp.groups5808333547571424918x_real H2) S))))))) (forall ((T3 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) T3) (@ (@ tptp.groups4541462559716669496nt_nat H2) S))))))) (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) T3) (@ (@ tptp.groups5693394587270226106ex_nat H2) S))))))) (forall ((T3 tptp.set_complex) (S tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ G X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) T3) (@ (@ tptp.groups5690904116761175830ex_int H2) S))))))) (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2800946370649118462d_enat G) T3) (@ (@ tptp.groups2800946370649118462d_enat H2) S))))))) (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T3) (@ (@ tptp.groups5754745047067104278omplex H2) S))))))) (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.extended_enat)) (G (-> tptp.int tptp.extended_enat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4225252721152677374d_enat G) S) (@ (@ tptp.groups4225252721152677374d_enat H2) T3))))))) (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.extended_enat)) (G (-> tptp.complex tptp.extended_enat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups1752964319039525884d_enat G) S) (@ (@ tptp.groups1752964319039525884d_enat H2) T3))))))) (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.zero_zero_complex))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S) (@ (@ tptp.groups3049146728041665814omplex H2) T3))))))) (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S) (@ (@ tptp.groups8778361861064173332t_real H2) T3))))))) (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.zero_zero_real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S) (@ (@ tptp.groups5808333547571424918x_real H2) T3))))))) (forall ((T3 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S) T3) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int T3) S)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) S) (@ (@ tptp.groups4541462559716669496nt_nat H2) T3))))))) (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.zero_zero_nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3))))))) (forall ((T3 tptp.set_complex) (S tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S) T3) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex T3) S)) (= (@ H2 X5) tptp.zero_zero_int))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) S) (@ (@ tptp.groups5690904116761175830ex_int H2) T3))))))) (forall ((T3 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.extended_enat)) (G (-> tptp.real tptp.extended_enat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ H2 X5) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (= (@ G X5) (@ H2 X5)))) (= (@ (@ tptp.groups2800946370649118462d_enat G) S) (@ (@ tptp.groups2800946370649118462d_enat H2) T3))))))) (forall ((T3 tptp.set_real) (S tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ 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T3) S)) (= (@ G X5) tptp.zero_zero_complex))) (= (@ _let_1 S) (@ _let_1 T3))))))) (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_real))) (= (@ _let_1 S) (@ _let_1 T3))))))) (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T3))))))) (forall ((T3 tptp.set_real) (S tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S) T3) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real T3) S)) (= (@ G X5) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T3))))))) (forall ((T3 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.extended_enat))) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S) T3) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat T3) S)) (= (@ G X5) tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 S) (@ _let_1 T3))))))) (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.groups4225252721152677374d_enat H2))) (let ((_let_2 (@ tptp.groups4225252721152677374d_enat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat H2))) (let ((_let_2 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) 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B2))))))))))) (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H2))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))) (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat H2))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat H2))) (let ((_let_2 (@ tptp.groups2800946370649118462d_enat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))) (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.extended_enat)) (H2 (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.groups4225252721152677374d_enat H2))) (let ((_let_2 (@ tptp.groups4225252721152677374d_enat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.extended_enat)) (H2 (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat H2))) (let ((_let_2 (@ tptp.groups1752964319039525884d_enat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex H2))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real H2))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real H2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_int) (A2 tptp.set_int) (B2 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat H2))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int C4) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int B2) C4) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int C4) B2)) (= (@ H2 B3) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C4) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex C4) B2)) (= (@ H2 B3) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.extended_enat)) (H2 (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat H2))) (let ((_let_2 (@ tptp.groups2800946370649118462d_enat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_z5237406670263579293d_enat))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.zero_z5237406670263579293d_enat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B2 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex H2))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B2) C4) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real C4) B2)) (= (@ H2 B3) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (=> (@ tptp.finite_finite_real A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (@ _let_1 B2))))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ _let_1 B2))))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ 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tptp.ord_le211207098394363844omplex B2) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (F (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex F))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((A2 tptp.set_real) (B2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((A2 tptp.set_complex) (B2 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((A2 tptp.set_int) (B2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B2)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((F (-> tptp.nat tptp.extended_enat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups7108830773950497114d_enat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_complex (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))) (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))) (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_complex (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups2073611262835488442omplex G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ G M)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_complex (@ F _let_1)) (@ F M)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))) (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (let ((_let_1 (@ tptp.groups4225252721152677374d_enat F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B2) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B3)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (let ((_let_1 (@ tptp.groups1752964319039525884d_enat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B3)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B3 tptp.complex)) (=> (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (let ((_let_1 (@ tptp.groups2800946370649118462d_enat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A2)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F B3)))) (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B3)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (forall ((B3 tptp.real)) (=> (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B2) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))) (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups5754745047067104278omplex G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.int)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) tptp.pi)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X)) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X) Y))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y))) (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real B)) (@ tptp.real_V1803761363581548252l_real A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))) (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))) (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2073611262835488442omplex 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_complex (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P5))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I6)) (@ tptp.suminf_int F)))))) (forall ((F (-> tptp.nat tptp.nat)) (I6 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I6)) (@ tptp.suminf_nat F)))))) (forall ((F (-> tptp.nat tptp.real)) (I6 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I6)) (@ tptp.suminf_real F)))))) (forall ((S 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 S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S 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 S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S 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 S) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S))) (=> (@ tptp.finite3207457112153483333omplex S) (and (=> _let_2 (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex)) (C (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.groups3049146728041665814omplex C) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S 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 S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat)) (C (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups4541462559716669496nt_nat C) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex)) (C (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.groups5754745047067104278omplex C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups8097168146408367636l_real C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.nat)) (C (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1935376822645274424al_nat C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (forall ((S tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.int)) (C (-> tptp.real tptp.int))) (let ((_let_1 (@ (@ tptp.groups1932886352136224148al_int C) (@ (@ tptp.minus_minus_set_real S) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S))) (=> (@ tptp.finite_finite_real S) (and (=> _let_2 (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C K3)))) S) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C K3)))) S) _let_1))))))) (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat _let_3)) (forall ((B2 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B2) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B2) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real A2) B2) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B2) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B2) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B2) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B2))))))))) (forall ((I2 tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.extended_enat))) (=> (@ (@ tptp.member_complex I2) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) (@ (@ tptp.groups1752964319039525884d_enat F) A2)))))) (forall ((I2 tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I2) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))) (forall ((I2 tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.extended_enat))) (=> (@ (@ tptp.member_int I2) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) (@ (@ tptp.groups4225252721152677374d_enat F) A2)))))) (forall ((I2 tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I2) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))) (forall ((I2 tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.extended_enat))) (=> (@ (@ tptp.member_real I2) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) (@ (@ tptp.groups2800946370649118462d_enat F) A2)))))) (forall ((I2 tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I2) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))) (forall ((I2 tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.extended_enat))) (=> (@ (@ tptp.member_nat I2) A2) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ F X5)))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.ord_le2932123472753598470d_enat (@ F I2)) (@ (@ tptp.groups7108830773950497114d_enat F) A2)))))) (forall ((I2 tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ (@ tptp.member_complex I2) A2) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I2) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))) (forall ((I2 tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int I2) A2) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))) (forall ((I2 tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ (@ tptp.member_real I2) A2) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I2) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (X (-> tptp.product_prod_nat_nat tptp.real)) (A (-> tptp.product_prod_nat_nat tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups4567486121110086003t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups4567486121110086003t_real (lambda ((I5 tptp.product_prod_nat_nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.int)) (A (-> tptp.nat tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups3539618377306564664at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.int)) (A (-> tptp.real tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups1932886352136224148al_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups1932886352136224148al_int (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.int)) (A (-> tptp.complex tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups5690904116761175830ex_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups5690904116761175830ex_int (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_Pr1261947904930325089at_nat) (X (-> tptp.product_prod_nat_nat tptp.int)) (A (-> tptp.product_prod_nat_nat tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups975429370522433651at_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups975429370522433651at_int (lambda ((I5 tptp.product_prod_nat_nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (A (-> tptp.nat tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups6591440286371151544t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.int)) (A (-> tptp.int tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I4)))) (=> (= (@ (@ tptp.groups4538972089207619220nt_int X) I6) tptp.one_one_int) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.times_times_int (@ A I5)) (@ X I5)))) I6)) B))) Delta))))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X)) tptp.zero_zero_real))))) (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X)))))) (forall ((M tptp.int) (X tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X))))) (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X)))))) (forall ((M tptp.int) (X tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X) (= (@ tptp.arccos (@ tptp.cos_real X)) (@ tptp.uminus_uminus_real X))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X)) tptp.zero_zero_real))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_complex (@ F N2)) (@ F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M))))) (forall ((F (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N8 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M2) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N9)))) E)))))))))) (forall ((F (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N8 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M2) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N9)))) E)))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((G (-> tptp.nat tptp.complex)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y)))))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X))))) (= tptp.cos_real (lambda ((X2 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)))) X2)))) (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X2)))) (= tptp.sin_real (lambda ((X2 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)))) X2)))) (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((X tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((X tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (forall ((A tptp.extended_enat) (D tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 A)) (@ (@ tptp.times_7803423173614009249d_enat _let_1) D))))))) (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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))))))) (forall ((A tptp.complex) (D tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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))))))) (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 A)) (@ (@ tptp.times_3573771949741848930nteger _let_1) D))))))) (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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))))))) (forall ((A tptp.real) (D tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I5) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N2) D)))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) 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))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) 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))))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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 Y))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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))))))) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X)) X))))) (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ 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))))) (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D)))) _let_1))))) (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ 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))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ 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)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ 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)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((X tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))) (forall ((X tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) 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 N2))))) (@ _let_1 X)))))))))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (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)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y))))))) (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X))))))))) (forall ((Theta tptp.real)) (not (forall ((K2 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ 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)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ 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)))))) (= tptp.arsinh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ 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))))))))) (forall ((H2 tptp.complex) (Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ 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)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q4)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H2 tptp.real) (Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ 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)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q4)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ (@ 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))))))) (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ 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))))))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_real (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo6980174941875973593q_real X8))) (forall ((X8 (-> tptp.nat tptp.set_real))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_set_real (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo2489691266198938127t_real X8))) (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_set_nat (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo7278393974255667507et_nat X8))) (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_num (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo1459490580787246023eq_num X8))) (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_nat (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo4902158794631467389eq_nat X8))) (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_int (@ X8 M5)) (@ X8 N4)))) (@ tptp.topolo4899668324122417113eq_int X8))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_real (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo6980174941875973593q_real X8))) (forall ((X8 (-> tptp.nat tptp.set_real))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_set_real (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo2489691266198938127t_real X8))) (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo7278393974255667507et_nat X8))) (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_num (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo1459490580787246023eq_num X8))) (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_nat (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo4902158794631467389eq_nat X8))) (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.ord_less_eq_int (@ X8 N4)) (@ X8 M5)))) (@ tptp.topolo4899668324122417113eq_int X8))) (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X4 N)) (@ X4 M6))))))) (= tptp.topolo2489691266198938127t_real (lambda ((X4 (-> tptp.nat tptp.set_real))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_real (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_real (@ X4 N)) (@ X4 M6))))))) (= tptp.topolo7278393974255667507et_nat (lambda ((X4 (-> tptp.nat tptp.set_nat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_nat (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_nat (@ X4 N)) (@ X4 M6))))))) (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X4 N)) (@ X4 M6))))))) (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X4 N)) (@ X4 M6))))))) (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X4 N)) (@ X4 M6))))))) (forall ((I2 tptp.extended_enat) (K tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I2) (@ tptp.set_or8419480210114673929d_enat K)) (@ (@ tptp.ord_le72135733267957522d_enat I2) K))) (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I2) K))) (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I2) K))) (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I2) K))) (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I2) K))) (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) X) (= (@ A tptp.zero_zero_nat) X))) (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) X) (= (@ A tptp.zero_zero_nat) X))) (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N2 tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N2))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))) (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S3 tptp.real) (T tptp.real)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ G N4))) (=> (@ (@ tptp.sums_real F) S3) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S3) T))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S3 tptp.nat) (T tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ G N4))) (=> (@ (@ tptp.sums_nat F) S3) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S3) T))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S3 tptp.int) (T tptp.int)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ G N4))) (=> (@ (@ tptp.sums_int F) S3) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S3) T))))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))) (@ (@ tptp.times_times_complex A) C)))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))) (@ (@ tptp.times_times_real A) C)))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) A)))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) A)))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (G (-> tptp.nat tptp.complex)) (B tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (=> (@ (@ tptp.sums_complex G) B) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_complex A) B))))) (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_real A) B))))) (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_nat A) B))))) (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_int A) B))))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real A) C)))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))) (= tptp.set_or8419480210114673929d_enat (lambda ((U2 tptp.extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X2 tptp.extended_enat)) (@ (@ tptp.ord_le72135733267957522d_enat X2) U2))))) (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U2))))) (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U2))))) (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U2))))) (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U2))))) (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (S3 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S3) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S3) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S3 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S3) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S3) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((F (-> tptp.nat tptp.complex)) (S3 tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.sums_complex F) S3) (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_complex S3) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((F (-> tptp.nat tptp.real)) (S3 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.sums_real F) S3) (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_real S3) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (S3 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_complex S3) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_complex F) S3))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S3 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_real S3) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_real F) S3))) (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2529575680413868914d_enat (@ tptp.set_or8419480210114673929d_enat M)) (@ tptp.set_or8419480210114673929d_enat N2)) (@ (@ tptp.ord_le72135733267957522d_enat M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.real) (N2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N2)) (@ (@ tptp.ord_less_real M) N2))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))) (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))) (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))) (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))) (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups977919841031483927at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups977919841031483927at_nat F) A2)) (@ (@ tptp.groups977919841031483927at_nat G) A2))))) (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) A2) (=> (not (= X2 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A2) (=> (not (= X2 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))) (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N2)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))) (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) A2) (=> (not (= X2 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A2) (=> (not (= X2 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))) (forall ((F (-> tptp.nat tptp.complex)) (S3 tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S3) (@ (@ tptp.sums_complex F) S3)))) (forall ((F (-> tptp.nat tptp.real)) (S3 tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S3) (@ (@ tptp.sums_real F) S3)))) (forall ((F (-> tptp.nat tptp.complex)) (L2 tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex L2) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L2) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.nat)) (L2 tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L2) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.int)) (L2 tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L2) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.complex)) (S3 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S3) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S3) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real)) (S3 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S3) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S3) (@ F tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.complex)) (S3 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (= (@ F I4) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S3) (@ (@ tptp.sums_complex F) S3)))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (S3 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (= (@ F I4) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S3) (@ (@ tptp.sums_real F) S3)))) (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))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))) (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))) tptp.zero_zero_complex))) (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.power_power_complex Z) M))) (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.power_power_real Z) M))) (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N)))) (@ (@ tptp.power_power_int Z) M))) (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ A tptp.zero_zero_nat))) (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ A tptp.zero_zero_nat))) (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B2) (=> (@ (@ tptp.ord_less_eq_set_real B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B2))))))) (forall ((G (-> tptp.nat tptp.complex)) (S tptp.complex) (A2 tptp.set_nat) (S5 tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.sums_complex G) S) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_complex S) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ G N)))) A2))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat N) A2)) (@ F N)) (@ G N)))) S5))))) (forall ((G (-> tptp.nat tptp.real)) (S tptp.real) (A2 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) A2))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N) A2)) (@ F N)) (@ G N)))) S5))))) (forall ((F (-> tptp.nat tptp.int)) (X tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X)))) (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X)))) (forall ((F (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X)))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_complex (@ F tptp.zero_zero_nat)) (@ F M)))) (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))) (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (R tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) R)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I5)) R))) _let_1)))) (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (R tptp.complex)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex F) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) R)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F I5)) R))) _let_1)))) (forall ((F (-> tptp.nat tptp.code_integer)) (N2 tptp.nat) (R tptp.code_integer)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger F) _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) R)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger (@ F I5)) R))) _let_1)))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (R tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) R)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I5)) R))) _let_1)))) (forall ((F (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ tptp.summable_int F)))) (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ tptp.summable_nat F)))) (forall ((F (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N4))) X)) (@ tptp.summable_real F)))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))) (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex F) (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K))))) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))) (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 ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))) (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))) (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P4)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P4))) (@ _let_1 P4))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P4))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P4)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P4)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P4)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P4))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_complex X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_int X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_real X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))) (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))))) (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))))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N)))) tptp.one_one_real) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.code_integer)) (K5 tptp.code_integer) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F P7)) K5))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) K5) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) K5))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) K5))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) K5))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) K5))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) X))) (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ F (@ (@ tptp.divide_divide_nat N) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X) Y))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ F I5)) (@ G I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) tptp.one_one_nat)))) _let_1))))) (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) 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)))))) (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))))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo6980174941875973593q_real X8))) (forall ((X8 (-> tptp.nat tptp.set_real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo2489691266198938127t_real X8))) (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo7278393974255667507et_nat X8))) (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo1459490580787246023eq_num X8))) (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo4902158794631467389eq_nat X8))) (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N4)) (@ X8 (@ tptp.suc N4)))) (@ tptp.topolo4899668324122417113eq_int X8))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo6980174941875973593q_real X8))) (forall ((X8 (-> tptp.nat tptp.set_real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo2489691266198938127t_real X8))) (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo7278393974255667507et_nat X8))) (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo1459490580787246023eq_num X8))) (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo4902158794631467389eq_nat X8))) (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N4))) (@ X8 N4))) (@ tptp.topolo4899668324122417113eq_int X8))) (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 (@ tptp.suc N))) (@ X4 N)))))) (= tptp.topolo2489691266198938127t_real (lambda ((X4 (-> tptp.nat tptp.set_real))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_real (@ X4 (@ tptp.suc N))) (@ X4 N)))))) (= tptp.topolo7278393974255667507et_nat (lambda ((X4 (-> tptp.nat tptp.set_nat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X4 (@ tptp.suc N))) (@ X4 N)))))) (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 (@ tptp.suc N))) (@ X4 N)))))) (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 (@ tptp.suc N))) (@ X4 N)))))) (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 (@ tptp.suc N))) (@ X4 N)))))) (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))) (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)) (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ C N))) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N))))))) (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ C N))) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N))))))) (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))) (= (@ tptp.semiri4449623510593786356d_enat tptp.zero_zero_nat) tptp.one_on7984719198319812577d_enat) (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex) (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int) (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real) (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat) (= (@ tptp.semiri4449623510593786356d_enat tptp.one_one_nat) tptp.one_on7984719198319812577d_enat) (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex) (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int) (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real) (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat) (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real) (= (@ tptp.semiri4449623510593786356d_enat _let_45) tptp.one_on7984719198319812577d_enat) (= (@ tptp.semiri5044797733671781792omplex _let_45) tptp.one_one_complex) (= (@ tptp.semiri1406184849735516958ct_int _let_45) tptp.one_one_int) (= (@ tptp.semiri2265585572941072030t_real _let_45) tptp.one_one_real) (= (@ tptp.semiri1408675320244567234ct_nat _let_45) tptp.one_one_nat) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri3624122377584611663nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ tptp.semiri3624122377584611663nteger N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N2))))) (= (@ tptp.semiri4449623510593786356d_enat _let_2) _let_60) (= (@ tptp.semiri5044797733671781792omplex _let_2) _let_56) (= (@ tptp.semiri1406184849735516958ct_int _let_2) _let_47) (= (@ tptp.semiri2265585572941072030t_real _let_2) _let_28) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) _let_2) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N2))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N2))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N2))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N2))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri3624122377584611663nteger N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1406184849735516958ct_int N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri2265585572941072030t_real N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat N2) N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N2) N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))) (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))) (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))) (= tptp.diffs_complex (lambda ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C2 _let_1))))) (= tptp.diffs_Code_integer (lambda ((C2 (-> tptp.nat tptp.code_integer)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ C2 _let_1))))) (forall ((K tptp.num)) (= (@ tptp.semiri4449623510593786356d_enat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.semiri4449623510593786356d_enat (@ tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K))))) (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))))) (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))))) (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)))))) (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((X5 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X5) N))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N)))))) (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((X5 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X5) N))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ 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))) N2))))) (= tptp.cos_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ tptp.semiri2265585572941072030t_real N))) tptp.zero_zero_real)))) (= tptp.semiri4449623510593786356d_enat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_Extended_enat (= M6 tptp.zero_zero_nat)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat M6)) (@ tptp.semiri4449623510593786356d_enat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri1406184849735516958ct_int (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri5044797733671781792omplex (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M6)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri3624122377584611663nteger (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M6 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M6)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri2265585572941072030t_real (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M6)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.semiri1408675320244567234ct_nat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M6)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1406184849735516958ct_int N2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri5044797733671781792omplex N2) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri3624122377584611663nteger N2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri2265585572941072030t_real N2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1408675320244567234ct_nat N2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.extended_enat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_z5237406670263579293d_enat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_z5237406670263579293d_enat))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))) (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))))) (forall ((X tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) K5) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X5)) K5) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X5) N)))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N))))))) (forall ((X tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) K5) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X5)) K5) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X5) N)))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N))))))) (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real X) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))) (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.cos_real X))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))) (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))) (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T4 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N2))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N2)))))))) (forall ((R tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R)))) (@ (@ tptp.power_power_nat N2) R)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N2)) (@ tptp.semiri5074537144036343181t_real _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N2))) (@ tptp.semiri5074537144036343181t_real _let_1))))) (= tptp.sin_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) 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 N) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N)))))) (forall ((B tptp.nat) (K tptp.nat) (N2 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 N2)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))) (forall ((Z tptp.real) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N2)))))))) (forall ((Z tptp.complex) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))) (= tptp.semiri4216267220026989637d_enat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8563196900006977889d_enat (lambda ((I5 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat I5) tptp.one_on7984719198319812577d_enat))) N) tptp.zero_z5237406670263579293d_enat))) (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I5 tptp.real)) (@ (@ tptp.plus_plus_real I5) tptp.one_one_real))) N) tptp.zero_zero_real))) (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I5 tptp.int)) (@ (@ tptp.plus_plus_int I5) tptp.one_one_int))) N) tptp.zero_zero_int))) (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat I5) tptp.one_one_nat))) N) tptp.zero_zero_nat))) (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.plus_plus_complex I5) tptp.one_one_complex))) N) tptp.zero_zero_complex))) (= tptp.semiri4939895301339042750nteger (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri4055485073559036834nteger (lambda ((I5 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger I5) tptp.one_one_Code_integer))) N) tptp.zero_z3403309356797280102nteger))) (forall ((R tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R) _let_1))))) (forall ((R tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R) _let_1))))) (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X)) X) (exists ((N tptp.int)) (= X (@ tptp.ring_1_of_int_real N))))) (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)) (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)) (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)) (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)) (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))) (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)) (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) tptp.zero_zero_nat) tptp.one_on7984719198319812577d_enat)) (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real V)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))) (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)))) (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)))) (forall ((X tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int))) (forall ((X tptp.num) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (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)))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))) (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))) (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)))) (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)))) (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))) (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))) (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)))) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))) X)) (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X) Y))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N2))))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N2))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N2))))) (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N2) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_complex))))) (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_real))))) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_complex)))))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_real)))))) (= tptp.semiri4449623510593786356d_enat (@ tptp.comm_s3181272606743183617d_enat tptp.one_on7984719198319812577d_enat)) (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)) (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)) (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)) (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)) (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X))) (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z)))) (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))) (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z))))) (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X)))) (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L2))) (@ (@ tptp.divide_divide_int K) L2))) (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A4)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))) (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A4)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))) (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))) (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (=> (= X (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_int _let_1) N2))))) (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)))))) (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)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N2)))) (forall ((X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N2)))) (forall ((X tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s3181272606743183617d_enat tptp.zero_z5237406670263579293d_enat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on7984719198319812577d_enat)) (=> (not _let_2) (= _let_1 tptp.zero_z5237406670263579293d_enat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)))) (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)))))) (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)))))) (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))))) (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))))) (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))))) (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)))))))) (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)))))))) (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)))))))) (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)))))))) (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N2))))) (forall ((R tptp.real)) (@ (@ tptp.ord_less_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))) (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))) (forall ((R tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))) (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))) (forall ((A tptp.extended_enat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s3181272606743183617d_enat A) (@ tptp.suc N2)) (@ (@ tptp.times_7803423173614009249d_enat A) (@ (@ tptp.comm_s3181272606743183617d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) tptp.one_on7984719198319812577d_enat)) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N2)))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger N2)))))) (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) (@ _let_1 N2))))) (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))) (forall ((Z tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))) (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ _let_1 N2))))) (forall ((Z tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N2))) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N2) K))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N2) K))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N2) K))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N2) K))) (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))) (forall ((Z tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) M))))) (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) M))))) (forall ((Z tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) M))))) (forall ((Z tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) M))))) (forall ((Z tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N2))) M))))) (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I5 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I5))) (=> (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 I5)))))) (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))) (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) Z))))) (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))))))) (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))) (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1)